Details

analyze1.0s (13.8%)

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 (17.3%)

Results

1.1s	8256×	body	128	valid
53.0ms	357×	body	128	invalid

Compiler

Compiled 65 to 41 computations (36.9% saved)

simplify95.0ms (1.3%)

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

8.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	8.3b	(/.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)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	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))
✓	11.7b	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))

series138.0ms (1.9%)

Counts

3 → 105

Calls

3 calls:

84.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
48.0ms	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))
5.0ms	(-.f64 (*.f64 y z) x)

rewrite34.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 97

Calls

3 calls:

19.0ms	(/.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 y z) x)

simplify165.0ms (2.3%)

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

202 → 238

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	400	8046
1	1239	7625
2	4866	7623
3	5312	7623

prune236.0ms (3.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	234	4	238
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	235	4	239

Error

0.0b

Counts

239 → 4

Alt Table

Status	Error	Program
	42.8b	(/.f64 (+.f64 x (/.f64 (-.f64 (pow.f64 (.f64 y z) 3) (pow.f64 x 3)) (.f64 (-.f64 (.f64 t z) x) (fma.f64 x (fma.f64 z y x) (.f64 (.f64 z y) (.f64 z y)))))) (+.f64 x 1))
▶	1.8b	(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)))
	8.3b	(/.f64 (+.f64 x (.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 t z) x)))) (+.f64 x 1))
	29.0b	(+.f64 (fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 x (.f64 t (.f64 t z))) (/.f64 x (+.f64 x 1))) (-.f64 (/.f64 y (.f64 t (+.f64 x 1))) (/.f64 x (.f64 z (*.f64 t (+.f64 x 1))))))

Compiler

Compiled 8776 to 3332 computations (62% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	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)))
✓	4.1b	(/.f64 x (-.f64 (*.f64 t z) x))
✓	8.2b	(/.f64 z (-.f64 (*.f64 t z) x))

series131.0ms (1.8%)

Counts

3 → 120

Calls

3 calls:

86.0ms	(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)))
24.0ms	(/.f64 x (-.f64 (*.f64 t z) x))
20.0ms	(/.f64 z (-.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)))

simplify167.0ms (2.3%)

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

prune214.0ms (3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	209	1	210
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	209	5	214

Error

0.0b

Counts

214 → 5

Alt Table

Status	Error	Program
	29.0b	(+.f64 (fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 x (.f64 t (.f64 t z))) (/.f64 x (+.f64 x 1))) (-.f64 (/.f64 y (.f64 t (+.f64 x 1))) (/.f64 x (.f64 z (*.f64 t (+.f64 x 1))))))
	12.5b	(fma.f64 (/.f64 y (+.f64 x 1)) (cbrt.f64 (.f64 (.f64 (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 z (-.f64 (.f64 t z) x))) (/.f64 z (-.f64 (.f64 t z) x)))) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	42.8b	(/.f64 (+.f64 x (/.f64 (-.f64 (pow.f64 (.f64 y z) 3) (pow.f64 x 3)) (.f64 (-.f64 (.f64 t z) x) (fma.f64 x (fma.f64 z y x) (.f64 (.f64 z y) (.f64 z y)))))) (+.f64 x 1))
✓	1.8b	(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)))
▶	8.3b	(/.f64 (+.f64 x (.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 t z) x)))) (+.f64 x 1))

Compiler

Compiled 8627 to 3386 computations (60.8% 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 t z) x))
✓	0.5b	(/.f64 (+.f64 x (.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 t z) x)))) (+.f64 x 1))
✓	11.8b	(.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 t z) x)))

series148.0ms (2.1%)

Counts

3 → 132

Calls

3 calls:

81.0ms	(/.f64 (+.f64 x (.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 t z) x)))) (+.f64 x 1))
47.0ms	(.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 t z) x)))
19.0ms	(/.f64 1 (-.f64 (*.f64 t z) x))

rewrite30.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64`
35×	`add-sqr-sqrt_binary64`
32×	`times-frac_binary64`
28×	`add-cube-cbrt_binary64`
18×	`add-exp-log_binary64`

Counts

3 → 116

Calls

3 calls:

11.0ms	(.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 t z) x)))
6.0ms	(/.f64 (+.f64 x (.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 t z) x)))) (+.f64 x 1))
4.0ms	(/.f64 1 (-.f64 (*.f64 t z) x))

simplify181.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

436×	`times-frac_binary64`
423×	`fma-neg_binary64`
326×	`associate-/l*_binary64`
270×	`associate-/r*_binary64`
243×	`associate-+l+_binary64`

