Details

analyze1.0s (12.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
3.1%	96.7%	0.2%	7
6.2%	93.6%	0.2%	8
8.6%	91.2%	0.2%	9
28.1%	71.7%	0.2%	10
31%	68.8%	0.2%	11
40.5%	59.3%	0.2%	12
49.6%	50.2%	0.2%	13
59%	40.8%	0.2%	14

Compiler

Compiled 22 to 14 computations (36.4% saved)

sample1.3s (15.1%)

Results

1.1s	8256×	body	128	valid
44.0ms	327×	body	128	invalid

Compiler

Compiled 65 to 41 computations (36.9% saved)

simplify92.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

573×	`neg-mul-1_binary64`
569×	`unsub-neg_binary64`
509×	`times-frac_binary64`
460×	`neg-sub0_binary64`
418×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	28	25
2	45	25
3	84	25
4	185	25
5	383	25
6	1133	25
7	3784	25
8	4245	25
9	4554	25
10	4899	25
11	4864	25

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

7.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	7.4b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))

Compiler

Compiled 80 to 46 computations (42.5% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 y z) x)
✓	0.0b	(+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))
✓	0.3b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
✓	9.6b	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))

series197.0ms (2.3%)

Counts

4 → 153

Calls

4 calls:

83.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
62.0ms	(+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))
46.0ms	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))
5.0ms	(-.f64 (*.f64 y z) x)

rewrite48.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`*-un-lft-identity_binary64`
25×	`times-frac_binary64`
25×	`add-sqr-sqrt_binary64`
25×	`add-cube-cbrt_binary64`
11×	`distribute-lft-out_binary64`

Counts

4 → 115

Calls

4 calls:

21.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
8.0ms	(+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))
7.0ms	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))
3.0ms	(-.f64 (*.f64 y z) x)

simplify153.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

550×	`times-frac_binary64`
420×	`associate-/l*_binary64`
300×	`associate-/r*_binary64`
290×	`associate--l+_binary64`
201×	`fma-def_binary64`

Counts

268 → 300

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	436	10267
1	1359	9717
2	5100	9717

prune324.0ms (3.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	294	6	300
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	295	6	301

Error

0.0b

Counts

301 → 6

Alt Table

Status	Error	Program
	7.4b	(/.f64 (+.f64 x (.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 t z) x)))) (+.f64 x 1))
	7.4b	(-.f64 (+.f64 (/.f64 (.f64 y z) (.f64 (+.f64 1 x) (-.f64 (.f64 t z) x))) (/.f64 x (+.f64 1 x))) (/.f64 x (.f64 (+.f64 1 x) (-.f64 (*.f64 t z) x))))
	7.8b	(/.f64 (+.f64 x (.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 y z) x)) (cbrt.f64 (-.f64 (.f64 y z) x))) (.f64 (cbrt.f64 (-.f64 (.f64 t z) x)) (cbrt.f64 (-.f64 (.f64 t z) x)))) (/.f64 (cbrt.f64 (-.f64 (.f64 y z) x)) (cbrt.f64 (-.f64 (*.f64 t z) x))))) (+.f64 x 1))
	19.7b	(/.f64 (+.f64 x (/.f64 y t)) (+.f64 x 1))
▶	2.8b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	33.0b	(/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)) 3)) (.f64 (+.f64 x 1) (+.f64 (.f64 x x) (-.f64 (.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)) (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))))))

Compiler

Compiled 10974 to 4027 computations (63.3% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x (/.f64 x (-.f64 (*.f64 t z) x))) (+.f64 x 1))
✓	0.1b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
✓	1.5b	(/.f64 x (-.f64 (*.f64 t z) x))
✓	8.0b	(/.f64 z (-.f64 (*.f64 t z) x))

series157.0ms (1.9%)

Counts

4 → 156

Calls

4 calls:

84.0ms	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
30.0ms	(/.f64 (-.f64 x (/.f64 x (-.f64 (*.f64 t z) x))) (+.f64 x 1))
22.0ms	(/.f64 z (-.f64 (*.f64 t z) x))
21.0ms	(/.f64 x (-.f64 (*.f64 t z) x))

rewrite30.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`add-sqr-sqrt_binary64`
56×	`*-un-lft-identity_binary64`
47×	`times-frac_binary64`
32×	`add-cube-cbrt_binary64`
12×	`associate-/l*_binary64`

