Details

analyze6.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
50%	12.5%	37.5%	5
50%	6.2%	43.8%	6
50%	3.1%	46.9%	7
50%	1.6%	48.5%	8
50%	0.8%	49.2%	9
50.4%	0.4%	49.2%	10
50.4%	0.2%	49.4%	11
50.4%	0.1%	49.5%	12

Compiler

Compiled 10 to 8 computations (20% saved)

sample3.7s (59.8%)

Results

2.5s	4160×	body	1024	valid
740.0ms	1998×	body	512	valid
254.0ms	1685×	body	256	valid
244.0ms	413×	body	2048	valid
1.0ms	6×	body	256	invalid

preprocess68.0ms (1.1%)

Algorithm

2×	egg-herbie

Rules

618×	`fma-neg_binary64`
579×	`fma-def_binary64`
523×	`cancel-sign-sub-inv_binary64`
509×	`associate-/l*_binary64`
425×	`times-frac_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	19	13
2	34	13
3	58	13
4	120	13
5	260	13
6	715	13
7	2155	13
8	5003	12
0	1	1

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

Inputs
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)

Outputs
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
(*.f64 -1/2 (-.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(*.f64 (-.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)) -1/2)
(fma.f64 1/2 (exp.f64 x) (/.f64 -1/2 (exp.f64 x)))

Compiler

Compiled 10 to 8 computations (20% saved)

simplify51.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

618×	`fma-neg_binary64`
579×	`fma-def_binary64`
523×	`cancel-sign-sub-inv_binary64`
509×	`associate-/l*_binary64`
425×	`times-frac_binary64`

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	19	13
2	34	13
3	58	13
4	120	13
5	260	13
6	715	13
7	2155	13
8	5003	12

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

Inputs
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)

Outputs
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
(*.f64 -1/2 (-.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(*.f64 (-.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)) -1/2)
(fma.f64 1/2 (exp.f64 x) (/.f64 -1/2 (exp.f64 x)))

eval1.0ms (0%)

Compiler: Compiled 17 to 11 computations (35.3% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

58.1b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	58.1b	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)

Compiler

Compiled 9 to 7 computations (22.2% saved)

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	7.2b	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

Compiler

Compiled 24 to 8 computations (66.7% saved)

series1.0ms (0%)

Counts

1 → 8

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
0.0ms	x	@	-inf	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
0.0ms	x	@	inf	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

rewrite33.0ms (0.5%)

Algorithm

1×	egg-rewrite-iter-limit
1×	batch-egg-rewrite

Rules

70×	`add-sqr-sqrt_binary64`
67×	`add-log-exp_binary64`
66×	`*-un-lft-identity_binary64`
66×	`pow1_binary64`
65×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	6
1	130	6
2	2188	6
0	6	6

Stop Event

1×	iter limit
1×	unsound

Counts

1 → 13

Calls

Call 1

Inputs
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (exp.f64 x) (neg.f64 (exp.f64 (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (.f64 2 (sinh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (cbrt.f64 (.f64 2 (sinh.f64 x))) (cbrt.f64 (.f64 2 (sinh.f64 x)))) (cbrt.f64 (.f64 2 (sinh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 2 (sinh.f64 x))) (sqrt.f64 (.f64 2 (sinh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 2 (sinh.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 (exp.f64 (neg.f64 x)) 3)) (+.f64 (.f64 (exp.f64 x) (exp.f64 x)) (+.f64 (.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 x))) (.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (exp.f64 x) (exp.f64 x)) (.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 x)))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 2 (sinh.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (.f64 2 (sinh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (.f64 (.f64 2 (sinh.f64 x)) (.f64 2 (sinh.f64 x))) (.f64 2 (sinh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 2 (sinh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 2 (sinh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 2 (sinh.f64 x))))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (exp.f64 x) (neg.f64 (exp.f64 (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 2 (sinh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (*.f64 2 (sinh.f64 x))) (cbrt.f64 (*.f64 2 (sinh.f64 x)))) (cbrt.f64 (*.f64 2 (sinh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 2 (sinh.f64 x))) (sqrt.f64 (*.f64 2 (sinh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (sinh.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 (exp.f64 (neg.f64 x)) 3)) (+.f64 (*.f64 (exp.f64 x) (exp.f64 x)) (+.f64 (*.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 x))) (*.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (exp.f64 x) (exp.f64 x)) (*.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 x)))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 2 (sinh.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (*.f64 2 (sinh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (*.f64 (*.f64 2 (sinh.f64 x)) (*.f64 2 (sinh.f64 x))) (*.f64 2 (sinh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 2 (sinh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 2 (sinh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 2 (sinh.f64 x))))))))

simplify62.0ms (1%)

Algorithm

1×	egg-herbie

Rules

700×	`fma-def_binary64`
676×	`unswap-sqr_binary64`
322×	`associate-l_binary64`
309×	`associate-*l/_binary64`
268×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	98
1	68	98
2	151	98
3	391	98
4	739	98
5	1651	98
6	2555	98
7	4148	98
8	7098	98

Stop Event

1×	node limit

Counts

21 → 22

Calls

Call 1

Inputs
(*.f64 2 x)
(+.f64 (.f64 2 x) (.f64 1/3 (pow.f64 x 3)))
(+.f64 (.f64 2 x) (+.f64 (.f64 1/3 (pow.f64 x 3)) (*.f64 1/60 (pow.f64 x 5))))
(+.f64 (.f64 2 x) (+.f64 (.f64 1/3 (pow.f64 x 3)) (+.f64 (.f64 1/2520 (pow.f64 x 7)) (.f64 1/60 (pow.f64 x 5)))))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))

Outputs
(*.f64 2 x)
(+.f64 (.f64 2 x) (.f64 1/3 (pow.f64 x 3)))
(fma.f64 2 x (*.f64 1/3 (pow.f64 x 3)))
(.f64 x (fma.f64 x (.f64 x 1/3) 2))
(+.f64 (.f64 2 x) (+.f64 (.f64 1/3 (pow.f64 x 3)) (*.f64 1/60 (pow.f64 x 5))))
(fma.f64 2 x (fma.f64 1/3 (pow.f64 x 3) (*.f64 1/60 (pow.f64 x 5))))
(fma.f64 x (fma.f64 x (.f64 x 1/3) 2) (.f64 1/60 (pow.f64 x 5)))
(+.f64 (.f64 2 x) (+.f64 (.f64 1/3 (pow.f64 x 3)) (+.f64 (.f64 1/2520 (pow.f64 x 7)) (.f64 1/60 (pow.f64 x 5)))))
(fma.f64 2 x (fma.f64 1/3 (pow.f64 x 3) (fma.f64 1/2520 (pow.f64 x 7) (*.f64 1/60 (pow.f64 x 5)))))
(fma.f64 2 x (fma.f64 1/3 (pow.f64 x 3) (fma.f64 1/60 (pow.f64 x 5) (*.f64 1/2520 (pow.f64 x 7)))))
(fma.f64 x (fma.f64 x (.f64 x 1/3) 2) (fma.f64 1/60 (pow.f64 x 5) (.f64 1/2520 (pow.f64 x 7))))
(fma.f64 2 x (fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/3 (pow.f64 x 3) (*.f64 1/2520 (pow.f64 x 7)))))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

eval6.0ms (0.1%)

