Details

analyze2.8s (32%)

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)

sample3.0s (34.1%)

Results

1.8s	8256×	body	128	valid
1.1s	5205×	body	128	invalid

Compiler

Compiled 122 to 89 computations (27% saved)

simplify49.0ms (0.6%)

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

3.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	3.2b	(/.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)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 z (sqrt.f64 (+.f64 t a)))
✓	0.4b	(/.f64 2/3 t)
✓	1.4b	(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))
✓	7.3b	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

series109.0ms (1.2%)

Counts

4 → 88

Calls

4 calls:

54.0ms	(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))
30.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
23.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
1.0ms	(/.f64 2/3 t)

rewrite16.0ms (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:

5.0ms	(*.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))

simplify129.0ms (1.5%)

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

prune224.0ms (2.6%)

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
	22.0b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 b (-.f64 (/.f64 2/3 t) (+.f64 a 5/6)))) x))
▶	14.7b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (+.f64 (.f64 c (+.f64 a 5/6)) (fma.f64 (/.f64 z t) (sqrt.f64 (+.f64 t a)) (.f64 (/.f64 c t) -2/3)))) x))
✓	3.2b	(/.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 6965 to 3517 computations (49.5% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 c (+.f64 a 5/6))
✓	0.3b	(*.f64 (/.f64 c t) -2/3)
✓	0.5b	(+.f64 (.f64 c (+.f64 a 5/6)) (fma.f64 (/.f64 z t) (sqrt.f64 (+.f64 t a)) (.f64 (/.f64 c t) -2/3)))
✓	3.5b	(fma.f64 (/.f64 z t) (sqrt.f64 (+.f64 t a)) (*.f64 (/.f64 c t) -2/3))

series87.0ms (1%)

Counts

4 → 116

Calls

4 calls:

40.0ms	(fma.f64 (/.f64 z t) (sqrt.f64 (+.f64 t a)) (*.f64 (/.f64 c t) -2/3))
36.0ms	(+.f64 (.f64 c (+.f64 a 5/6)) (fma.f64 (/.f64 z t) (sqrt.f64 (+.f64 t a)) (.f64 (/.f64 c t) -2/3)))
6.0ms	(*.f64 (/.f64 c t) -2/3)
4.0ms	(*.f64 c (+.f64 a 5/6))

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
16×	`associate-l_binary64`
16×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`
11×	`add-cbrt-cube_binary64`

Counts

4 → 86

Calls

4 calls:

6.0ms	(+.f64 (.f64 c (+.f64 a 5/6)) (fma.f64 (/.f64 z t) (sqrt.f64 (+.f64 t a)) (.f64 (/.f64 c t) -2/3)))
4.0ms	(*.f64 (/.f64 c t) -2/3)
4.0ms	(*.f64 c (+.f64 a 5/6))
0.0ms	(fma.f64 (/.f64 z t) (sqrt.f64 (+.f64 t a)) (*.f64 (/.f64 c t) -2/3))

simplify85.0ms (1%)

Algorithm

1×	egg-herbie

Rules

589×	`distribute-rgt-in_binary64`
572×	`distribute-lft-in_binary64`
463×	`cancel-sign-sub-inv_binary64`
211×	`fma-neg_binary64`
200×	`times-frac_binary64`

Counts

202 → 177

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	254	3520
1	683	3375
2	2120	3371
3	4982	3371

prune178.0ms (2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	177	0	177
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	177	3	180

Error

Counts

180 → 3

Alt Table

Status	Error	Program
▶	22.0b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 b (-.f64 (/.f64 2/3 t) (+.f64 a 5/6)))) x))
✓	14.7b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (+.f64 (.f64 c (+.f64 a 5/6)) (fma.f64 (/.f64 z t) (sqrt.f64 (+.f64 t a)) (.f64 (/.f64 c t) -2/3)))) x))
✓	3.2b	(/.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 6391 to 3217 computations (49.7% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (exp.f64 2) (*.f64 b (-.f64 (/.f64 2/3 t) (+.f64 a 5/6))))
✓	0.0b	(+.f64 a 5/6)
	0.4b	(/.f64 2/3 t)
✓	0.4b	(*.f64 b (-.f64 (/.f64 2/3 t) (+.f64 a 5/6)))

series32.0ms (0.4%)

Counts

3 → 84

Calls

3 calls:

17.0ms	(pow.f64 (exp.f64 2) (*.f64 b (-.f64 (/.f64 2/3 t) (+.f64 a 5/6))))
13.0ms	(*.f64 b (-.f64 (/.f64 2/3 t) (+.f64 a 5/6)))
1.0ms	(+.f64 a 5/6)

rewrite73.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

296×	`*-un-lft-identity_binary64`
208×	`prod-diff_binary64`
183×	`add-sqr-sqrt_binary64`
176×	`add-cube-cbrt_binary64`
145×	`times-frac_binary64`

Counts

3 → 294

Calls

3 calls:

15.0ms	(*.f64 b (-.f64 (/.f64 2/3 t) (+.f64 a 5/6)))
11.0ms	(pow.f64 (exp.f64 2) (*.f64 b (-.f64 (/.f64 2/3 t) (+.f64 a 5/6))))
2.0ms	(+.f64 a 5/6)

simplify258.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

495×	`times-frac_binary64`
343×	`fma-neg_binary64`
299×	`associate-r_binary64`
238×	`associate-l_binary64`
217×	`*-commutative_binary64`

Counts

378 → 327

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	511	11248
1	917	9949
2	3336	8408
3	4874	8408
4	4941	8408

prune432.0ms (4.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	360	0	360
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	360	3	363

Error

Counts

363 → 3

Alt Table

Status	Error	Program
✓	22.0b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 b (-.f64 (/.f64 2/3 t) (+.f64 a 5/6)))) x))
✓	14.7b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (+.f64 (.f64 c (+.f64 a 5/6)) (fma.f64 (/.f64 z t) (sqrt.f64 (+.f64 t a)) (.f64 (/.f64 c t) -2/3)))) x))
✓	3.2b	(/.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 14231 to 10191 computations (28.4% saved)

regimes1.1s (12.6%)

Accuracy

Total 1.6b remaining (85.1%)

Threshold costs 0b (0%)

Counts

75 → 2

Compiler

Compiled 28117 to 20454 computations (27.3% saved)

bsearch18.0ms (0.2%)

Steps

Iters	Range		Point
2	7.968626149891842e-302	4.745879403359511e-301	3.04319920050061e-301

Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	80
1	44	80
2	54	80
3	58	80
4	60	80
5	58	80

end94.0ms (1.1%)

Compiler: Compiled 214 to 144 computations (32.7% saved)

Details

analyze2.8s (32%)

sample3.0s (34.1%)

simplify49.0ms (0.6%)

prune4.0ms (0.1%)

localize24.0ms (0.3%)

series109.0ms (1.2%)

rewrite16.0ms (0.2%)

simplify129.0ms (1.5%)

prune224.0ms (2.6%)

localize20.0ms (0.2%)

series87.0ms (1%)

rewrite18.0ms (0.2%)

simplify85.0ms (1%)

prune178.0ms (2%)

localize14.0ms (0.2%)

series32.0ms (0.4%)

rewrite73.0ms (0.8%)

simplify258.0ms (2.9%)

prune432.0ms (4.9%)

regimes1.1s (12.6%)

bsearch18.0ms (0.2%)

simplify4.0ms (0%)

end94.0ms (1.1%)

Profiling