Counts

4 → 125

Calls

4 calls:

12.0ms	(/.f64 (-.f64 x (/.f64 x (-.f64 (*.f64 t z) x))) (+.f64 x 1))
5.0ms	(/.f64 z (-.f64 (*.f64 t z) x))
4.0ms	(/.f64 x (-.f64 (*.f64 t z) x))
0.0ms	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))

simplify146.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

424×	`times-frac_binary64`
336×	`associate-/l*_binary64`
323×	`associate-+r+_binary64`
277×	`associate-/r*_binary64`
249×	`associate-+l+_binary64`

Counts

281 → 312

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	444	9950
1	1287	9517
2	5205	9517

prune362.0ms (4.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	310	2	312
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	313	5	318

Error

0.0b

Counts

318 → 5

Alt Table

Status	Error	Program
	7.4b	(+.f64 (/.f64 (.f64 z y) (.f64 (+.f64 x 1) (-.f64 (.f64 z t) x))) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	7.4b	(/.f64 (+.f64 x (.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 t z) x)))) (+.f64 x 1))
	33.0b	(/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)) 3)) (.f64 (+.f64 x 1) (+.f64 (.f64 x x) (-.f64 (.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)) (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))))))
▶	3.0b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 (.f64 t z) x)) (cbrt.f64 (-.f64 (.f64 t z) x)))) (cbrt.f64 (-.f64 (*.f64 t z) x)))) (+.f64 x 1)))
	19.7b	(/.f64 (+.f64 x (/.f64 y t)) (+.f64 x 1))

Compiler

Compiled 13061 to 4961 computations (62% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(/.f64 x (.f64 (cbrt.f64 (-.f64 (.f64 t z) x)) (cbrt.f64 (-.f64 (*.f64 t z) x))))
✓	0.5b	(.f64 (cbrt.f64 (-.f64 (.f64 t z) x)) (cbrt.f64 (-.f64 (*.f64 t z) x)))
	8.0b	(/.f64 z (-.f64 (*.f64 t z) x))
✓	8.6b	(cbrt.f64 (-.f64 (*.f64 t z) x))

series256.0ms (3.1%)

Counts

3 → 108

Calls

3 calls:

114.0ms	(/.f64 x (.f64 (cbrt.f64 (-.f64 (.f64 t z) x)) (cbrt.f64 (-.f64 (*.f64 t z) x))))
79.0ms	(.f64 (cbrt.f64 (-.f64 (.f64 t z) x)) (cbrt.f64 (-.f64 (*.f64 t z) x)))
62.0ms	(cbrt.f64 (-.f64 (*.f64 t z) x))

rewrite30.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`cbrt-div_binary64`
22×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
14×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`

Counts

3 → 96

Calls

3 calls:

10.0ms	(.f64 (cbrt.f64 (-.f64 (.f64 t z) x)) (cbrt.f64 (-.f64 (*.f64 t z) x)))
9.0ms	(/.f64 x (.f64 (cbrt.f64 (-.f64 (.f64 t z) x)) (cbrt.f64 (-.f64 (*.f64 t z) x))))
3.0ms	(cbrt.f64 (-.f64 (*.f64 t z) x))

simplify143.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

835×	`times-frac_binary64`
609×	`associate-/r*_binary64`
377×	`associate-/l*_binary64`
306×	`fma-def_binary64`
176×	`*-commutative_binary64`

Counts

204 → 264

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	538	9008
1	1710	8395
2	5276	8395

prune601.0ms (7.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	480	1	481
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	480	6	486

Error

Counts

486 → 6

Alt Table

Status	Error	Program
	8.1b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 (/.f64 x (cbrt.f64 (.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 t z) x)))) (cbrt.f64 (-.f64 (*.f64 t z) x)))) (+.f64 x 1)))
▶	7.4b	(+.f64 (/.f64 (.f64 z y) (.f64 (+.f64 x 1) (-.f64 (.f64 z t) x))) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	7.4b	(/.f64 (+.f64 x (.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 t z) x)))) (+.f64 x 1))
	33.0b	(/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)) 3)) (.f64 (+.f64 x 1) (+.f64 (.f64 x x) (-.f64 (.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)) (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))))))
✓	3.0b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 (.f64 t z) x)) (cbrt.f64 (-.f64 (.f64 t z) x)))) (cbrt.f64 (-.f64 (*.f64 t z) x)))) (+.f64 x 1)))
	19.7b	(/.f64 (+.f64 x (/.f64 y t)) (+.f64 x 1))