Compiler: Compiled 286 to 189 computations (33.9% saved)

prune5.0ms (0.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	18	4	22
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	19	4	23

Error

Counts

23 → 4

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.7b	(/.f64 (+.f64 (.f64 2 x) (+.f64 (.f64 1/3 (pow.f64 x 3)) (*.f64 1/60 (pow.f64 x 5)))) 2)
▶	0.7b	(/.f64 (.f64 x (fma.f64 x (.f64 x 1/3) 2)) 2)
▶	1.1b	(/.f64 (*.f64 2 x) 2)
▶	0.0b	(/.f64 (*.f64 2 (sinh.f64 x)) 2)

Compiler

Compiled 42 to 34 computations (19% saved)

localize6.0ms (0.1%)

Compiler: Compiled 11 to 8 computations (27.3% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(sinh.f64 x)

Compiler

Compiled 15 to 9 computations (40% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(sinh.f64 x)
1.0ms	x	@	-inf	(sinh.f64 x)
1.0ms	x	@	0	(sinh.f64 x)

rewrite54.0ms (0.9%)

Algorithm

1×	egg-rewrite-iter-limit
1×	batch-egg-rewrite

Rules

318×	`pow1_binary64`
311×	`add-sqr-sqrt_binary64`
302×	`*-un-lft-identity_binary64`
297×	`add-log-exp_binary64`
296×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	3
1	63	3
2	785	3
0	3	3

Stop Event

1×	iter limit
1×	node limit

Counts

1 → 10

Calls

Call 1

Inputs
(sinh.f64 x)

Outputs
((#(struct:change #<rule egg-rr> (2) ((x .f64 1 (sinh.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (cbrt.f64 (sinh.f64 x)) (cbrt.f64 (sinh.f64 x))) (cbrt.f64 (sinh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (sinh.f64 x)) (sqrt.f64 (sinh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sinh.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sinh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (.f64 (sinh.f64 x) (sinh.f64 x)) (sinh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sinh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sinh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sinh.f64 x)))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sinh.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (sinh.f64 x)) (cbrt.f64 (sinh.f64 x))) (cbrt.f64 (sinh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (sinh.f64 x)) (sqrt.f64 (sinh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sinh.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sinh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (*.f64 (sinh.f64 x) (sinh.f64 x)) (sinh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sinh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sinh.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sinh.f64 x)))))))

simplify79.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

878×	`fma-def_binary64`
626×	`distribute-rgt-neg-in_binary64`
624×	`unswap-sqr_binary64`
560×	`distribute-lft-neg-in_binary64`
308×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	25	150
1	67	150
2	151	142
3	370	142
4	684	142
5	1506	142
6	2337	142
7	3591	142
8	4578	142
9	7248	142

Stop Event

1×	node limit

Counts

22 → 19

Calls

Call 1

Inputs
x
(+.f64 (*.f64 1/6 (pow.f64 x 3)) x)
(+.f64 (.f64 1/6 (pow.f64 x 3)) (+.f64 (.f64 1/120 (pow.f64 x 5)) x))
(+.f64 (.f64 1/6 (pow.f64 x 3)) (+.f64 (.f64 1/5040 (pow.f64 x 7)) (+.f64 (*.f64 1/120 (pow.f64 x 5)) x)))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))

Outputs
x
(+.f64 (*.f64 1/6 (pow.f64 x 3)) x)
(fma.f64 1/6 (pow.f64 x 3) x)
(+.f64 (.f64 1/6 (pow.f64 x 3)) (+.f64 (.f64 1/120 (pow.f64 x 5)) x))
(fma.f64 1/6 (pow.f64 x 3) (fma.f64 1/120 (pow.f64 x 5) x))
(+.f64 (.f64 1/6 (pow.f64 x 3)) (+.f64 (.f64 1/5040 (pow.f64 x 7)) (+.f64 (*.f64 1/120 (pow.f64 x 5)) x)))
(fma.f64 1/6 (pow.f64 x 3) (fma.f64 1/5040 (pow.f64 x 7) (fma.f64 1/120 (pow.f64 x 5) x)))
(fma.f64 1/6 (pow.f64 x 3) (fma.f64 1/120 (pow.f64 x 5) (fma.f64 1/5040 (pow.f64 x 7) x)))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(fma.f64 1/2 (exp.f64 x) (/.f64 -1/2 (exp.f64 x)))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(fma.f64 1/2 (exp.f64 x) (/.f64 -1/2 (exp.f64 x)))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(fma.f64 1/2 (exp.f64 x) (/.f64 -1/2 (exp.f64 x)))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(fma.f64 1/2 (exp.f64 x) (/.f64 -1/2 (exp.f64 x)))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(fma.f64 1/2 (exp.f64 x) (/.f64 -1/2 (exp.f64 x)))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(fma.f64 1/2 (exp.f64 x) (/.f64 -1/2 (exp.f64 x)))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(fma.f64 1/2 (exp.f64 x) (/.f64 -1/2 (exp.f64 x)))
(*.f64 1/2 (-.f64 (exp.f64 x) (/.f64 1 (exp.f64 x))))
(*.f64 1/2 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(fma.f64 1/2 (exp.f64 x) (/.f64 -1/2 (exp.f64 x)))

localize15.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 x (fma.f64 x (.f64 x 1/3) 2))
✓	0.0b	(fma.f64 x (*.f64 x 1/3) 2)
✓	0.4b	(*.f64 x 1/3)

Compiler

Compiled 31 to 21 computations (32.3% saved)

series5.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(*.f64 x 1/3)
1.0ms	x	@	inf	(fma.f64 x (*.f64 x 1/3) 2)
1.0ms	x	@	-inf	(fma.f64 x (*.f64 x 1/3) 2)
1.0ms	x	@	-inf	(.f64 x (fma.f64 x (.f64 x 1/3) 2))
1.0ms	x	@	0	(*.f64 x 1/3)

rewrite57.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

641×	`pow1_binary64`
593×	`add-log-exp_binary64`
593×	`log1p-expm1-u_binary64`
593×	`expm1-log1p-u_binary64`
582×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	23
1	142	23
2	1588	23

