Details

analyze6.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.8%	0.1%	0.1%	12
99.8%	0%	0.1%	13
99.8%	0%	0.2%	14

Compiler

Compiled 11 to 10 computations (9.1% saved)

sample890.0ms (23.7%)

Results

860.0ms	8251×	body	128	valid
1.0ms	4×	body	1024	valid
0.0ms	3×	body	128	invalid
0.0ms	1×	body	512	valid

Compiler

Compiled 32 to 29 computations (9.4% saved)

simplify35.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

2×	`fma-def_binary64`
1×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	5
1	15	5
2	16	5
3	14	5

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

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 841/108 x 4/29)

Compiler

Compiled 24 to 20 computations (16.7% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 841/108 x 4/29)

series2.0ms (0%)

Counts

1 → 12

Calls

1 calls:

2.0ms

(fma.f64 841/108 x 4/29)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 841/108 x 4/29)

simplify108.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

639×	`associate-*r/_binary64`
493×	`distribute-rgt-in_binary64`
446×	`distribute-lft-out_binary64`
406×	`distribute-rgt-out_binary64`
402×	`associate-l_binary64`

Counts

22 → 15

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	142
1	19	131
2	42	131
3	104	131
4	284	131
5	900	131
6	1555	131
7	2510	131
8	2614	131
9	3104	131
10	4503	131
11	4867	131
12	4989	131
13	4799	131

prune10.0ms (0.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	13	2	15
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	13	3	16

Error

0.1b

Counts

16 → 3

Alt Table

Status	Error	Program
	17.1b	(*.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) (sqrt.f64 (fma.f64 841/108 x 4/29)))
▶	1.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (fma.f64 841/108 x 4/29)))
✓	0.1b	(fma.f64 841/108 x 4/29)

Compiler

Compiled 170 to 140 computations (17.6% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 841/108 x 4/29)
✓	0.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (fma.f64 841/108 x 4/29)))
✓	0.7b	(*.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29)))
✓	0.8b	(cbrt.f64 (fma.f64 841/108 x 4/29))

series15.0ms (0.4%)

Counts

3 → 36

Calls

3 calls:

6.0ms

(cbrt.f64 (fma.f64 841/108 x 4/29))

6.0ms

(*.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29)))

3.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (fma.f64 841/108 x 4/29)))

rewrite16.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

6.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (fma.f64 841/108 x 4/29)))

4.0ms

(*.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29)))

1.0ms

(cbrt.f64 (fma.f64 841/108 x 4/29))

simplify106.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

492×	`times-frac_binary64`
423×	`fma-def_binary64`
413×	`fma-neg_binary64`
239×	`unswap-sqr_binary64`
210×	`*-commutative_binary64`

Counts

129 → 185

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	177	2495
1	418	2285
2	1171	1923
3	3158	1699
4	4947	1699
5	4970	1699

prune262.0ms (7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	319	5	324
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	320	7	327

Error

0.0b

Counts

327 → 7

Alt Table

Status	Error	Program
	2.1b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (fma.f64 841/108 x 4/29)))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (fma.f64 841/108 x 4/29))))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (fma.f64 841/108 x 4/29)))))
	1.8b	(.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (fma.f64 841/108 x 4/29)))))
	17.1b	(*.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) (sqrt.f64 (fma.f64 841/108 x 4/29)))
	46.0b	(.f64 (cbrt.f64 (.f64 (*.f64 x x) 707281/11664)) (cbrt.f64 (fma.f64 841/108 x 4/29)))
	18.1b	(.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)))) (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))))) (cbrt.f64 (fma.f64 841/108 x 4/29)))
▶	1.8b	(.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))))) (cbrt.f64 (fma.f64 841/108 x 4/29)))
✓	0.1b	(fma.f64 841/108 x 4/29)

Compiler

Compiled 8329 to 7022 computations (15.7% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))))
✓	0.3b	(cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))
✓	0.7b	(.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (.f64 (*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))))
	0.8b	(cbrt.f64 (fma.f64 841/108 x 4/29))

series20.0ms (0.5%)

Counts

3 → 36

Calls

3 calls:

8.0ms

(cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))

6.0ms

(*.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (*.f64 (*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))))

6.0ms

(*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))))

rewrite27.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`cbrt-prod_binary64`
37×	`add-sqr-sqrt_binary64`
21×	`pow1_binary64`
20×	`add-cube-cbrt_binary64`
19×	`*-un-lft-identity_binary64`

Counts

3 → 102

Calls

3 calls:

11.0ms

(*.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (*.f64 (*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))))

7.0ms

(*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))))

1.0ms

(cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))

simplify183.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

624×	`fma-def_binary64`
461×	`fma-neg_binary64`
345×	`*-commutative_binary64`
207×	`cancel-sign-sub-inv_binary64`
180×	`times-frac_binary64`

