Details

analyze2.5s (27.1%)

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)

sample3.1s (33.7%)

Results

1.9s	8256×	body	128	valid
1.1s	5218×	body	128	invalid

Compiler

Compiled 122 to 89 computations (27% saved)

simplify48.0ms (0.5%)

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%)

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

3.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	3.1b	(/.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)

localize21.0ms (0.2%)

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)
✓	1.9b	(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))
✓	4.9b	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

series136.0ms (1.5%)

Counts

4 → 88

Calls

4 calls:

62.0ms	(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))
43.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
29.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
1.0ms	(/.f64 2/3 t)

rewrite19.0ms (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 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
6.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
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))

simplify179.0ms (2%)

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

prune221.0ms (2.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	186	3	189
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	187	3	190

Error

Counts

190 → 3

Alt Table

Status	Error	Program
	18.7b	(/.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 (sqrt.f64 (/.f64 1 t)) z))) x))
▶	2.4b	(/.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 t) (sqrt.f64 (+.f64 a t))))) x))
	19.1b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 c (+.f64 a 5/6) (*.f64 b (-.f64 -5/6 a)))) x))

Compiler

Compiled 6997 to 3540 computations (49.4% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 a 5/6)
	0.3b	(/.f64 2/3 t)
✓	1.9b	(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (/.f64 z t) (sqrt.f64 (+.f64 a t))))
✓	6.8b	(*.f64 (/.f64 z t) (sqrt.f64 (+.f64 a t)))

series103.0ms (1.1%)

Counts

3 → 68

Calls

3 calls:

62.0ms	(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (/.f64 z t) (sqrt.f64 (+.f64 a t))))
40.0ms	(*.f64 (/.f64 z t) (sqrt.f64 (+.f64 a t)))
1.0ms	(+.f64 a 5/6)

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`
13×	`associate-l_binary64`
13×	`add-cube-cbrt_binary64`
11×	`times-frac_binary64`

Counts

3 → 71

Calls

3 calls:

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

simplify103.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

335×	`cancel-sign-sub-inv_binary64`
281×	`distribute-rgt-in_binary64`
273×	`fma-neg_binary64`
264×	`sub-neg_binary64`
243×	`distribute-lft-in_binary64`

Counts

139 → 148

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	276	3485
1	778	3325
2	2400	3306
3	4709	3303
4	5047	3303

prune235.0ms (2.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	180	1	181
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	181	3	184

Error

Counts

184 → 3

Alt Table

Status	Error	Program
✓	2.4b	(/.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 t) (sqrt.f64 (+.f64 a t))))) x))
▶	18.6b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b))) x))
	18.7b	(/.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 (sqrt.f64 (/.f64 1 t)) z))) x))

Compiler

Compiled 6585 to 3222 computations (51.1% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y (pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b))) x)
	0.0b	(+.f64 a 5/6)
✓	0.0b	(pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b)))
✓	0.1b	(*.f64 (+.f64 a 5/6) (-.f64 c b))

series156.0ms (1.7%)

Counts

3 → 132

Calls

3 calls:

131.0ms	(fma.f64 y (pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b))) x)
17.0ms	(pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b)))
8.0ms	(*.f64 (+.f64 a 5/6) (-.f64 c b))

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`*-un-lft-identity_binary64`
39×	`add-sqr-sqrt_binary64`
36×	`prod-diff_binary64`
35×	`add-cube-cbrt_binary64`
26×	`unpow-prod-up_binary64`

Counts

3 → 114

Calls

3 calls:

7.0ms	(*.f64 (+.f64 a 5/6) (-.f64 c b))
6.0ms	(pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b)))
0.0ms	(fma.f64 y (pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b))) x)

simplify157.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

546×	`fma-def_binary64`
508×	`*-commutative_binary64`
305×	`associate-+r+_binary64`
262×	`+-commutative_binary64`
215×	`unswap-sqr_binary64`

Counts

246 → 228

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	535	7010
1	1512	6461
2	4154	6269
3	5227	6269

prune259.0ms (2.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	250	0	250
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	250	3	253

Error

Counts

253 → 3

Alt Table

Status	Error	Program
✓	2.4b	(/.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 t) (sqrt.f64 (+.f64 a t))))) x))
✓	18.6b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b))) x))
▶	18.7b	(/.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 (sqrt.f64 (/.f64 1 t)) z))) x))

Compiler

Compiled 8989 to 5238 computations (41.7% 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))

series64.0ms (0.7%)

Counts

3 → 51

Calls

3 calls:

46.0ms	(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))

rewrite12.0ms (0.1%)

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:

6.0ms	(*.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))

simplify84.0ms (0.9%)

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

prune169.0ms (1.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	152	3	155

Error

Counts

155 → 3

Alt Table

Status	Error	Program
✓	2.4b	(/.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 t) (sqrt.f64 (+.f64 a t))))) x))
✓	18.6b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b))) x))
✓	18.7b	(/.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 (sqrt.f64 (/.f64 1 t)) z))) x))

Compiler

Compiled 4725 to 2957 computations (37.4% saved)

regimes1.3s (14.5%)

Accuracy

Total 1.7b remaining (86.7%)

Threshold costs 0b (0%)

Counts

79 → 3

Compiler

Compiled 27283 to 19862 computations (27.2% saved)

bsearch82.0ms (0.9%)

Steps

Iters	Range		Point
4	2.1972429134161038e-302	6.34050944584029e-290	2.9706712496914734e-292
4	-5.878789380006067e-118	-1.6351368805099344e-128	-1.2797425918545752e-118

Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
8×	`sub-neg_binary64`
7×	`*-commutative_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	117
1	62	117
2	78	117
3	86	117
4	90	117
5	89	117

end128.0ms (1.4%)

Compiler: Compiled 262 to 174 computations (33.6% saved)

Details

analyze2.5s (27.1%)

sample3.1s (33.7%)

simplify48.0ms (0.5%)

prune4.0ms (0%)

localize21.0ms (0.2%)

series136.0ms (1.5%)

rewrite19.0ms (0.2%)

simplify179.0ms (2%)

prune221.0ms (2.4%)

localize20.0ms (0.2%)

series103.0ms (1.1%)

rewrite14.0ms (0.2%)

simplify103.0ms (1.1%)

prune235.0ms (2.6%)

localize13.0ms (0.1%)

series156.0ms (1.7%)

rewrite22.0ms (0.2%)

simplify157.0ms (1.7%)

prune259.0ms (2.8%)

localize18.0ms (0.2%)

series64.0ms (0.7%)

rewrite12.0ms (0.1%)

simplify84.0ms (0.9%)

prune169.0ms (1.8%)

regimes1.3s (14.5%)

bsearch82.0ms (0.9%)

simplify6.0ms (0.1%)

end128.0ms (1.4%)

Profiling