Details

analyze0.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	25%	75%	0
25%	0%	75%	1

Compiler

Compiled 17 to 9 computations (47.1% saved)

sample878.0ms (48%)

Results

866.0ms	8252×	body	64	valid
1.0ms	4×	body	128	valid

preprocess166.0ms (9.1%)

Algorithm

2×	egg-herbie

Rules

1331×	`sqr-pow_binary64`
715×	`pow-sqr_binary64`
636×	`cube-prod_binary64`
562×	`fabs-mul_binary64`
362×	`unswap-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	10
1	15	8
2	31	8
3	46	8
4	71	8
5	123	8
6	239	8
7	673	8
8	1364	8
9	1465	8
10	1598	8
11	1756	8
12	1987	8
13	2311	8
14	2732	8
15	3232	8
16	3825	8
17	4547	8
18	4868	8
19	5154	8
20	5376	8
21	5554	8
22	5636	8
23	6576	8
24	7550	8
0	1	1

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

Inputs
(+.f64 (.f64 x (.f64 x x)) (*.f64 x x))

Outputs
(+.f64 (.f64 x (.f64 x x)) (*.f64 x x))
(+.f64 (*.f64 x x) (pow.f64 x 3))
(fma.f64 x x (pow.f64 x 3))
(*.f64 x (fma.f64 x x x))

Compiler

Compiled 10 to 4 computations (60% saved)

simplify118.0ms (6.5%)

Algorithm

1×	egg-herbie

Rules

1331×	`sqr-pow_binary64`
715×	`pow-sqr_binary64`
636×	`cube-prod_binary64`
562×	`fabs-mul_binary64`
362×	`unswap-sqr_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	5	10
1	15	8
2	31	8
3	46	8
4	71	8
5	123	8
6	239	8
7	673	8
8	1364	8
9	1465	8
10	1598	8
11	1756	8
12	1987	8
13	2311	8
14	2732	8
15	3232	8
16	3825	8
17	4547	8
18	4868	8
19	5154	8
20	5376	8
21	5554	8
22	5636	8
23	6576	8
24	7550	8

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

Inputs
(+.f64 (.f64 x (.f64 x x)) (*.f64 x x))

Outputs
(+.f64 (.f64 x (.f64 x x)) (*.f64 x x))
(+.f64 (*.f64 x x) (pow.f64 x 3))
(fma.f64 x x (pow.f64 x 3))
(*.f64 x (fma.f64 x x x))

prune2.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(*.f64 x (fma.f64 x x x))

Compiler

Compiled 30 to 12 computations (60% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 x (fma.f64 x x x))

series3.0ms (0.2%)

Counts

1 → 12

Calls

3 calls:

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

rewrite36.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

378×	`pow1_binary64`
361×	`add-sqr-sqrt_binary64`
356×	`*-un-lft-identity_binary64`
347×	`add-log-exp_binary64`
347×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	8
1	79	8
2	949	8