Stop Event

1×	node limit

Counts

3 → 45

Calls

Call 1

Inputs
(*.f64 x 1/3)
(fma.f64 x (*.f64 x 1/3) 2)
(.f64 x (fma.f64 x (.f64 x 1/3) 2))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 x 1/3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x 1/3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x 1/3) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x 1/3)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x 1/3)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 1/9 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (*.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x 1/3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x 1/3)))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 2 (*.f64 x (*.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (*.f64 x 1/3)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x (*.f64 x 1/3)) 1) 2)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 x (*.f64 x 1/3) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x (*.f64 x 1/3) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 x (*.f64 x 1/3) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x (*.f64 x 1/3) 2)) (pow.f64 (cbrt.f64 (fma.f64 x (*.f64 x 1/3) 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 x (*.f64 x 1/3) 2)) 2) (cbrt.f64 (fma.f64 x (*.f64 x 1/3) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 x (*.f64 x 1/3) 2)) (sqrt.f64 (fma.f64 x (*.f64 x 1/3) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 x (*.f64 x 1/3)) 3) 8) (+.f64 (*.f64 (*.f64 x (*.f64 x 1/3)) (*.f64 x (*.f64 x 1/3))) (-.f64 4 (*.f64 (*.f64 x (*.f64 x 1/3)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x 1/3)) (*.f64 x (*.f64 x 1/3))) 4) (-.f64 (*.f64 x (*.f64 x 1/3)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x (*.f64 x 1/3) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x (*.f64 x 1/3) 2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x (*.f64 x 1/3) 2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 x (*.f64 x 1/3) 2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x (*.f64 x 1/3) 2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x (*.f64 x 1/3) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x (*.f64 x 1/3) 2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x (*.f64 x 1/3) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x (*.f64 x 1/3) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x (*.f64 x 1/3) 2)))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x (*.f64 x 1/3)) x) (*.f64 2 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (*.f64 x (*.f64 x 1/3))) (*.f64 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 x (fma.f64 x (*.f64 x 1/3) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (fma.f64 x (*.f64 x 1/3) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (fma.f64 x (*.f64 x 1/3) 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (fma.f64 x (*.f64 x 1/3) 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x (fma.f64 x (*.f64 x 1/3) 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 x (fma.f64 x (*.f64 x 1/3) 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (fma.f64 x (*.f64 x 1/3) 2)) x))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (fma.f64 x (*.f64 x 1/3) 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (fma.f64 x (*.f64 x 1/3) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (fma.f64 x (*.f64 x 1/3) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (fma.f64 x (*.f64 x 1/3) 2))))))))

simplify281.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

944×	`sqr-pow_binary64`
564×	`cube-prod_binary64`
536×	`unswap-sqr_binary64`
536×	`fabs-mul_binary64`
413×	`associate-l_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	270
1	32	252
2	60	252
3	124	252
4	362	252
5	1404	252
6	2786	252
7	2972	252
8	3223	252
9	3510	252
10	3889	252
11	4399	252
12	5006	252
13	5716	252
14	6187	252
15	6508	252
16	6780	252
17	6950	252
18	7044	252
19	7721	252

Stop Event

1×	node limit

Counts

81 → 56

Calls

Call 1

Inputs
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
2
(+.f64 2 (*.f64 1/3 (pow.f64 x 2)))
(+.f64 2 (*.f64 1/3 (pow.f64 x 2)))
(+.f64 2 (*.f64 1/3 (pow.f64 x 2)))
(*.f64 1/3 (pow.f64 x 2))
(+.f64 2 (*.f64 1/3 (pow.f64 x 2)))
(+.f64 2 (*.f64 1/3 (pow.f64 x 2)))
(+.f64 2 (*.f64 1/3 (pow.f64 x 2)))
(*.f64 1/3 (pow.f64 x 2))
(+.f64 2 (*.f64 1/3 (pow.f64 x 2)))
(+.f64 2 (*.f64 1/3 (pow.f64 x 2)))
(+.f64 2 (*.f64 1/3 (pow.f64 x 2)))
(*.f64 2 x)
(+.f64 (.f64 2 x) (.f64 1/3 (pow.f64 x 3)))
(+.f64 (.f64 2 x) (.f64 1/3 (pow.f64 x 3)))
(+.f64 (.f64 2 x) (.f64 1/3 (pow.f64 x 3)))
(*.f64 1/3 (pow.f64 x 3))
(+.f64 (.f64 2 x) (.f64 1/3 (pow.f64 x 3)))
(+.f64 (.f64 2 x) (.f64 1/3 (pow.f64 x 3)))
(+.f64 (.f64 2 x) (.f64 1/3 (pow.f64 x 3)))
(*.f64 1/3 (pow.f64 x 3))
(+.f64 (.f64 2 x) (.f64 1/3 (pow.f64 x 3)))
(+.f64 (.f64 2 x) (.f64 1/3 (pow.f64 x 3)))
(+.f64 (.f64 2 x) (.f64 1/3 (pow.f64 x 3)))

