Details

analyze1.0s (16.8%)

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 (20.4%)

Results

1.1s	8256×	body	128	valid
49.0ms	346×	body	128	invalid

Compiler

Compiled 65 to 41 computations (36.9% saved)

simplify91.0ms (1.5%)

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

7.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	7.3b	(/.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)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 t z) x)
✓	0.0b	(-.f64 (*.f64 y z) x)
✓	0.5b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
✓	9.7b	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))

series144.0ms (2.3%)

Counts

4 → 114

Calls

4 calls:

86.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
47.0ms	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))
5.0ms	(-.f64 (*.f64 y z) x)
5.0ms	(-.f64 (*.f64 t z) x)

rewrite32.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`*-un-lft-identity_binary64`
26×	`add-sqr-sqrt_binary64`
26×	`add-cube-cbrt_binary64`
25×	`times-frac_binary64`
10×	`distribute-lft-out_binary64`

Counts

4 → 117

Calls

4 calls:

13.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
6.0ms	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))
3.0ms	(-.f64 (*.f64 t z) x)
3.0ms	(-.f64 (*.f64 y z) x)

simplify167.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

550×	`times-frac_binary64`
544×	`fma-neg_binary64`
420×	`associate-/l*_binary64`
300×	`associate-/r*_binary64`
201×	`associate--l+_binary64`

Counts

231 → 263

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	412	8297
1	1260	7857
2	4933	7855
3	5379	7855

prune275.0ms (4.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	257	6	263
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	258	6	264

Error

0.0b

Counts

264 → 6

Alt Table

Status	Error	Program
	19.6b	(/.f64 (+.f64 x (/.f64 y t)) (+.f64 x 1))
	7.3b	(/.f64 (+.f64 x (/.f64 (fma.f64 y z (neg.f64 x)) (-.f64 (*.f64 t z) x))) (+.f64 x 1))
	7.3b	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))
	7.6b	(/.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))
▶	2.5b	(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)))
	26.1b	(-.f64 (+.f64 (/.f64 x (+.f64 1 x)) (/.f64 y (.f64 (+.f64 1 x) t))) (/.f64 x (.f64 (+.f64 1 x) (*.f64 t z))))

Compiler

Compiled 9453 to 3538 computations (62.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (*.f64 t z) x)
✓	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)))
✓	2.2b	(/.f64 x (-.f64 (*.f64 t z) x))
✓	8.1b	(/.f64 z (-.f64 (*.f64 t z) x))

series126.0ms (2%)

Counts

3 → 120

Calls

3 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)))
22.0ms	(/.f64 z (-.f64 (*.f64 t z) x))
20.0ms	(/.f64 x (-.f64 (*.f64 t z) x))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64`
19×	`add-sqr-sqrt_binary64`
19×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`
7×	`add-cbrt-cube_binary64`

Counts

3 → 72

Calls

3 calls:

4.0ms	(/.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)))

simplify190.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

400×	`times-frac_binary64`
326×	`fma-neg_binary64`
313×	`associate-/l*_binary64`
305×	`sub-neg_binary64`
241×	`associate-+r+_binary64`

Counts

192 → 210

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	331	6888
1	973	6477
2	4210	6352
3	4995	6350
4	5047	6350

prune357.0ms (5.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	257	3	260
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	260	6	266

Error

Counts

266 → 6

Alt Table

Status	Error	Program
	15.0b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (cbrt.f64 (pow.f64 (-.f64 (.f64 t z) x) 3))) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
▶	7.3b	(/.f64 (+.f64 x (/.f64 (fma.f64 y z (neg.f64 x)) (-.f64 (*.f64 t z) x))) (+.f64 x 1))
	7.3b	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))
✓	2.5b	(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)))
	32.8b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 (/.f64 z (sqrt.f64 (-.f64 (.f64 t z) x))) (sqrt.f64 (-.f64 (.f64 t z) x))) (/.f64 (-.f64 x (/.f64 x (-.f64 (*.f64 t z) x))) (+.f64 x 1)))
	19.3b	(+.f64 (/.f64 x (+.f64 1 x)) (/.f64 y (*.f64 (+.f64 1 x) t)))

Compiler

Compiled 10265 to 3909 computations (61.9% saved)

localize14.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (*.f64 t z) x)
✓	0.5b	(/.f64 (+.f64 x (/.f64 (fma.f64 y z (neg.f64 x)) (-.f64 (*.f64 t z) x))) (+.f64 x 1))
✓	9.7b	(/.f64 (fma.f64 y z (neg.f64 x)) (-.f64 (*.f64 t z) x))

series122.0ms (2%)

Counts

2 → 96

Calls

2 calls:

74.0ms	(/.f64 (+.f64 x (/.f64 (fma.f64 y z (neg.f64 x)) (-.f64 (*.f64 t z) x))) (+.f64 x 1))
47.0ms	(/.f64 (fma.f64 y z (neg.f64 x)) (-.f64 (*.f64 t z) x))

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`*-un-lft-identity_binary64`
25×	`times-frac_binary64`
20×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`
10×	`distribute-lft-out_binary64`

Counts

2 → 73

Calls

2 calls:

11.0ms	(/.f64 (+.f64 x (/.f64 (fma.f64 y z (neg.f64 x)) (-.f64 (*.f64 t z) x))) (+.f64 x 1))
4.0ms	(/.f64 (fma.f64 y z (neg.f64 x)) (-.f64 (*.f64 t z) x))

simplify184.0ms (3%)