Stop Event

1×	node limit

Counts

1 → 27

Calls

Call 1

Inputs
(*.f64 x (fma.f64 x x x))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x 3) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 x (fma.f64 x x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x x x)) x)) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x x x)) x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (fma.f64 x x x)) x))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (fma.f64 x x x)) x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (.f64 x (fma.f64 x x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 x (fma.f64 x x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 (pow.f64 x 3/2) x) 4) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 (pow.f64 x 3/2) x) 6) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 x (fma.f64 x x x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 (pow.f64 x 3/2) x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (hypot.f64 (pow.f64 x 3/2) x) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (fma.f64 x x x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 (pow.f64 x 3)) (exp.f64 (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (hypot.f64 (pow.f64 x 3/2) x) 6))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (.f64 x x) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (pow.f64 x 3) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 x x) x (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 3/2) (pow.f64 x 3/2) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (pow.f64 x 3)) (sqrt.f64 (pow.f64 x 3)) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (.f64 x (cbrt.f64 x)) 2) (cbrt.f64 x) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 5/2) (sqrt.f64 x) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 x (fma.f64 x x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 x (fma.f64 x x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (pow.f64 (hypot.f64 (pow.f64 x 3/2) x) 6)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 x (fma.f64 x x x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (hypot.f64 (pow.f64 x 3/2) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 x (fma.f64 x x x))))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x 3) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 x (fma.f64 x x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x x x)) x)) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x x x)) x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (fma.f64 x x x)) x))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (fma.f64 x x x)) x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 x (fma.f64 x x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (fma.f64 x x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 (pow.f64 x 3/2) x) 4) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 (pow.f64 x 3/2) x) 6) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (fma.f64 x x x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 (pow.f64 x 3/2) x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (hypot.f64 (pow.f64 x 3/2) x) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (fma.f64 x x x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (pow.f64 x 3)) (exp.f64 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (hypot.f64 (pow.f64 x 3/2) x) 6))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (*.f64 x x) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (pow.f64 x 3) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x x) x (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 3/2) (pow.f64 x 3/2) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (pow.f64 x 3)) (sqrt.f64 (pow.f64 x 3)) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (*.f64 x (cbrt.f64 x)) 2) (cbrt.f64 x) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 5/2) (sqrt.f64 x) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (fma.f64 x x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (fma.f64 x x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (hypot.f64 (pow.f64 x 3/2) x) 6)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 x (fma.f64 x x x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (hypot.f64 (pow.f64 x 3/2) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (fma.f64 x x x))))))))

simplify116.0ms (6.3%)

Algorithm

1×	egg-herbie

Rules

1262×	`fma-def_binary64`
969×	`sqr-pow_binary64`
536×	`unswap-sqr_binary64`
502×	`cube-prod_binary64`
460×	`fabs-mul_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	102
1	20	84
2	44	84
3	81	84
4	207	84
5	843	84
6	2540	84
7	3291	84
8	3585	84
9	3905	84
10	4315	84
11	4839	84
12	5507	84
13	6236	84
14	6812	84
15	7142	84
16	7416	84
17	7585	84
18	7676	84

Stop Event

1×	node limit

Counts

39 → 32

Calls

Call 1

Inputs
(pow.f64 x 2)
(+.f64 (pow.f64 x 2) (pow.f64 x 3))
(+.f64 (pow.f64 x 2) (pow.f64 x 3))
(+.f64 (pow.f64 x 2) (pow.f64 x 3))
(pow.f64 x 3)
(+.f64 (pow.f64 x 2) (pow.f64 x 3))
(+.f64 (pow.f64 x 2) (pow.f64 x 3))
(+.f64 (pow.f64 x 2) (pow.f64 x 3))
(pow.f64 x 3)
(+.f64 (pow.f64 x 2) (pow.f64 x 3))
(+.f64 (pow.f64 x 2) (pow.f64 x 3))
(+.f64 (pow.f64 x 2) (pow.f64 x 3))

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

prune35.0ms (1.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	31	1	32
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	31	2	33

Error

0.0b

Counts

33 → 2

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 x (fma.f64 x x x))
▶	0.0b	(pow.f64 (hypot.f64 (pow.f64 x 3/2) x) 2)

Compiler

Compiled 309 to 144 computations (53.4% saved)

localize7.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 (pow.f64 x 3/2) x)
✓	0.0b	(pow.f64 (hypot.f64 (pow.f64 x 3/2) x) 2)

series11.0ms (0.6%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	x	@	0	(pow.f64 (hypot.f64 (pow.f64 x 3/2) x) 2)
3.0ms	x	@	-inf	(pow.f64 (hypot.f64 (pow.f64 x 3/2) x) 2)
2.0ms	x	@	inf	(pow.f64 (hypot.f64 (pow.f64 x 3/2) x) 2)
1.0ms	x	@	inf	(hypot.f64 (pow.f64 x 3/2) x)
1.0ms	x	@	-inf	(hypot.f64 (pow.f64 x 3/2) x)

rewrite44.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

570×	`pow1_binary64`
532×	`add-log-exp_binary64`
532×	`log1p-expm1-u_binary64`
532×	`expm1-log1p-u_binary64`
519×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	150	17
2	1571	17

Stop Event

1×	node limit

Counts

2 → 40

Calls

Call 1

Inputs
(pow.f64 (hypot.f64 (pow.f64 x 3/2) x) 2)
(hypot.f64 (pow.f64 x 3/2) x)