Outputs
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
2
(+.f64 2 (*.f64 1/3 (pow.f64 x 2)))
(+.f64 2 (.f64 1/3 (.f64 x x)))
(fma.f64 1/3 (*.f64 x x) 2)
(fma.f64 x (*.f64 1/3 x) 2)
(+.f64 2 (*.f64 1/3 (pow.f64 x 2)))
(+.f64 2 (.f64 1/3 (.f64 x x)))
(fma.f64 1/3 (*.f64 x x) 2)
(fma.f64 x (*.f64 1/3 x) 2)
(+.f64 2 (*.f64 1/3 (pow.f64 x 2)))
(+.f64 2 (.f64 1/3 (.f64 x x)))
(fma.f64 1/3 (*.f64 x x) 2)
(fma.f64 x (*.f64 1/3 x) 2)
(*.f64 1/3 (pow.f64 x 2))
(.f64 1/3 (.f64 x x))
(+.f64 2 (*.f64 1/3 (pow.f64 x 2)))
(+.f64 2 (.f64 1/3 (.f64 x x)))
(fma.f64 1/3 (*.f64 x x) 2)
(fma.f64 x (*.f64 1/3 x) 2)
(+.f64 2 (*.f64 1/3 (pow.f64 x 2)))
(+.f64 2 (.f64 1/3 (.f64 x x)))
(fma.f64 1/3 (*.f64 x x) 2)
(fma.f64 x (*.f64 1/3 x) 2)
(+.f64 2 (*.f64 1/3 (pow.f64 x 2)))
(+.f64 2 (.f64 1/3 (.f64 x x)))
(fma.f64 1/3 (*.f64 x x) 2)
(fma.f64 x (*.f64 1/3 x) 2)
(*.f64 1/3 (pow.f64 x 2))
(.f64 1/3 (.f64 x x))
(+.f64 2 (*.f64 1/3 (pow.f64 x 2)))
(+.f64 2 (.f64 1/3 (.f64 x x)))
(fma.f64 1/3 (*.f64 x x) 2)
(fma.f64 x (*.f64 1/3 x) 2)
(+.f64 2 (*.f64 1/3 (pow.f64 x 2)))
(+.f64 2 (.f64 1/3 (.f64 x x)))
(fma.f64 1/3 (*.f64 x x) 2)
(fma.f64 x (*.f64 1/3 x) 2)
(+.f64 2 (*.f64 1/3 (pow.f64 x 2)))
(+.f64 2 (.f64 1/3 (.f64 x x)))
(fma.f64 1/3 (*.f64 x x) 2)
(fma.f64 x (*.f64 1/3 x) 2)
(*.f64 2 x)
(*.f64 x 2)
(+.f64 (.f64 2 x) (.f64 1/3 (pow.f64 x 3)))
(fma.f64 2 x (*.f64 1/3 (pow.f64 x 3)))
(fma.f64 1/3 (pow.f64 x 3) (*.f64 x 2))
(.f64 x (fma.f64 x (.f64 1/3 x) 2))
(.f64 x (fma.f64 1/3 (.f64 x x) 2))
(+.f64 (.f64 2 x) (.f64 1/3 (pow.f64 x 3)))
(fma.f64 2 x (*.f64 1/3 (pow.f64 x 3)))
(fma.f64 1/3 (pow.f64 x 3) (*.f64 x 2))
(.f64 x (fma.f64 x (.f64 1/3 x) 2))
(.f64 x (fma.f64 1/3 (.f64 x x) 2))
(+.f64 (.f64 2 x) (.f64 1/3 (pow.f64 x 3)))
(fma.f64 2 x (*.f64 1/3 (pow.f64 x 3)))
(fma.f64 1/3 (pow.f64 x 3) (*.f64 x 2))
(.f64 x (fma.f64 x (.f64 1/3 x) 2))
(.f64 x (fma.f64 1/3 (.f64 x x) 2))
(*.f64 1/3 (pow.f64 x 3))
(+.f64 (.f64 2 x) (.f64 1/3 (pow.f64 x 3)))
(fma.f64 2 x (*.f64 1/3 (pow.f64 x 3)))
(fma.f64 1/3 (pow.f64 x 3) (*.f64 x 2))
(.f64 x (fma.f64 x (.f64 1/3 x) 2))
(.f64 x (fma.f64 1/3 (.f64 x x) 2))
(+.f64 (.f64 2 x) (.f64 1/3 (pow.f64 x 3)))
(fma.f64 2 x (*.f64 1/3 (pow.f64 x 3)))
(fma.f64 1/3 (pow.f64 x 3) (*.f64 x 2))
(.f64 x (fma.f64 x (.f64 1/3 x) 2))
(.f64 x (fma.f64 1/3 (.f64 x x) 2))
(+.f64 (.f64 2 x) (.f64 1/3 (pow.f64 x 3)))
(fma.f64 2 x (*.f64 1/3 (pow.f64 x 3)))
(fma.f64 1/3 (pow.f64 x 3) (*.f64 x 2))
(.f64 x (fma.f64 x (.f64 1/3 x) 2))
(.f64 x (fma.f64 1/3 (.f64 x x) 2))
(*.f64 1/3 (pow.f64 x 3))
(+.f64 (.f64 2 x) (.f64 1/3 (pow.f64 x 3)))
(fma.f64 2 x (*.f64 1/3 (pow.f64 x 3)))
(fma.f64 1/3 (pow.f64 x 3) (*.f64 x 2))
(.f64 x (fma.f64 x (.f64 1/3 x) 2))
(.f64 x (fma.f64 1/3 (.f64 x x) 2))
(+.f64 (.f64 2 x) (.f64 1/3 (pow.f64 x 3)))
(fma.f64 2 x (*.f64 1/3 (pow.f64 x 3)))
(fma.f64 1/3 (pow.f64 x 3) (*.f64 x 2))
(.f64 x (fma.f64 x (.f64 1/3 x) 2))
(.f64 x (fma.f64 1/3 (.f64 x x) 2))
(+.f64 (.f64 2 x) (.f64 1/3 (pow.f64 x 3)))
(fma.f64 2 x (*.f64 1/3 (pow.f64 x 3)))
(fma.f64 1/3 (pow.f64 x 3) (*.f64 x 2))
(.f64 x (fma.f64 x (.f64 1/3 x) 2))
(.f64 x (fma.f64 1/3 (.f64 x x) 2))

localize58.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 2 x) (+.f64 (.f64 1/3 (pow.f64 x 3)) (*.f64 1/60 (pow.f64 x 5))))
✓	0.0b	(+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 1/60 (pow.f64 x 5)))
✓	0.1b	(*.f64 1/60 (pow.f64 x 5))
✓	0.1b	(*.f64 1/3 (pow.f64 x 3))

Compiler

Compiled 69 to 55 computations (20.3% saved)

series6.0ms (0.1%)

Counts

4 → 9

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(*.f64 1/3 (pow.f64 x 3))
1.0ms	x	@	0	(*.f64 1/60 (pow.f64 x 5))
1.0ms	x	@	inf	(+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 1/60 (pow.f64 x 5)))
1.0ms	x	@	inf	(*.f64 1/3 (pow.f64 x 3))
1.0ms	x	@	-inf	(*.f64 1/60 (pow.f64 x 5))

rewrite110.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

642×	`log-prod_binary64`
629×	`fma-def_binary64`
373×	`pow2_binary64`
327×	`fma-neg_binary64`
258×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	46
1	320	46
2	3979	46

Stop Event

1×	node limit

Counts

4 → 185

Calls

Call 1

Inputs
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/60 (pow.f64 x 5))
(+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 1/60 (pow.f64 x 5)))
(+.f64 (.f64 2 x) (+.f64 (.f64 1/3 (pow.f64 x 3)) (*.f64 1/60 (pow.f64 x 5))))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 1/3 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (exp.f64 (pow.f64 x 3)))) 2)) (log.f64 (cbrt.f64 (cbrt.f64 (exp.f64 (pow.f64 x 3))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (cbrt.f64 (exp.f64 (pow.f64 x 3))))) (log.f64 (sqrt.f64 (cbrt.f64 (exp.f64 (pow.f64 x 3))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 1/3 (pow.f64 x 3)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 1/3 (pow.f64 x 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 x (cbrt.f64 1/3)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (sqrt.f64 1/3) (pow.f64 x 3/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (pow.f64 x 3) 3) 1/27) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 (pow.f64 x 6) 1/9))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (cbrt.f64 (exp.f64 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 1/3 (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (pow.f64 x 3) 3) 1/27))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 1/3 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 1/3 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 1/3 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 1/3 (pow.f64 x 3))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 1/60 (pow.f64 x 5)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x 5)) 1/60)) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x 5)) 1/60))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 x 5)) 1/60))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 x 5)) 1/60))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 1/60 (pow.f64 x 5)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 1/60 (pow.f64 x 5)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 1/60 (pow.f64 x 5))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (sqrt.f64 1/60) (pow.f64 x 5/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (pow.f64 x 5) 3) 1/216000) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 (pow.f64 x 10) 1/3600))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (pow.f64 x 5)) 1/60))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 1/60 (pow.f64 x 5)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (pow.f64 x 5) 3) 1/216000))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 1/60 (pow.f64 x 5))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 1/60 (pow.f64 x 5))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (fma.f64 5 (log.f64 x) (log1p.f64 -59/60)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (fma.f64 5 (log.f64 x) (log1p.f64 -59/60)) 1))))))
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simplify145.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