Counts

138 → 221

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	245	3931
1	579	3676
2	1666	3000
3	4454	2936
4	4956	2936

prune763.0ms (20.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	553	1	554
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	554	7	561

Error

0.0b

Counts

561 → 7

Alt Table

Status	Error	Program
▶	1.8b	(.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (fma.f64 841/108 x 4/29)))))
	17.1b	(*.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) (sqrt.f64 (fma.f64 841/108 x 4/29)))
	46.0b	(.f64 (cbrt.f64 (.f64 (*.f64 x x) 707281/11664)) (cbrt.f64 (fma.f64 841/108 x 4/29)))
	18.1b	(.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)))) (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))))) (cbrt.f64 (fma.f64 841/108 x 4/29)))
	2.1b	(.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (*.f64 (expm1.f64 (log1p.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29)))) 6))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))))) (cbrt.f64 (fma.f64 841/108 x 4/29)))
✓	1.8b	(.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))))) (cbrt.f64 (fma.f64 841/108 x 4/29)))
✓	0.1b	(fma.f64 841/108 x 4/29)

Compiler

Compiled 23625 to 20149 computations (14.7% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (fma.f64 841/108 x 4/29)))))
	0.7b	(*.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29)))
✓	0.8b	(cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (fma.f64 841/108 x 4/29))))
	0.8b	(cbrt.f64 (fma.f64 841/108 x 4/29))

series8.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

6.0ms

(cbrt.f64 (*.f64 (*.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (fma.f64 841/108 x 4/29))))

2.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (*.f64 (*.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (fma.f64 841/108 x 4/29)))))

rewrite14.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-exp-log_binary64`
7×	`pow1_binary64`
5×	`pow-prod-down_binary64`
4×	`associate-r_binary64`
4×	`add-sqr-sqrt_binary64`

Counts

2 → 35

Calls

2 calls:

7.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (*.f64 (*.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (fma.f64 841/108 x 4/29)))))

6.0ms

(cbrt.f64 (*.f64 (*.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (fma.f64 841/108 x 4/29))))

simplify75.0ms (2%)

Algorithm

1×	egg-herbie

Rules

656×	`fma-neg_binary64`
506×	`times-frac_binary64`
301×	`cancel-sign-sub-inv_binary64`
283×	`distribute-rgt-in_binary64`
238×	`associate-l_binary64`

Counts

59 → 85

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	107	998
1	245	928
2	649	834
3	2035	705
4	4820	701
5	5142	701

prune586.0ms (15.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	492	0	492
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	492	7	499

Error

0.0b

Counts

499 → 7

Alt Table

Status	Error	Program
✓	1.8b	(.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (fma.f64 841/108 x 4/29)))))
	17.1b	(*.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) (sqrt.f64 (fma.f64 841/108 x 4/29)))
	46.0b	(.f64 (cbrt.f64 (.f64 (*.f64 x x) 707281/11664)) (cbrt.f64 (fma.f64 841/108 x 4/29)))
	18.1b	(.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)))) (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))))) (cbrt.f64 (fma.f64 841/108 x 4/29)))
	2.1b	(.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (*.f64 (expm1.f64 (log1p.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29)))) 6))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))))) (cbrt.f64 (fma.f64 841/108 x 4/29)))
✓	1.8b	(.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))))) (cbrt.f64 (fma.f64 841/108 x 4/29)))
✓	0.1b	(fma.f64 841/108 x 4/29)

Compiler

Compiled 19123 to 16147 computations (15.6% saved)

regimes448.0ms (11.9%)

Accuracy

Total 0.0b remaining (37.5%)

Threshold costs 0.0b (37.5%)

Counts

118 → 1

Compiler

Compiled 7988 to 6788 computations (15% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	5
1	5	5

end146.0ms (3.9%)

Compiler: Compiled 169 to 142 computations (16% saved)

Details

analyze6.0ms (0.2%)

sample890.0ms (23.7%)

simplify35.0ms (0.9%)

prune2.0ms (0.1%)

localize3.0ms (0.1%)

series2.0ms (0%)

rewrite1.0ms (0%)

simplify108.0ms (2.9%)

prune10.0ms (0.3%)

localize6.0ms (0.2%)

series15.0ms (0.4%)

rewrite16.0ms (0.4%)

simplify106.0ms (2.8%)

prune262.0ms (7%)

localize9.0ms (0.2%)

series20.0ms (0.5%)

rewrite27.0ms (0.7%)

simplify183.0ms (4.9%)

prune763.0ms (20.3%)

localize8.0ms (0.2%)

series8.0ms (0.2%)

rewrite14.0ms (0.4%)

simplify75.0ms (2%)

prune586.0ms (15.6%)

regimes448.0ms (11.9%)

simplify2.0ms (0%)

end146.0ms (3.9%)

Profiling