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

Outputs

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

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

simplify40.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

581×	`associate-*l/_binary64`
449×	`fma-def_binary64`
405×	`unswap-sqr_binary64`
268×	`associate-/l/_binary64`
264×	`associate-+l+_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	111	526
1	304	488
2	921	433
3	3840	350

Stop Event

1×	node limit

Counts

64 → 76

Calls

Call 1

Inputs
(pow.f64 x 3)
(+.f64 (pow.f64 x 2) (pow.f64 x 3))
(+.f64 (pow.f64 x 2) (pow.f64 x 3))
(+.f64 (pow.f64 x 2) (+.f64 (.f64 (+.f64 (.f64 5/64 (/.f64 1 (pow.f64 x 9))) (.f64 -1 (+.f64 (pow.f64 (.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 9)))) 2) (*.f64 1/16 (/.f64 1 (pow.f64 x 9)))))) (pow.f64 x 8)) (pow.f64 x 3)))
(pow.f64 x 2)
(+.f64 (pow.f64 x 2) (pow.f64 x 3))
(+.f64 (pow.f64 x 2) (pow.f64 x 3))
(+.f64 (.f64 1/16 (pow.f64 x 6)) (+.f64 (.f64 1/64 (pow.f64 x 6)) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 1/16 (pow.f64 x 12)) (pow.f64 (*.f64 -1/8 (pow.f64 x 6)) 2)) (pow.f64 x 6))) (+.f64 (pow.f64 x 2) (pow.f64 x 3)))))
(pow.f64 x 2)
(+.f64 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2))
(+.f64 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 4) (pow.f64 x 2))) (+.f64 (pow.f64 x 2) (.f64 1/4 (/.f64 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 4) (pow.f64 x 2))))))
(+.f64 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 4) (pow.f64 x 2))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 6) (pow.f64 x 4))) (+.f64 (pow.f64 x 2) (+.f64 (.f64 1/4 (/.f64 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 4) (pow.f64 x 2))) (.f64 1/8 (/.f64 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 6) (pow.f64 x 4))))))))
(sqrt.f64 (pow.f64 x 3))
(+.f64 (*.f64 1/2 (sqrt.f64 x)) (sqrt.f64 (pow.f64 x 3)))
(+.f64 (.f64 -1/8 (sqrt.f64 (/.f64 1 x))) (+.f64 (.f64 1/2 (sqrt.f64 x)) (sqrt.f64 (pow.f64 x 3))))
(+.f64 (.f64 -1/8 (sqrt.f64 (/.f64 1 x))) (+.f64 (.f64 1/2 (sqrt.f64 x)) (+.f64 (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (sqrt.f64 (pow.f64 x 3)))))
x
(+.f64 (*.f64 1/2 (pow.f64 x 2)) x)
(+.f64 (.f64 -1/8 (pow.f64 x 3)) (+.f64 (.f64 1/2 (pow.f64 x 2)) x))
(+.f64 (.f64 1/16 (pow.f64 x 4)) (+.f64 (.f64 -1/8 (pow.f64 x 3)) (+.f64 (*.f64 1/2 (pow.f64 x 2)) x)))
(*.f64 -1 x)
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x)) (.f64 -1 x))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 4) (pow.f64 x 3))) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x)) (*.f64 -1 x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 4) (pow.f64 x 3))) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 6) (pow.f64 x 5))) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x)) (.f64 -1 x))))