Compiler

Compiled 31325 to 13219 computations (57.8% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 x (/.f64 x (-.f64 (*.f64 t z) x))) (+.f64 x 1))
✓	0.0b	(.f64 (+.f64 x 1) (-.f64 (.f64 z t) x))
	1.5b	(/.f64 x (-.f64 (*.f64 t z) x))
✓	12.8b	(/.f64 (.f64 z y) (.f64 (+.f64 x 1) (-.f64 (*.f64 z t) x)))

series167.0ms (2%)

Counts

2 → 84

Calls

2 calls:

154.0ms	(/.f64 (.f64 z y) (.f64 (+.f64 x 1) (-.f64 (*.f64 z t) x)))
12.0ms	(.f64 (+.f64 x 1) (-.f64 (.f64 z t) x))

rewrite25.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
8×	`associate-/r/_binary64`

Counts

2 → 74

Calls

2 calls:

12.0ms	(/.f64 (.f64 z y) (.f64 (+.f64 x 1) (-.f64 (*.f64 z t) x)))
8.0ms	(.f64 (+.f64 x 1) (-.f64 (.f64 z t) x))

simplify135.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

848×	`times-frac_binary64`
503×	`associate-/r*_binary64`
460×	`associate-/l*_binary64`
218×	`fma-def_binary64`
133×	`distribute-rgt-in_binary64`

Counts

158 → 174

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	372	6299
1	1235	5455
2	4866	5450
3	4986	5450

prune423.0ms (5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	346	1	347
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	347	6	353

Error

Counts

353 → 6

Alt Table

Status	Error	Program
	8.1b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 (/.f64 x (cbrt.f64 (.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 t z) x)))) (cbrt.f64 (-.f64 (*.f64 t z) x)))) (+.f64 x 1)))
✓	7.4b	(+.f64 (/.f64 (.f64 z y) (.f64 (+.f64 x 1) (-.f64 (.f64 z t) x))) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	7.4b	(/.f64 (+.f64 x (.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 t z) x)))) (+.f64 x 1))
	33.0b	(/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)) 3)) (.f64 (+.f64 x 1) (+.f64 (.f64 x x) (-.f64 (.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)) (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))))))
✓	3.0b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 (.f64 t z) x)) (cbrt.f64 (-.f64 (.f64 t z) x)))) (cbrt.f64 (-.f64 (*.f64 t z) x)))) (+.f64 x 1)))
	15.1b	(+.f64 (/.f64 y (fma.f64 x t t)) (/.f64 (-.f64 x (/.f64 x (-.f64 (*.f64 t z) x))) (+.f64 x 1)))

Compiler

Compiled 15459 to 5987 computations (61.3% saved)

regimes2.6s (30.9%)

Accuracy

Total 0.7b remaining (97.1%)

Threshold costs 0.7b (97.1%)

Counts

342 → 2

Compiler

Compiled 56498 to 31734 computations (43.8% saved)

bsearch16.0ms (0.2%)

Compiler: Compiled 21 to 13 computations (38.1% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
7×	`sub-neg_binary64`
5×	`*-commutative_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	90
1	44	90
2	57	90
3	63	90
4	66	90
5	65	90

end120.0ms (1.4%)

Compiler: Compiled 364 to 176 computations (51.6% saved)

Details

analyze1.0s (12.5%)

sample1.3s (15.1%)

simplify92.0ms (1.1%)

prune2.0ms (0%)

localize11.0ms (0.1%)

series197.0ms (2.3%)

rewrite48.0ms (0.6%)

simplify153.0ms (1.8%)

prune324.0ms (3.9%)

localize13.0ms (0.1%)

series157.0ms (1.9%)

rewrite30.0ms (0.4%)

simplify146.0ms (1.7%)

prune362.0ms (4.3%)

localize16.0ms (0.2%)

series256.0ms (3.1%)

rewrite30.0ms (0.4%)

simplify143.0ms (1.7%)

prune601.0ms (7.2%)

localize15.0ms (0.2%)

series167.0ms (2%)

rewrite25.0ms (0.3%)

simplify135.0ms (1.6%)

prune423.0ms (5%)

regimes2.6s (30.9%)

bsearch16.0ms (0.2%)

simplify4.0ms (0.1%)

end120.0ms (1.4%)

Profiling