1204×	`sqr-pow_binary64`
708×	`cube-prod_binary64`
676×	`fabs-mul_binary64`
660×	`pow-sqr_binary64`
416×	`unswap-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	78
1	32	78
2	64	78
3	141	78
4	268	78
5	722	78
6	1038	78
7	1674	78
8	1782	78
9	1944	78
10	2157	78
11	2487	78
12	2943	78
13	3542	78
14	4294	78
15	5226	78
16	5732	78
17	6220	78
18	6616	78
19	6940	78
20	7100	78

Stop Event

1×	node limit

Counts

194 → 192

Calls

Call 1

Inputs
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/60 (pow.f64 x 5))
(*.f64 1/60 (pow.f64 x 5))
(*.f64 2 x)
(+.f64 (.f64 2 x) (.f64 1/3 (pow.f64 x 3)))
(*.f64 1/60 (pow.f64 x 5))
(+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 1/60 (pow.f64 x 5)))
(*.f64 1/60 (pow.f64 x 5))
(+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 1/60 (pow.f64 x 5)))

Outputs
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/60 (pow.f64 x 5))
(*.f64 1/60 (pow.f64 x 5))
(*.f64 2 x)
(*.f64 x 2)
(+.f64 (.f64 2 x) (.f64 1/3 (pow.f64 x 3)))
(fma.f64 2 x (*.f64 1/3 (pow.f64 x 3)))
(fma.f64 1/3 (pow.f64 x 3) (*.f64 x 2))
(.f64 x (fma.f64 1/3 (.f64 x x) 2))
(*.f64 1/60 (pow.f64 x 5))
(+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 1/60 (pow.f64 x 5)))
(fma.f64 1/3 (pow.f64 x 3) (*.f64 1/60 (pow.f64 x 5)))
(*.f64 1/60 (pow.f64 x 5))
(+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 1/60 (pow.f64 x 5)))
(fma.f64 1/3 (pow.f64 x 3) (*.f64 1/60 (pow.f64 x 5)))

eval210.0ms (3.4%)

Compiler: Compiled 5377 to 4154 computations (22.7% saved)

prune171.0ms (2.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	264	3	267
Fresh	0	0	0
Picked	0	1	1
Done	1	2	3
Total	265	6	271

Error

Counts

271 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.7b	(/.f64 (+.f64 (.f64 2 x) (+.f64 (.f64 1/3 (pow.f64 x 3)) (*.f64 1/60 (pow.f64 x 5)))) 2)
▶	0.7b	(/.f64 (.f64 x (+.f64 (.f64 x (*.f64 x 1/3)) 2)) 2)
✓	1.1b	(/.f64 (*.f64 2 x) 2)
▶	60.0b	(/.f64 (.f64 x (.f64 1/3 (*.f64 x x))) 2)
✓	0.0b	(/.f64 (*.f64 2 (sinh.f64 x)) 2)
▶	0.7b	(/.f64 (+.f64 (.f64 (.f64 x (.f64 x 1/3)) x) (.f64 2 x)) 2)

Compiler

Compiled 67 to 52 computations (22.4% saved)

localize22.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 x (.f64 1/3 (*.f64 x x)))
✓	0.2b	(.f64 1/3 (.f64 x x))

Compiler

Compiled 28 to 14 computations (50% saved)

series3.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(.f64 1/3 (.f64 x x))
1.0ms	x	@	inf	(.f64 1/3 (.f64 x x))
0.0ms	x	@	inf	(.f64 x (.f64 1/3 (*.f64 x x)))
0.0ms	x	@	-inf	(.f64 x (.f64 1/3 (*.f64 x x)))
0.0ms	x	@	-inf	(.f64 1/3 (.f64 x x))

rewrite72.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

540×	`pow1_binary64`
521×	`add-sqr-sqrt_binary64`
500×	`add-log-exp_binary64`
500×	`log1p-expm1-u_binary64`
500×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	17
1	124	14
2	1461	14

Stop Event

1×	node limit

Counts

2 → 22

Calls

Call 1

Inputs
(.f64 1/3 (.f64 x x))
(.f64 x (.f64 1/3 (*.f64 x x)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 1/3 (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/3 (*.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 1/3 (*.f64 x x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 1/3 (*.f64 x x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (sqrt.f64 1/3)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 1/9 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 1/3) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 1/3 (*.f64 x x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 1/3 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 1/3 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 1/3 (*.f64 x x))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 1/3 (pow.f64 x 3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/3 (pow.f64 x 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 1/3 (pow.f64 x 3)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 1/3 (pow.f64 x 3))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 (*.f64 1/3 x)) x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 1/3 (pow.f64 x 3)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (*.f64 1/3 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 1/3 (pow.f64 x 3)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 1/3 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 1/3 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 1/3 (pow.f64 x 3))))))))

simplify175.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

1208×	`sqr-pow_binary64`
564×	`cube-prod_binary64`
537×	`fabs-mul_binary64`
536×	`unswap-sqr_binary64`
502×	`pow-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	168
1	23	168
2	48	168
3	105	168
4	296	168
5	1235	168
6	2405	168
7	2571	168
8	2821	168
9	3108	168
10	3487	168
11	3993	168
12	4591	168
13	5301	168
14	5768	168
15	6093	168
16	6367	168
17	6537	168
18	6631	168
19	7308	168

Stop Event

1×	node limit

Counts

46 → 25

Calls

Call 1

Inputs
(*.f64 1/3 (pow.f64 x 2))
(*.f64 1/3 (pow.f64 x 2))
(*.f64 1/3 (pow.f64 x 2))
(*.f64 1/3 (pow.f64 x 2))
(*.f64 1/3 (pow.f64 x 2))
(*.f64 1/3 (pow.f64 x 2))
(*.f64 1/3 (pow.f64 x 2))
(*.f64 1/3 (pow.f64 x 2))
(*.f64 1/3 (pow.f64 x 2))
(*.f64 1/3 (pow.f64 x 2))
(*.f64 1/3 (pow.f64 x 2))
(*.f64 1/3 (pow.f64 x 2))
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/3 (pow.f64 x 3))