Outputs
(pow.f64 x 3)
(+.f64 (pow.f64 x 2) (pow.f64 x 3))
(+.f64 (pow.f64 x 3) (*.f64 x x))
(fma.f64 x x (pow.f64 x 3))
(*.f64 x (fma.f64 x x x))
(+.f64 (pow.f64 x 2) (pow.f64 x 3))
(+.f64 (pow.f64 x 3) (*.f64 x x))
(fma.f64 x x (pow.f64 x 3))
(*.f64 x (fma.f64 x x x))
(+.f64 (pow.f64 x 2) (+.f64 (.f64 (+.f64 (.f64 5/64 (/.f64 1 (pow.f64 x 9))) (.f64 -1 (+.f64 (pow.f64 (.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 9)))) 2) (*.f64 1/16 (/.f64 1 (pow.f64 x 9)))))) (pow.f64 x 8)) (pow.f64 x 3)))
(+.f64 (.f64 x x) (fma.f64 (+.f64 (/.f64 5/64 (pow.f64 x 9)) (neg.f64 (+.f64 (pow.f64 (.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 9)))) 2) (/.f64 1/16 (pow.f64 x 9))))) (pow.f64 x 8) (pow.f64 x 3)))
(fma.f64 x x (fma.f64 (-.f64 (/.f64 5/64 (pow.f64 x 9)) (+.f64 (pow.f64 (*.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 9)))) 2) (/.f64 1/16 (pow.f64 x 9)))) (pow.f64 x 8) (pow.f64 x 3)))
(fma.f64 (+.f64 (.f64 (/.f64 1 (pow.f64 x 9)) 1/64) (.f64 (/.f64 1 (pow.f64 x 9)) -1/64)) (pow.f64 x 8) (*.f64 x (fma.f64 x x x)))
(fma.f64 (.f64 (/.f64 1 (pow.f64 x 9)) 0) (pow.f64 x 8) (.f64 x (fma.f64 x x x)))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 x 2) (pow.f64 x 3))
(+.f64 (pow.f64 x 3) (*.f64 x x))
(fma.f64 x x (pow.f64 x 3))
(*.f64 x (fma.f64 x x x))
(+.f64 (pow.f64 x 2) (pow.f64 x 3))
(+.f64 (pow.f64 x 3) (*.f64 x x))
(fma.f64 x x (pow.f64 x 3))
(*.f64 x (fma.f64 x x x))
(+.f64 (.f64 1/16 (pow.f64 x 6)) (+.f64 (.f64 1/64 (pow.f64 x 6)) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 1/16 (pow.f64 x 12)) (pow.f64 (*.f64 -1/8 (pow.f64 x 6)) 2)) (pow.f64 x 6))) (+.f64 (pow.f64 x 2) (pow.f64 x 3)))))
(fma.f64 1/16 (pow.f64 x 6) (fma.f64 1/64 (pow.f64 x 6) (fma.f64 -1 (/.f64 (fma.f64 1/16 (pow.f64 x 12) (pow.f64 (.f64 -1/8 (pow.f64 x 6)) 2)) (pow.f64 x 6)) (+.f64 (pow.f64 x 3) (.f64 x x)))))
(+.f64 (-.f64 (fma.f64 x x (pow.f64 x 3)) (/.f64 (fma.f64 1/16 (pow.f64 x 12) (.f64 1/64 (pow.f64 x 12))) (pow.f64 x 6))) (.f64 (pow.f64 x 6) 5/64))
(-.f64 (fma.f64 (pow.f64 x 6) 5/64 (.f64 x (fma.f64 x x x))) (/.f64 (.f64 (pow.f64 x 12) 5/64) (pow.f64 x 6)))
(fma.f64 (pow.f64 x 6) 5/64 (fma.f64 x (fma.f64 x x x) (/.f64 (*.f64 (pow.f64 x 12) -5/64) (pow.f64 x 6))))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2))
(+.f64 (*.f64 x x) (pow.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2))
(fma.f64 x x (pow.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2))
(fma.f64 x x (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2)) 2))
(fma.f64 x x (pow.f64 (exp.f64 (log.f64 x)) 3))