Algorithm

1×	egg-herbie

Rules

417×	`times-frac_binary64`
356×	`fma-neg_binary64`
316×	`associate-/l*_binary64`
280×	`+-commutative_binary64`
256×	`associate-+r+_binary64`

Counts

169 → 197

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	360	7835
1	1126	7288
2	4815	7286
3	5126	7286

prune208.0ms (3.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	222	0	222
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	222	6	228

Error

Counts

228 → 6

Alt Table

Status	Error	Program
	15.0b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (cbrt.f64 (pow.f64 (-.f64 (.f64 t z) x) 3))) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
✓	7.3b	(/.f64 (+.f64 x (/.f64 (fma.f64 y z (neg.f64 x)) (-.f64 (*.f64 t z) x))) (+.f64 x 1))
▶	7.3b	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))
✓	2.5b	(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)))
	32.8b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 (/.f64 z (sqrt.f64 (-.f64 (.f64 t z) x))) (sqrt.f64 (-.f64 (.f64 t z) x))) (/.f64 (-.f64 x (/.f64 x (-.f64 (*.f64 t z) x))) (+.f64 x 1)))
	19.3b	(+.f64 (/.f64 x (+.f64 1 x)) (/.f64 y (*.f64 (+.f64 1 x) t)))

Compiler

Compiled 8398 to 3220 computations (61.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (*.f64 y z) x)
✓	0.2b	(/.f64 1 (/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x)))
✓	0.5b	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))
✓	9.7b	(/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x))

series195.0ms (3.1%)

Counts

3 → 144

Calls

3 calls:

97.0ms

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

49.0ms

(/.f64 (-.f64 (*.f64 t z) x) (-.f64 (*.f64 y z) x))

48.0ms

(/.f64 1 (/.f64 (-.f64 (*.f64 t z) x) (-.f64 (*.f64 y z) x)))

rewrite51.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

110×	`times-frac_binary64`
93×	`*-un-lft-identity_binary64`
66×	`add-sqr-sqrt_binary64`
66×	`add-cube-cbrt_binary64`
22×	`associate-/r*_binary64`

Counts

3 → 167

Calls

3 calls:

18.0ms

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

8.0ms

(/.f64 (-.f64 (*.f64 t z) x) (-.f64 (*.f64 y z) x))

8.0ms

(/.f64 1 (/.f64 (-.f64 (*.f64 t z) x) (-.f64 (*.f64 y z) x)))

simplify272.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

513×	`times-frac_binary64`
389×	`associate-/l*_binary64`
324×	`associate-/r*_binary64`
266×	`associate--l+_binary64`
179×	`sub-neg_binary64`

Counts

311 → 360

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	480	13006
1	1499	12060
2	5108	12060

prune497.0ms (8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	394	0	394
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	394	6	400

Error

Counts

400 → 6

Alt Table

Status	Error	Program
	15.0b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (cbrt.f64 (pow.f64 (-.f64 (.f64 t z) x) 3))) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
✓	7.3b	(/.f64 (+.f64 x (/.f64 (fma.f64 y z (neg.f64 x)) (-.f64 (*.f64 t z) x))) (+.f64 x 1))
✓	7.3b	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))
✓	2.5b	(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)))
	32.8b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 (/.f64 z (sqrt.f64 (-.f64 (.f64 t z) x))) (sqrt.f64 (-.f64 (.f64 t z) x))) (/.f64 (-.f64 x (/.f64 x (-.f64 (*.f64 t z) x))) (+.f64 x 1)))
	19.3b	(+.f64 (/.f64 x (+.f64 1 x)) (/.f64 y (*.f64 (+.f64 1 x) t)))

Compiler

Compiled 14530 to 5569 computations (61.7% saved)

regimes765.0ms (12.4%)

Accuracy

Total 1.6b remaining (98.7%)

Threshold costs 0b (0%)

Counts

129 → 2

Compiler

Compiled 16100 to 9777 computations (39.3% saved)

bsearch7.0ms (0.1%)

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

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	105
1	52	105
2	65	105
3	71	105
4	74	105
5	73	105

end112.0ms (1.8%)

Compiler: Compiled 312 to 171 computations (45.2% saved)

Details

analyze1.0s (16.8%)

sample1.3s (20.4%)

simplify91.0ms (1.5%)

prune2.0ms (0%)

localize10.0ms (0.2%)

series144.0ms (2.3%)

rewrite32.0ms (0.5%)

simplify167.0ms (2.7%)

prune275.0ms (4.4%)

localize12.0ms (0.2%)

series126.0ms (2%)

rewrite12.0ms (0.2%)

simplify190.0ms (3.1%)

prune357.0ms (5.8%)

localize14.0ms (0.2%)

series122.0ms (2%)

rewrite20.0ms (0.3%)

simplify184.0ms (3%)

prune208.0ms (3.4%)

localize12.0ms (0.2%)

series195.0ms (3.1%)

rewrite51.0ms (0.8%)

simplify272.0ms (4.4%)

prune497.0ms (8%)

regimes765.0ms (12.4%)

bsearch7.0ms (0.1%)

simplify4.0ms (0.1%)

end112.0ms (1.8%)

Profiling