Outputs
(*.f64 1/3 (pow.f64 x 2))
(.f64 1/3 (.f64 x x))
(*.f64 1/3 (pow.f64 x 2))
(.f64 1/3 (.f64 x x))
(*.f64 1/3 (pow.f64 x 2))
(.f64 1/3 (.f64 x x))
(*.f64 1/3 (pow.f64 x 2))
(.f64 1/3 (.f64 x x))
(*.f64 1/3 (pow.f64 x 2))
(.f64 1/3 (.f64 x x))
(*.f64 1/3 (pow.f64 x 2))
(.f64 1/3 (.f64 x x))
(*.f64 1/3 (pow.f64 x 2))
(.f64 1/3 (.f64 x x))
(*.f64 1/3 (pow.f64 x 2))
(.f64 1/3 (.f64 x x))
(*.f64 1/3 (pow.f64 x 2))
(.f64 1/3 (.f64 x x))
(*.f64 1/3 (pow.f64 x 2))
(.f64 1/3 (.f64 x x))
(*.f64 1/3 (pow.f64 x 2))
(.f64 1/3 (.f64 x x))
(*.f64 1/3 (pow.f64 x 2))
(.f64 1/3 (.f64 x x))
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/3 (pow.f64 x 3))

localize28.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 x (+.f64 (.f64 x (*.f64 x 1/3)) 2))
✓	0.1b	(.f64 x (.f64 x 1/3))
	0.4b	(*.f64 x 1/3)

Compiler

Compiled 39 to 27 computations (30.8% saved)

series5.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(.f64 x (.f64 x 1/3))
1.0ms	x	@	inf	(.f64 x (+.f64 (.f64 x (*.f64 x 1/3)) 2))
1.0ms	x	@	0	(.f64 x (+.f64 (.f64 x (*.f64 x 1/3)) 2))
1.0ms	x	@	0	(.f64 x (.f64 x 1/3))
1.0ms	x	@	-inf	(.f64 x (+.f64 (.f64 x (*.f64 x 1/3)) 2))

rewrite105.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

905×	`pow1_binary64`
847×	`add-log-exp_binary64`
846×	`log1p-expm1-u_binary64`
846×	`expm1-log1p-u_binary64`
832×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	180	18
2	2313	18

Stop Event

1×	node limit

Counts

2 → 35

Calls

Call 1

Inputs
(.f64 x (.f64 x 1/3))
(.f64 x (+.f64 (.f64 x (*.f64 x 1/3)) 2))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 x (*.f64 x 1/3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (*.f64 x 1/3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (*.f64 x 1/3))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (sqrt.f64 1/3)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (*.f64 x x) 3) 1/27) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 x (*.f64 x 1/3)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (*.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 x x) 3) 1/27))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (*.f64 x 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (*.f64 x 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (*.f64 x 1/3))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (pow.f64 x 3) 1/3) (*.f64 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x 2) (*.f64 (pow.f64 x 3) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 (pow.f64 x 3) 1/3) 1) (*.f64 (*.f64 x 2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 x (fma.f64 (*.f64 x x) 1/3 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 (pow.f64 x 3) 1/3) 3) (pow.f64 (*.f64 x 2) 3)) (+.f64 (*.f64 (*.f64 (pow.f64 x 3) 1/3) (*.f64 (pow.f64 x 3) 1/3)) (-.f64 (*.f64 (*.f64 x 2) (*.f64 x 2)) (*.f64 (*.f64 (pow.f64 x 3) 1/3) (*.f64 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 (pow.f64 x 3) 1/3) (*.f64 (pow.f64 x 3) 1/3)) (*.f64 (*.f64 x 2) (*.f64 x 2))) (-.f64 (*.f64 (pow.f64 x 3) 1/3) (*.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 8 (*.f64 (pow.f64 (*.f64 x x) 3) 1/27)) x) (+.f64 (pow.f64 (*.f64 x (*.f64 x 1/3)) 2) (-.f64 4 (*.f64 (*.f64 x x) 2/3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (pow.f64 (*.f64 x (*.f64 x 1/3)) 2) -4) x) (fma.f64 (*.f64 x x) 1/3 -2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x (+.f64 8 (*.f64 (pow.f64 (*.f64 x x) 3) 1/27))) (+.f64 (pow.f64 (*.f64 x (*.f64 x 1/3)) 2) (-.f64 4 (*.f64 (*.f64 x x) 2/3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x (+.f64 (pow.f64 (*.f64 x (*.f64 x 1/3)) 2) -4)) (fma.f64 (*.f64 x x) 1/3 -2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (fma.f64 (*.f64 x x) 1/3 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (fma.f64 (*.f64 x x) 1/3 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (fma.f64 (*.f64 x x) 1/3 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x (fma.f64 (*.f64 x x) 1/3 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 x (fma.f64 (*.f64 x x) 1/3 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (fma.f64 (*.f64 x x) 1/3 2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (fma.f64 (*.f64 x x) 1/3 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 3) (pow.f64 (fma.f64 (*.f64 x x) 1/3 2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (fma.f64 (*.f64 x x) 1/3 2) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (fma.f64 (*.f64 x x) 1/3 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (fma.f64 (*.f64 x x) 1/3 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (fma.f64 (*.f64 x x) 1/3 2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (*.f64 x (*.f64 x 1/3)) (*.f64 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (*.f64 x 1/3)) x (*.f64 x 2))))))

simplify190.0ms (3%)

Algorithm

1×	egg-herbie

Rules

944×	`sqr-pow_binary64`
564×	`cube-prod_binary64`
536×	`unswap-sqr_binary64`
533×	`fabs-mul_binary64`
502×	`pow-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	201
1	28	201
2	56	201
3	129	201
4	331	201
5	1379	201
6	2751	201
7	2937	201
8	3187	201
9	3474	201
10	3853	201
11	4362	201
12	4967	201
13	5675	201
14	6148	201
15	6467	201
16	6739	201
17	6905	201
18	6997	201
19	7674	201

Stop Event

1×	node limit

Counts

59 → 42

Calls

Call 1

Inputs
(*.f64 1/3 (pow.f64 x 2))
(*.f64 1/3 (pow.f64 x 2))
(*.f64 1/3 (pow.f64 x 2))
(*.f64 1/3 (pow.f64 x 2))
(*.f64 1/3 (pow.f64 x 2))
(*.f64 1/3 (pow.f64 x 2))
(*.f64 1/3 (pow.f64 x 2))
(*.f64 1/3 (pow.f64 x 2))
(*.f64 1/3 (pow.f64 x 2))
(*.f64 1/3 (pow.f64 x 2))
(*.f64 1/3 (pow.f64 x 2))
(*.f64 1/3 (pow.f64 x 2))
(*.f64 2 x)
(+.f64 (.f64 2 x) (.f64 1/3 (pow.f64 x 3)))
(+.f64 (.f64 2 x) (.f64 1/3 (pow.f64 x 3)))
(+.f64 (.f64 2 x) (.f64 1/3 (pow.f64 x 3)))
(*.f64 1/3 (pow.f64 x 3))
(+.f64 (.f64 2 x) (.f64 1/3 (pow.f64 x 3)))
(+.f64 (.f64 2 x) (.f64 1/3 (pow.f64 x 3)))
(+.f64 (.f64 2 x) (.f64 1/3 (pow.f64 x 3)))
(*.f64 1/3 (pow.f64 x 3))
(+.f64 (.f64 2 x) (.f64 1/3 (pow.f64 x 3)))
(+.f64 (.f64 2 x) (.f64 1/3 (pow.f64 x 3)))
(+.f64 (.f64 2 x) (.f64 1/3 (pow.f64 x 3)))

