Details

analyze2.3s (30.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
3.1%	96.5%	0.3%	9
4.7%	95%	0.3%	10
4.7%	95%	0.3%	11
5.1%	82.1%	12.8%	12
6.2%	74.7%	19%	13
6.4%	74.5%	19%	14

Compiler

Compiled 41 to 30 computations (26.8% saved)

sample2.9s (37.8%)

Results

1.7s	8256×	body	128	valid
1.0s	5214×	body	128	invalid

Compiler

Compiled 122 to 89 computations (27% saved)

simplify66.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

829×	`fma-neg_binary64`
433×	`exp-sum_binary64`
321×	`distribute-rgt-in_binary64`
303×	`distribute-lft-in_binary64`
279×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	30	47
1	55	42
2	136	40
3	512	40
4	2106	40
5	4520	40
6	4992	40

prune4.0ms (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

1.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.7b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))) x))

Compiler

Compiled 135 to 87 computations (35.6% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 z (sqrt.f64 (+.f64 t a)))
✓	0.3b	(/.f64 2/3 t)
✓	1.1b	(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))
✓	6.4b	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

series136.0ms (1.8%)

Counts

4 → 88

Calls

4 calls:

61.0ms	(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))
41.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
30.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
4.0ms	(/.f64 2/3 t)

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
13×	`add-cbrt-cube_binary64`
13×	`add-exp-log_binary64`

Counts

4 → 91

Calls

4 calls:

7.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
5.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
2.0ms	(/.f64 2/3 t)
0.0ms	(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))

simplify124.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

801×	`times-frac_binary64`
430×	`cancel-sign-sub-inv_binary64`
324×	`fma-neg_binary64`
272×	`sub-neg_binary64`
270×	`fma-def_binary64`

Counts

179 → 189

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	321	4150
1	864	3932
2	2992	3925
3	4865	3924
4	4956	3924

prune220.0ms (2.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	187	2	189
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	187	3	190

Error

Counts

190 → 3

Alt Table

Status	Error	Program
✓	1.7b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))) x))
	17.9b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 c (+.f64 a 5/6) (*.f64 b (-.f64 -5/6 a)))) x))
▶	15.0b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (sqrt.f64 (/.f64 1 t)) z))) x))

Compiler

Compiled 6963 to 3517 computations (49.5% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (/.f64 1 t))
✓	0.2b	(*.f64 (sqrt.f64 (/.f64 1 t)) z)
	0.3b	(/.f64 2/3 t)
✓	0.6b	(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (sqrt.f64 (/.f64 1 t)) z))

series69.0ms (0.9%)

Counts

3 → 51

Calls

3 calls:

51.0ms	(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (sqrt.f64 (/.f64 1 t)) z))
13.0ms	(*.f64 (sqrt.f64 (/.f64 1 t)) z)
5.0ms	(sqrt.f64 (/.f64 1 t))

rewrite64.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64`
29×	`sqrt-prod_binary64`
22×	`times-frac_binary64`
21×	`*-un-lft-identity_binary64`
19×	`add-cube-cbrt_binary64`

Counts

3 → 77

Calls

3 calls:

58.0ms	(*.f64 (sqrt.f64 (/.f64 1 t)) z)
2.0ms	(sqrt.f64 (/.f64 1 t))
0.0ms	(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (sqrt.f64 (/.f64 1 t)) z))

simplify90.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

659×	`distribute-rgt-in_binary64`
617×	`distribute-lft-in_binary64`
462×	`fma-neg_binary64`
279×	`sub-neg_binary64`
268×	`fma-def_binary64`

Counts

128 → 119

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	132	2796
1	292	2685
2	862	2514
3	2230	2438
4	5267	2438

prune201.0ms (2.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	151	1	152
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	152	3	155