(+.f64 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 4) (pow.f64 x 2))) (+.f64 (pow.f64 x 2) (.f64 1/4 (/.f64 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 4) (pow.f64 x 2))))))
(+.f64 (*.f64 x x) (pow.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2))
(fma.f64 x x (pow.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2))
(fma.f64 x x (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2)) 2))
(fma.f64 x x (pow.f64 (exp.f64 (log.f64 x)) 3))
(+.f64 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 4) (pow.f64 x 2))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 6) (pow.f64 x 4))) (+.f64 (pow.f64 x 2) (+.f64 (.f64 1/4 (/.f64 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 4) (pow.f64 x 2))) (.f64 1/8 (/.f64 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 6) (pow.f64 x 4))))))))
(+.f64 (*.f64 x x) (pow.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2))
(fma.f64 x x (pow.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2))
(fma.f64 x x (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2)) 2))
(fma.f64 x x (pow.f64 (exp.f64 (log.f64 x)) 3))
(sqrt.f64 (pow.f64 x 3))
(pow.f64 x 3/2)
(+.f64 (*.f64 1/2 (sqrt.f64 x)) (sqrt.f64 (pow.f64 x 3)))
(fma.f64 1/2 (sqrt.f64 x) (sqrt.f64 (pow.f64 x 3)))
(fma.f64 1/2 (sqrt.f64 x) (pow.f64 x 3/2))
(+.f64 (.f64 -1/8 (sqrt.f64 (/.f64 1 x))) (+.f64 (.f64 1/2 (sqrt.f64 x)) (sqrt.f64 (pow.f64 x 3))))
(fma.f64 -1/8 (sqrt.f64 (/.f64 1 x)) (fma.f64 1/2 (sqrt.f64 x) (sqrt.f64 (pow.f64 x 3))))
(fma.f64 -1/8 (sqrt.f64 (/.f64 1 x)) (fma.f64 1/2 (sqrt.f64 x) (pow.f64 x 3/2)))
(+.f64 (.f64 -1/8 (sqrt.f64 (/.f64 1 x))) (+.f64 (.f64 1/2 (sqrt.f64 x)) (+.f64 (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (sqrt.f64 (pow.f64 x 3)))))
(fma.f64 -1/8 (sqrt.f64 (/.f64 1 x)) (fma.f64 1/2 (sqrt.f64 x) (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (sqrt.f64 (pow.f64 x 3)))))
(fma.f64 -1/8 (sqrt.f64 (/.f64 1 x)) (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 1/2 (sqrt.f64 x) (pow.f64 x 3/2))))
x
(+.f64 (*.f64 1/2 (pow.f64 x 2)) x)
(fma.f64 1/2 (*.f64 x x) x)
(fma.f64 (*.f64 x x) 1/2 x)
(fma.f64 x (*.f64 x 1/2) x)
(+.f64 (.f64 -1/8 (pow.f64 x 3)) (+.f64 (.f64 1/2 (pow.f64 x 2)) x))
(fma.f64 -1/8 (pow.f64 x 3) (fma.f64 1/2 (*.f64 x x) x))
(fma.f64 (pow.f64 x 3) -1/8 (fma.f64 (*.f64 x x) 1/2 x))
(fma.f64 x (*.f64 x 1/2) (fma.f64 (pow.f64 x 3) -1/8 x))
(+.f64 (.f64 1/16 (pow.f64 x 4)) (+.f64 (.f64 -1/8 (pow.f64 x 3)) (+.f64 (*.f64 1/2 (pow.f64 x 2)) x)))
(fma.f64 1/16 (pow.f64 x 4) (fma.f64 -1/8 (pow.f64 x 3) (fma.f64 1/2 (*.f64 x x) x)))
(fma.f64 1/16 (pow.f64 x 4) (fma.f64 (pow.f64 x 3) -1/8 (fma.f64 (*.f64 x x) 1/2 x)))
(fma.f64 (pow.f64 x 3) -1/8 (fma.f64 1/16 (pow.f64 x 4) (fma.f64 (*.f64 x x) 1/2 x)))