Outputs
(*.f64 1/3 (pow.f64 x 2))
(.f64 1/3 (.f64 x x))
(*.f64 1/3 (pow.f64 x 2))
(.f64 1/3 (.f64 x x))
(*.f64 1/3 (pow.f64 x 2))
(.f64 1/3 (.f64 x x))
(*.f64 1/3 (pow.f64 x 2))
(.f64 1/3 (.f64 x x))
(*.f64 1/3 (pow.f64 x 2))
(.f64 1/3 (.f64 x x))
(*.f64 1/3 (pow.f64 x 2))
(.f64 1/3 (.f64 x x))
(*.f64 1/3 (pow.f64 x 2))
(.f64 1/3 (.f64 x x))
(*.f64 1/3 (pow.f64 x 2))
(.f64 1/3 (.f64 x x))
(*.f64 1/3 (pow.f64 x 2))
(.f64 1/3 (.f64 x x))
(*.f64 1/3 (pow.f64 x 2))
(.f64 1/3 (.f64 x x))
(*.f64 1/3 (pow.f64 x 2))
(.f64 1/3 (.f64 x x))
(*.f64 1/3 (pow.f64 x 2))
(.f64 1/3 (.f64 x x))
(*.f64 2 x)
(*.f64 x 2)
(+.f64 (.f64 2 x) (.f64 1/3 (pow.f64 x 3)))
(fma.f64 2 x (*.f64 1/3 (pow.f64 x 3)))
(fma.f64 1/3 (pow.f64 x 3) (*.f64 x 2))
(.f64 x (fma.f64 1/3 (.f64 x x) 2))
(.f64 x (fma.f64 x (.f64 1/3 x) 2))
(+.f64 (.f64 2 x) (.f64 1/3 (pow.f64 x 3)))
(fma.f64 2 x (*.f64 1/3 (pow.f64 x 3)))
(fma.f64 1/3 (pow.f64 x 3) (*.f64 x 2))
(.f64 x (fma.f64 1/3 (.f64 x x) 2))
(.f64 x (fma.f64 x (.f64 1/3 x) 2))
(+.f64 (.f64 2 x) (.f64 1/3 (pow.f64 x 3)))
(fma.f64 2 x (*.f64 1/3 (pow.f64 x 3)))
(fma.f64 1/3 (pow.f64 x 3) (*.f64 x 2))
(.f64 x (fma.f64 1/3 (.f64 x x) 2))
(.f64 x (fma.f64 x (.f64 1/3 x) 2))
(*.f64 1/3 (pow.f64 x 3))
(+.f64 (.f64 2 x) (.f64 1/3 (pow.f64 x 3)))
(fma.f64 2 x (*.f64 1/3 (pow.f64 x 3)))
(fma.f64 1/3 (pow.f64 x 3) (*.f64 x 2))
(.f64 x (fma.f64 1/3 (.f64 x x) 2))
(.f64 x (fma.f64 x (.f64 1/3 x) 2))
(+.f64 (.f64 2 x) (.f64 1/3 (pow.f64 x 3)))
(fma.f64 2 x (*.f64 1/3 (pow.f64 x 3)))
(fma.f64 1/3 (pow.f64 x 3) (*.f64 x 2))
(.f64 x (fma.f64 1/3 (.f64 x x) 2))
(.f64 x (fma.f64 x (.f64 1/3 x) 2))
(+.f64 (.f64 2 x) (.f64 1/3 (pow.f64 x 3)))
(fma.f64 2 x (*.f64 1/3 (pow.f64 x 3)))
(fma.f64 1/3 (pow.f64 x 3) (*.f64 x 2))
(.f64 x (fma.f64 1/3 (.f64 x x) 2))
(.f64 x (fma.f64 x (.f64 1/3 x) 2))
(*.f64 1/3 (pow.f64 x 3))
(+.f64 (.f64 2 x) (.f64 1/3 (pow.f64 x 3)))
(fma.f64 2 x (*.f64 1/3 (pow.f64 x 3)))
(fma.f64 1/3 (pow.f64 x 3) (*.f64 x 2))
(.f64 x (fma.f64 1/3 (.f64 x x) 2))
(.f64 x (fma.f64 x (.f64 1/3 x) 2))
(+.f64 (.f64 2 x) (.f64 1/3 (pow.f64 x 3)))
(fma.f64 2 x (*.f64 1/3 (pow.f64 x 3)))
(fma.f64 1/3 (pow.f64 x 3) (*.f64 x 2))
(.f64 x (fma.f64 1/3 (.f64 x x) 2))
(.f64 x (fma.f64 x (.f64 1/3 x) 2))
(+.f64 (.f64 2 x) (.f64 1/3 (pow.f64 x 3)))
(fma.f64 2 x (*.f64 1/3 (pow.f64 x 3)))
(fma.f64 1/3 (pow.f64 x 3) (*.f64 x 2))
(.f64 x (fma.f64 1/3 (.f64 x x) 2))
(.f64 x (fma.f64 x (.f64 1/3 x) 2))

localize33.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 x (*.f64 x 1/3)) x)
	0.1b	(.f64 x (.f64 x 1/3))
	0.4b	(*.f64 x 1/3)

Compiler

Compiled 46 to 30 computations (34.8% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(.f64 (.f64 x (*.f64 x 1/3)) x)
0.0ms	x	@	inf	(.f64 (.f64 x (*.f64 x 1/3)) x)
0.0ms	x	@	-inf	(.f64 (.f64 x (*.f64 x 1/3)) x)

rewrite61.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

548×	`pow1_binary64`
526×	`add-sqr-sqrt_binary64`
505×	`add-log-exp_binary64`
505×	`log1p-expm1-u_binary64`
505×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	122	7
2	1400	7

