Details

analyze2.3s (26.6%)

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)

sample75.0ms (0.9%)

Algorithm

1×

intervals

Results

30.0ms	256×	body	128	valid
22.0ms	171×	body	128	nan

Compiler

Compiled 88 to 66 computations (25% saved)

simplify54.0ms (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

prune5.0ms (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

1.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.9b	(/.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)

localize22.0ms (0.2%)

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)
✓	1.1b	(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))
✓	5.6b	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

series149.0ms (1.7%)

Counts

4 → 88

Calls

4 calls:

66.0ms	(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))
47.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
34.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
1.0ms	(/.f64 2/3 t)

rewrite17.0ms (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 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
5.0ms	(*.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))

simplify137.0ms (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

prune218.0ms (2.5%)

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

0.0b

Counts

190 → 3

Alt Table

Status	Error	Program
	21.6b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)))) x))
▶	19.2b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 c (+.f64 a 5/6) (*.f64 b (-.f64 -5/6 a)))) x))
✓	1.9b	(/.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 6947 to 3507 computations (49.5% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 a 5/6)
✓	0.0b	(-.f64 -5/6 a)
✓	0.2b	(*.f64 b (-.f64 -5/6 a))
✓	0.6b	(fma.f64 c (+.f64 a 5/6) (*.f64 b (-.f64 -5/6 a)))

series20.0ms (0.2%)

Counts

4 → 84

Calls

4 calls:

12.0ms	(fma.f64 c (+.f64 a 5/6) (*.f64 b (-.f64 -5/6 a)))
5.0ms	(*.f64 b (-.f64 -5/6 a))
1.0ms	(-.f64 -5/6 a)
1.0ms	(+.f64 a 5/6)

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`*-un-lft-identity_binary64`
35×	`add-sqr-sqrt_binary64`
29×	`add-cube-cbrt_binary64`
27×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

4 → 107

Calls

4 calls:

6.0ms	(*.f64 b (-.f64 -5/6 a))
3.0ms	(-.f64 -5/6 a)
2.0ms	(+.f64 a 5/6)
0.0ms	(fma.f64 c (+.f64 a 5/6) (*.f64 b (-.f64 -5/6 a)))

simplify118.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

521×	`distribute-rgt-neg-out_binary64`
497×	`fma-neg_binary64`
472×	`fma-def_binary64`
383×	`unsub-neg_binary64`
330×	`distribute-rgt-in_binary64`

Counts

191 → 153

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	181	2022
1	314	1597
2	1014	1516
3	3017	1435
4	4714	1435
5	4972	1435
6	4778	1435

prune214.0ms (2.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	153	3	156

Error

0.0b

Counts

156 → 3

Alt Table

Status	Error	Program
▶	21.6b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)))) x))
✓	19.2b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 c (+.f64 a 5/6) (*.f64 b (-.f64 -5/6 a)))) x))
✓	1.9b	(/.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 3993 to 2302 computations (42.3% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (exp.f64 2) (*.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
✓	0.0b	(-.f64 (+.f64 a 5/6) (/.f64 2/3 t))
✓	0.1b	(*.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)))
	0.4b	(/.f64 2/3 t)

series43.0ms (0.5%)

Counts

3 → 96

Calls

3 calls:

20.0ms	(pow.f64 (exp.f64 2) (*.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
18.0ms	(*.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)))
5.0ms	(-.f64 (+.f64 a 5/6) (/.f64 2/3 t))

rewrite104.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

391×	`*-un-lft-identity_binary64`
260×	`prod-diff_binary64`
260×	`add-sqr-sqrt_binary64`
248×	`add-cube-cbrt_binary64`
227×	`times-frac_binary64`

Counts

3 → 407

Calls

3 calls:

15.0ms	(*.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)))
13.0ms	(pow.f64 (exp.f64 2) (*.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
9.0ms	(-.f64 (+.f64 a 5/6) (/.f64 2/3 t))

simplify340.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

625×	`times-frac_binary64`
373×	`associate-r_binary64`
326×	`associate-l_binary64`
231×	`fma-def_binary64`
221×	`associate-/l*_binary64`

Counts

503 → 444

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	645	20111
1	1370	12492
2	4121	12201
3	5342	12201

prune623.0ms (7.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	477	0	477
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	477	3	480

Error

0.0b

Counts

480 → 3

Alt Table

Status	Error	Program
✓	21.6b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 c (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)))) x))
✓	19.2b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 c (+.f64 a 5/6) (*.f64 b (-.f64 -5/6 a)))) x))
✓	1.9b	(/.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 18911 to 13130 computations (30.6% saved)

regimes1.3s (15.4%)

Accuracy

Total 1.9b remaining (93.9%)

Threshold costs 0b (0%)

Counts

83 → 1

Compiler

Compiled 28984 to 21380 computations (26.2% saved)

simplify4.0ms (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

end1.0ms (0%)

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

sample2.9s (32.9%)

Algorithm

1×

intervals

Results

1.2s	8000×	body	128	valid
902.0ms	5186×	body	128	nan

Compiler

Compiled 165 to 119 computations (27.9% saved)

Details

analyze2.3s (26.6%)

sample75.0ms (0.9%)

simplify54.0ms (0.6%)

prune5.0ms (0.1%)

localize22.0ms (0.2%)

series149.0ms (1.7%)

rewrite17.0ms (0.2%)

simplify137.0ms (1.6%)

prune218.0ms (2.5%)

localize13.0ms (0.1%)

series20.0ms (0.2%)

rewrite17.0ms (0.2%)

simplify118.0ms (1.4%)

prune214.0ms (2.5%)

localize13.0ms (0.1%)

series43.0ms (0.5%)

rewrite104.0ms (1.2%)

simplify340.0ms (3.9%)

prune623.0ms (7.2%)

regimes1.3s (15.4%)

simplify4.0ms (0%)

end1.0ms (0%)

sample2.9s (32.9%)

Profiling