(fma.f64 (pow.f64 x 3) -1/8 (fma.f64 1/16 (pow.f64 x 4) (fma.f64 x (*.f64 x 1/2) x)))
(*.f64 -1 x)
(neg.f64 x)
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x)) (.f64 -1 x))
(fma.f64 -1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) x) (neg.f64 x))
(-.f64 (*.f64 -1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) x)) x)
(-.f64 (.f64 (/.f64 -1/2 x) (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2)) 2)) x)
(-.f64 (*.f64 (/.f64 -1/2 x) (pow.f64 (exp.f64 (log.f64 x)) 3)) x)
(+.f64 (.f64 1/8 (/.f64 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 4) (pow.f64 x 3))) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x)) (*.f64 -1 x)))
(fma.f64 1/8 (/.f64 (pow.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 4) (pow.f64 x 3)) (fma.f64 -1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) x) (neg.f64 x)))
(-.f64 (fma.f64 1/8 (/.f64 (pow.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 4) (pow.f64 x 3)) (*.f64 -1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) x))) x)
(-.f64 (fma.f64 1/8 (/.f64 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2)) 4) (pow.f64 x 3)) (.f64 (/.f64 -1/2 x) (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2)) 2))) x)
(fma.f64 1/8 (/.f64 (pow.f64 (exp.f64 (log.f64 x)) 6) (pow.f64 x 3)) (-.f64 (*.f64 (/.f64 -1/2 x) (pow.f64 (exp.f64 (log.f64 x)) 3)) x))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 4) (pow.f64 x 3))) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 6) (pow.f64 x 5))) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x)) (.f64 -1 x))))
(fma.f64 1/8 (/.f64 (pow.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 4) (pow.f64 x 3)) (fma.f64 -1/16 (/.f64 (pow.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 6) (pow.f64 x 5)) (fma.f64 -1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) x) (neg.f64 x))))
(fma.f64 1/8 (/.f64 (pow.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 4) (pow.f64 x 3)) (fma.f64 -1/16 (/.f64 (pow.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 6) (pow.f64 x 5)) (-.f64 (*.f64 -1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) x)) x)))
(fma.f64 1/8 (/.f64 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2)) 4) (pow.f64 x 3)) (fma.f64 -1/2 (/.f64 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2)) 2) x) (-.f64 (.f64 (/.f64 -1/16 (pow.f64 x 5)) (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2)) 6)) x)))
(-.f64 (fma.f64 1/8 (/.f64 (pow.f64 (exp.f64 (log.f64 x)) 6) (pow.f64 x 3)) (fma.f64 -1/2 (/.f64 (pow.f64 (exp.f64 (log.f64 x)) 3) x) (*.f64 (/.f64 -1/16 (pow.f64 x 5)) (pow.f64 (pow.f64 (exp.f64 3/2) (log.f64 x)) 6)))) x)

