Details

analyze3.6s (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)

sample153.0ms (1.2%)

Algorithm

1×

intervals

Results

64.0ms	256×	body	128	valid
34.0ms	141×	body	128	nan

Compiler

Compiled 88 to 66 computations (25% saved)

simplify61.0ms (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

prune9.0ms (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)

localize43.0ms (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)
✓	1.3b	(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))
✓	2.7b	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

series285.0ms (2.1%)

Counts

4 → 88

Calls

4 calls:

133.0ms	(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))
82.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
66.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
3.0ms	(/.f64 2/3 t)

rewrite37.0ms (0.3%)

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:

12.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
12.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
4.0ms	(/.f64 2/3 t)
1.0ms	(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))

simplify180.0ms (1.4%)

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

prune246.0ms (1.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	187	2	189
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	188	2	190

Error

Counts

190 → 2

Alt Table

Status	Error	Program
▶	1.2b	(/.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 t) (sqrt.f64 (+.f64 a t))))) x))
	22.8b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)))) x))

Status

Error

Program

▶

1.2b

(/.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 t) (sqrt.f64 (+.f64 a t))))) x))

22.8b

(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)))) x))

Compiler

Compiled 6931 to 3494 computations (49.6% saved)

localize40.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 a 5/6) (/.f64 2/3 t))
	0.3b	(/.f64 2/3 t)
✓	1.3b	(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (/.f64 z t) (sqrt.f64 (+.f64 a t))))
✓	5.8b	(*.f64 (/.f64 z t) (sqrt.f64 (+.f64 a t)))

series185.0ms (1.4%)

Counts

3 → 80

Calls

3 calls:

92.0ms	(*.f64 (/.f64 z t) (sqrt.f64 (+.f64 a t)))
86.0ms	(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (/.f64 z t) (sqrt.f64 (+.f64 a t))))
5.0ms	(-.f64 (+.f64 a 5/6) (/.f64 2/3 t))

rewrite31.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

96×	`*-un-lft-identity_binary64`
76×	`add-sqr-sqrt_binary64`
61×	`add-cube-cbrt_binary64`
57×	`times-frac_binary64`
52×	`prod-diff_binary64`

Counts

3 → 144

Calls

3 calls:

11.0ms	(-.f64 (+.f64 a 5/6) (/.f64 2/3 t))
8.0ms	(*.f64 (/.f64 z t) (sqrt.f64 (+.f64 a t)))
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))))

simplify197.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

464×	`cancel-sign-sub-inv_binary64`
321×	`sub-neg_binary64`
288×	`fma-def_binary64`
268×	`fma-neg_binary64`
234×	`times-frac_binary64`

Counts

224 → 222

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	438	5625
1	1180	4819
2	3524	4470
3	4855	4470

prune509.0ms (3.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	255	0	255
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	255	2	257

Error

Counts

257 → 2

Alt Table

Status	Error	Program
✓	1.2b	(/.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 t) (sqrt.f64 (+.f64 a t))))) x))
▶	22.8b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)))) x))

Status

Error

Program

✓

1.2b

(/.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 t) (sqrt.f64 (+.f64 a t))))) x))

▶

22.8b

(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)))) x))

Compiler

Compiled 10309 to 5310 computations (48.5% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (+.f64 a 5/6) (/.f64 2/3 t))
✓	0.0b	(pow.f64 (exp.f64 2) (*.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
✓	0.2b	(*.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)))
	0.3b	(/.f64 2/3 t)

series73.0ms (0.5%)

Counts

2 → 72

Calls

2 calls:

40.0ms	(pow.f64 (exp.f64 2) (*.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
33.0ms	(*.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)))

rewrite162.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

308×	`*-un-lft-identity_binary64`
208×	`prod-diff_binary64`
205×	`add-sqr-sqrt_binary64`
198×	`add-cube-cbrt_binary64`
181×	`times-frac_binary64`

Counts

2 → 317

Calls

2 calls:

27.0ms	(pow.f64 (exp.f64 2) (*.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
22.0ms	(*.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)))

simplify339.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

637×	`times-frac_binary64`
366×	`associate-r_binary64`
316×	`*-commutative_binary64`
313×	`associate-l_binary64`
218×	`associate-/l*_binary64`

Counts

389 → 341

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	626	16791
1	1333	10690
2	3914	10453
3	5028	10453

prune1.1s (8.2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	470	0	470
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	470	2	472

Error

Counts

472 → 2

Alt Table

Status	Error	Program
✓	1.2b	(/.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 t) (sqrt.f64 (+.f64 a t))))) x))
✓	22.8b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)))) x))

Status

Error

Program

✓

1.2b

(/.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 t) (sqrt.f64 (+.f64 a t))))) x))

✓

22.8b

(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)))) x))

Compiler

Compiled 18702 to 12984 computations (30.6% saved)

regimes1.6s (12.2%)

Accuracy

Total 1.4b remaining (77.4%)

Threshold costs 0b (0%)

Counts

59 → 1

Compiler

Compiled 21501 to 15639 computations (27.3% saved)

simplify6.0ms (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

end2.0ms (0%)

Compiler: Compiled 34 to 23 computations (32.4% saved)

sample4.4s (33.1%)

Algorithm

1×

intervals

Results

1.9s	8000×	body	128	valid
1.2s	5118×	body	128	nan

Compiler

Compiled 140 to 101 computations (27.9% saved)

Details

analyze3.6s (27.1%)

sample153.0ms (1.2%)

simplify61.0ms (0.5%)

prune9.0ms (0.1%)

localize43.0ms (0.3%)

series285.0ms (2.1%)

rewrite37.0ms (0.3%)

simplify180.0ms (1.4%)

prune246.0ms (1.8%)

localize40.0ms (0.3%)

series185.0ms (1.4%)

rewrite31.0ms (0.2%)

simplify197.0ms (1.5%)

prune509.0ms (3.8%)

localize27.0ms (0.2%)

series73.0ms (0.5%)

rewrite162.0ms (1.2%)

simplify339.0ms (2.6%)

prune1.1s (8.2%)

regimes1.6s (12.2%)

simplify6.0ms (0%)

end2.0ms (0%)

sample4.4s (33.1%)

Profiling