Stop Event

1×	node limit

Counts

1 → 11

Calls

Call 1

Inputs
(.f64 (.f64 x (*.f64 x 1/3)) x)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (pow.f64 x 3) 1/3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x 3) 1/3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (pow.f64 x 3) 1/3) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (pow.f64 x 3) 1/3)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (pow.f64 x 3) 1/3)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (pow.f64 x 3) 1/3) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (*.f64 (pow.f64 x 3) 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (pow.f64 x 3) 1/3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 x 3) 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 x 3) 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (pow.f64 x 3) 1/3)))))))

simplify164.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

1274×	`sqr-pow_binary64`
666×	`pow-sqr_binary64`
529×	`cube-prod_binary64`
471×	`fabs-mul_binary64`
438×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	84
1	15	84
2	32	84
3	56	84
4	114	84
5	326	84
6	1180	84
7	1869	84
8	1956	84
9	2089	84
10	2247	84
11	2486	84
12	2808	84
13	3231	84
14	3733	84
15	4335	84
16	5057	84
17	5378	84
18	5664	84
19	5886	84
20	6064	84
21	6144	84
22	7084	84

Stop Event

1×	node limit

Counts

23 → 12

Calls

Call 1

Inputs
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/3 (pow.f64 x 3))

Outputs
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/3 (pow.f64 x 3))

eval54.0ms (0.9%)

Compiler: Compiled 1579 to 1196 computations (24.3% saved)

prune32.0ms (0.5%)

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	0	0
Picked	0	1	1
Done	0	5	5
Total	116	6	122

Error

Counts

122 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.7b	(/.f64 (+.f64 (.f64 2 x) (+.f64 (.f64 1/3 (pow.f64 x 3)) (*.f64 1/60 (pow.f64 x 5)))) 2)
✓	0.7b	(/.f64 (.f64 x (+.f64 (.f64 x (*.f64 x 1/3)) 2)) 2)
✓	1.1b	(/.f64 (*.f64 2 x) 2)
✓	60.0b	(/.f64 (.f64 x (.f64 1/3 (*.f64 x x))) 2)
✓	0.0b	(/.f64 (*.f64 2 (sinh.f64 x)) 2)
✓	0.7b	(/.f64 (+.f64 (.f64 (.f64 x (.f64 x 1/3)) x) (.f64 2 x)) 2)

Compiler

Compiled 67 to 52 computations (22.4% saved)

regimes29.0ms (0.5%)

Counts

8 → 1

Calls

Call 1

Inputs
(/.f64 (*.f64 2 x) 2)
(/.f64 (.f64 x (.f64 1/3 (*.f64 x x))) 2)
(/.f64 (.f64 x (+.f64 (.f64 x (*.f64 x 1/3)) 2)) 2)
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x 1/3)) x) (.f64 2 x)) 2)
(/.f64 (*.f64 2 (sinh.f64 x)) 2)
(/.f64 (.f64 x (fma.f64 x (.f64 x 1/3) 2)) 2)
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
(/.f64 (+.f64 (.f64 2 x) (+.f64 (.f64 1/3 (pow.f64 x 3)) (*.f64 1/60 (pow.f64 x 5)))) 2)

Outputs
(/.f64 (*.f64 2 (sinh.f64 x)) 2)

Calls

3 calls:

13.0ms	x
6.0ms	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
5.0ms	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

Results

Error	Segments	Branch
0.0b	1	`x`
0.0b	1	`(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)`
0.0b	1	`(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`

Compiler

Compiled 98 to 73 computations (25.5% saved)

regimes11.0ms (0.2%)

Counts

4 → 1

Calls

Call 1

Inputs
(/.f64 (*.f64 2 x) 2)
(/.f64 (.f64 x (.f64 1/3 (*.f64 x x))) 2)
(/.f64 (.f64 x (+.f64 (.f64 x (*.f64 x 1/3)) 2)) 2)
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x 1/3)) x) (.f64 2 x)) 2)

Outputs
(/.f64 (.f64 x (+.f64 (.f64 x (*.f64 x 1/3)) 2)) 2)

Calls

1 calls:

8.0ms

Results

Error	Segments	Branch
0.7b	1	`x`

Compiler

Compiled 41 to 29 computations (29.3% saved)

regimes12.0ms (0.2%)

Accuracy

Total -58.9b remaining (-5259.7%)

Threshold costs -58.9b (-5259.7%)

Counts

2 → 1

Calls

Call 1

Inputs
(/.f64 (*.f64 2 x) 2)
(/.f64 (.f64 x (.f64 1/3 (*.f64 x x))) 2)

Outputs
(/.f64 (*.f64 2 x) 2)

Calls

1 calls:

11.0ms

Results

Error	Segments	Branch
1.1b	1	`x`

Compiler

Compiled 17 to 12 computations (29.4% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	32
1	20	32

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(/.f64 (*.f64 2 (sinh.f64 x)) 2)
(/.f64 (.f64 x (+.f64 (.f64 x (*.f64 x 1/3)) 2)) 2)
(/.f64 (*.f64 2 x) 2)

Outputs
(/.f64 (*.f64 2 (sinh.f64 x)) 2)
(/.f64 (.f64 x (+.f64 (.f64 x (*.f64 x 1/3)) 2)) 2)
(/.f64 (.f64 x (+.f64 2 (.f64 x (*.f64 x 1/3)))) 2)
(/.f64 (*.f64 2 x) 2)

Compiler

Compiled 25 to 20 computations (20% saved)

soundness0.0ms (0%)

end53.0ms (0.8%)

Compiler: Compiled 23 to 18 computations (21.7% saved)

Details

analyze6.0ms (0.1%)

sample3.7s (59.8%)

preprocess68.0ms (1.1%)

simplify51.0ms (0.8%)

eval1.0ms (0%)

prune1.0ms (0%)

localize8.0ms (0.1%)

series1.0ms (0%)

rewrite33.0ms (0.5%)

simplify62.0ms (1%)

eval6.0ms (0.1%)

prune5.0ms (0.1%)

localize6.0ms (0.1%)

localize6.0ms (0.1%)

series2.0ms (0%)

rewrite54.0ms (0.9%)

simplify79.0ms (1.3%)

localize15.0ms (0.2%)

series5.0ms (0.1%)

rewrite57.0ms (0.9%)

simplify281.0ms (4.5%)

localize58.0ms (0.9%)

series6.0ms (0.1%)

rewrite110.0ms (1.8%)

simplify145.0ms (2.3%)

eval210.0ms (3.4%)

prune171.0ms (2.7%)

localize22.0ms (0.4%)

series3.0ms (0.1%)

rewrite72.0ms (1.2%)

simplify175.0ms (2.8%)

localize28.0ms (0.5%)

series5.0ms (0.1%)

rewrite105.0ms (1.7%)

simplify190.0ms (3%)

localize33.0ms (0.5%)

series1.0ms (0%)

rewrite61.0ms (1%)

simplify164.0ms (2.6%)

eval54.0ms (0.9%)

prune32.0ms (0.5%)

regimes29.0ms (0.5%)

regimes11.0ms (0.2%)

regimes12.0ms (0.2%)

simplify6.0ms (0.1%)

soundness0.0ms (0%)

end53.0ms (0.8%)

Profiling