Error

Counts

155 → 3

Alt Table

Status	Error	Program
✓	1.7b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))) x))
▶	11.1b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 c (+.f64 5/6 a) (fma.f64 (/.f64 2/3 t) (-.f64 b c) (*.f64 b (-.f64 -5/6 a))))) x))
✓	15.0b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (sqrt.f64 (/.f64 1 t)) z))) x))

Compiler

Compiled 4767 to 2985 computations (37.4% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 b (-.f64 -5/6 a))
	0.3b	(/.f64 2/3 t)
✓	0.8b	(fma.f64 (/.f64 2/3 t) (-.f64 b c) (*.f64 b (-.f64 -5/6 a)))
✓	2.0b	(fma.f64 c (+.f64 5/6 a) (fma.f64 (/.f64 2/3 t) (-.f64 b c) (*.f64 b (-.f64 -5/6 a))))

series56.0ms (0.7%)

Counts

3 → 120

Calls

3 calls:

29.0ms	(fma.f64 c (+.f64 5/6 a) (fma.f64 (/.f64 2/3 t) (-.f64 b c) (*.f64 b (-.f64 -5/6 a))))
22.0ms	(fma.f64 (/.f64 2/3 t) (-.f64 b c) (*.f64 b (-.f64 -5/6 a)))
5.0ms	(*.f64 b (-.f64 -5/6 a))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64`
19×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

3 → 70

Calls

3 calls:

5.0ms	(*.f64 b (-.f64 -5/6 a))
0.0ms	(fma.f64 c (+.f64 5/6 a) (fma.f64 (/.f64 2/3 t) (-.f64 b c) (*.f64 b (-.f64 -5/6 a))))
0.0ms	(fma.f64 (/.f64 2/3 t) (-.f64 b c) (*.f64 b (-.f64 -5/6 a)))

simplify153.0ms (2%)

Algorithm

1×	egg-herbie

Rules

787×	`fma-neg_binary64`
636×	`fma-def_binary64`
294×	`distribute-rgt-in_binary64`
288×	`exp-prod_binary64`
273×	`distribute-lft-in_binary64`

Counts

190 → 125

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	191	3737
1	365	3325
2	1168	2773
3	3240	2773
4	4882	2773
5	4911	2773

prune172.0ms (2.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	158	3	161

Error

Counts

161 → 3

Alt Table

Status	Error	Program
✓	1.7b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))) x))
✓	11.1b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 c (+.f64 5/6 a) (fma.f64 (/.f64 2/3 t) (-.f64 b c) (*.f64 b (-.f64 -5/6 a))))) x))
✓	15.0b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (sqrt.f64 (/.f64 1 t)) z))) x))

Compiler

Compiled 5070 to 2848 computations (43.8% saved)

regimes859.0ms (11.4%)

Accuracy

Total 1.7b remaining (98%)

Threshold costs 0b (0%)

Counts

49 → 1

Compiler

Compiled 18203 to 13119 computations (27.9% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
4×	`sub-neg_binary64`
3×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	40
1	31	40
2	42	40
3	46	40
4	48	40
5	47	40

end90.0ms (1.2%)

Compiler: Compiled 166 to 114 computations (31.3% saved)

Details

analyze2.3s (30.5%)

sample2.9s (37.8%)

simplify66.0ms (0.9%)

prune4.0ms (0.1%)

localize20.0ms (0.3%)

series136.0ms (1.8%)

rewrite18.0ms (0.2%)

simplify124.0ms (1.6%)

prune220.0ms (2.9%)

localize18.0ms (0.2%)

series69.0ms (0.9%)

rewrite64.0ms (0.8%)

simplify90.0ms (1.2%)

prune201.0ms (2.7%)

localize18.0ms (0.2%)

series56.0ms (0.7%)

rewrite10.0ms (0.1%)

simplify153.0ms (2%)

prune172.0ms (2.3%)

regimes859.0ms (11.4%)

simplify3.0ms (0%)

end90.0ms (1.2%)

Profiling