prune122.0ms (6.7%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	0	0	0
Picked	1	0	1
Done	1	0	1
Total	77	1	78

Error

Counts

78 → 1

Alt Table

Status	Error	Program
▶	0b	(fma.f64 x x (pow.f64 (exp.f64 (log.f64 x)) 3))

Compiler

Compiled 1268 to 936 computations (26.2% saved)

localize8.0ms (0.5%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	5.7b	(exp.f64 (log.f64 x))

series1.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite79.0ms (4.3%)

Algorithm

1×	batch-egg-rewrite

Rules

479×	`fma-neg_binary64`
374×	`expm1-udef_binary64`
374×	`log1p-udef_binary64`
257×	`associate-r_binary64`
246×	`pow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	1
1	63	1
2	635	1
3	6671	1

Stop Event

1×	node limit

Counts

1 → 60

Calls

Call 1

Inputs
(exp.f64 (log.f64 x))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 x -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (+.f64 x -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 x 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 x)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 x))) (log.f64 (sqrt.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 2))) (log.f64 (cbrt.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 x 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 x) (pow.f64 (cbrt.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 2) (*.f64 (cbrt.f64 (cbrt.f64 x)) (pow.f64 (cbrt.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x (cbrt.f64 x))) (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 2) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x 1/4) (sqrt.f64 (pow.f64 x 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x 1/4) (*.f64 (pow.f64 x 1/4) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x 1/6) (*.f64 (pow.f64 x 1/6) (pow.f64 (cbrt.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 x) (pow.f64 x 1/4)) (pow.f64 x 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 x 5/2)) (pow.f64 x 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x (pow.f64 (cbrt.f64 x) 5))) (cbrt.f64 (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 5)) (pow.f64 x 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 x 3/2)) (pow.f64 x 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 x (pow.f64 (cbrt.f64 x) 5)) 1/3) (cbrt.f64 (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 x 5/2) 1/3) (pow.f64 x 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (E.f64) (log.f64 (sqrt.f64 x))) (pow.f64 (E.f64) (log.f64 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (E.f64) (*.f64 2 (log.f64 (cbrt.f64 x)))) (pow.f64 (E.f64) (log.f64 (cbrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 x) (cbrt.f64 x)) (pow.f64 x 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 (*.f64 x (cbrt.f64 x)))) (pow.f64 (cbrt.f64 (cbrt.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 x 1/6)) (pow.f64 x 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 (cbrt.f64 x)) 2)) (cbrt.f64 (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (exp.f64 (+.f64 (log.f64 x) 1)) (E.f64))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (E.f64) (+.f64 (log.f64 x) 1)) (E.f64))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 x 1) 3) 1) (+.f64 (*.f64 (+.f64 x 1) (+.f64 x 1)) (+.f64 1 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 x -1) 3)) (+.f64 1 (-.f64 (pow.f64 (+.f64 x -1) 2) (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (+.f64 x 1) (+.f64 x 1) -1) (+.f64 (+.f64 x 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (+.f64 x -1) 2)) (-.f64 1 (+.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 x) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 x)) 2)) (cbrt.f64 (log.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 x))) (sqrt.f64 (log.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (cbrt.f64 (log.f64 x))) (pow.f64 (cbrt.f64 (log.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 x)) 2)) (pow.f64 (cbrt.f64 (cbrt.f64 (log.f64 x))) 2)) (cbrt.f64 (cbrt.f64 (log.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 x)) 2)) (pow.f64 (log.f64 x) 1/6)) (pow.f64 (log.f64 x) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (sqrt.f64 (log.f64 x))) (cbrt.f64 (log.f64 x))) (pow.f64 (log.f64 x) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (sqrt.f64 (log.f64 x))) (pow.f64 (log.f64 x) 1/4)) (pow.f64 (log.f64 x) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 x)))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 x 3))))) (#(struct:change #<rule egg-rr> (2) ((x . x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 x 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 x 1) 1 -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1))) (cbrt.f64 (+.f64 x 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 x))))))

simplify6.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	12

Stop Event

1×

saturated

Counts

72 → 61

Calls

Call 1

Inputs
x
x
x
x
x
x
x
x
x
x
x
x

Outputs
x
x
x
x
x
x
x
x
x
x
x
x

prune128.0ms (7%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	61	0	61
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	61	1	62

Error

Counts

62 → 1

Alt Table

Status	Error	Program
✓	0b	(fma.f64 x x (pow.f64 (exp.f64 (log.f64 x)) 3))

Compiler

Compiled 839 to 500 computations (40.4% saved)

regimes6.0ms (0.4%)

Accuracy

Total -0.0b remaining (-∞%)

Threshold costs -0.0b (-∞%)

Counts

4 → 1

Calls

Call 1

Inputs
(fma.f64 x x (pow.f64 (exp.f64 (log.f64 x)) 3))
(pow.f64 (hypot.f64 (pow.f64 x 3/2) x) 2)
(*.f64 x (fma.f64 x x x))
(+.f64 (.f64 x (.f64 x x)) (*.f64 x x))

Outputs
(fma.f64 x x (pow.f64 (exp.f64 (log.f64 x)) 3))

Results

3.0ms	0b	`x`
2.0ms	0b	`(+.f64 (.f64 x (.f64 x x)) (*.f64 x x))`

Compiler

Compiled 43 to 21 computations (51.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 x x (pow.f64 (exp.f64 (log.f64 x)) 3))

Outputs
(fma.f64 x x (pow.f64 (exp.f64 (log.f64 x)) 3))

end18.0ms (1%)

Stop Event

1×

done

Compiler

Compiled 18 to 12 computations (33.3% saved)

Details

analyze0.0ms (0%)

sample878.0ms (48%)

preprocess166.0ms (9.1%)

simplify118.0ms (6.5%)

prune2.0ms (0.1%)

localize3.0ms (0.2%)

series3.0ms (0.2%)

rewrite36.0ms (2%)

simplify116.0ms (6.3%)

prune35.0ms (1.9%)

localize7.0ms (0.4%)

series11.0ms (0.6%)

rewrite44.0ms (2.4%)

simplify40.0ms (2.2%)

prune122.0ms (6.7%)

localize8.0ms (0.5%)

series1.0ms (0.1%)

rewrite79.0ms (4.3%)

simplify6.0ms (0.3%)

prune128.0ms (7%)

regimes6.0ms (0.4%)

simplify2.0ms (0.1%)

end18.0ms (1%)

Profiling