Counts

248 → 267

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	403	9431
1	1270	8756
2	4988	8754
3	5353	8754

prune335.0ms (4.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	301	0	301
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	301	5	306

Error

0.0b

Counts

306 → 5

Alt Table

Status	Error	Program
	29.0b	(+.f64 (fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 x (.f64 t (.f64 t z))) (/.f64 x (+.f64 x 1))) (-.f64 (/.f64 y (.f64 t (+.f64 x 1))) (/.f64 x (.f64 z (*.f64 t (+.f64 x 1))))))
▶	12.5b	(fma.f64 (/.f64 y (+.f64 x 1)) (cbrt.f64 (.f64 (.f64 (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 z (-.f64 (.f64 t z) x))) (/.f64 z (-.f64 (.f64 t z) x)))) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	42.8b	(/.f64 (+.f64 x (/.f64 (-.f64 (pow.f64 (.f64 y z) 3) (pow.f64 x 3)) (.f64 (-.f64 (.f64 t z) x) (fma.f64 x (fma.f64 z y x) (.f64 (.f64 z y) (.f64 z y)))))) (+.f64 x 1))
✓	1.8b	(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)))
✓	8.3b	(/.f64 (+.f64 x (.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 t z) x)))) (+.f64 x 1))

Compiler

Compiled 10868 to 4574 computations (57.9% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 z (-.f64 (*.f64 t z) x)))
	4.1b	(/.f64 x (-.f64 (*.f64 t z) x))
	8.2b	(/.f64 z (-.f64 (*.f64 t z) x))
✓	33.9b	(cbrt.f64 (.f64 (.f64 (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 z (-.f64 (.f64 t z) x))) (/.f64 z (-.f64 (*.f64 t z) x))))

series62.0ms (0.9%)

Counts

2 → 72

Calls

2 calls:

32.0ms	(.f64 (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 z (-.f64 (*.f64 t z) x)))
30.0ms	(cbrt.f64 (.f64 (.f64 (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 z (-.f64 (.f64 t z) x))) (/.f64 z (-.f64 (*.f64 t z) x))))

rewrite105.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
30×	`*-un-lft-identity_binary64`
30×	`add-cube-cbrt_binary64`
15×	`associate-r_binary64`

Counts

2 → 94

Calls

2 calls:

39.0ms	(.f64 (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 z (-.f64 (*.f64 t z) x)))
13.0ms	(cbrt.f64 (.f64 (.f64 (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 z (-.f64 (.f64 t z) x))) (/.f64 z (-.f64 (*.f64 t z) x))))

simplify186.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

586×	`associate-/l/_binary64`
499×	`fma-def_binary64`
222×	`distribute-rgt-in_binary64`
200×	`associate-/l*_binary64`
185×	`distribute-lft-in_binary64`

Counts

166 → 190

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	247	5391
1	705	4757
2	2562	4298
3	5204	4298

prune562.0ms (7.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	474	0	474
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	474	5	479

Error

0.0b

Counts

479 → 5

Alt Table

Status	Error	Program
	29.0b	(+.f64 (fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 x (.f64 t (.f64 t z))) (/.f64 x (+.f64 x 1))) (-.f64 (/.f64 y (.f64 t (+.f64 x 1))) (/.f64 x (.f64 z (*.f64 t (+.f64 x 1))))))
✓	12.5b	(fma.f64 (/.f64 y (+.f64 x 1)) (cbrt.f64 (.f64 (.f64 (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 z (-.f64 (.f64 t z) x))) (/.f64 z (-.f64 (.f64 t z) x)))) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	42.8b	(/.f64 (+.f64 x (/.f64 (-.f64 (pow.f64 (.f64 y z) 3) (pow.f64 x 3)) (.f64 (-.f64 (.f64 t z) x) (fma.f64 x (fma.f64 z y x) (.f64 (.f64 z y) (.f64 z y)))))) (+.f64 x 1))
✓	1.8b	(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)))
✓	8.3b	(/.f64 (+.f64 x (.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 t z) x)))) (+.f64 x 1))

Compiler

Compiled 24930 to 6346 computations (74.5% saved)

regimes2.0s (27.1%)

Accuracy

Total 0.6b remaining (95.8%)

Threshold costs 0.6b (95.8%)

Counts

251 → 2

Compiler

Compiled 36213 to 21174 computations (41.5% saved)

bsearch11.0ms (0.2%)

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

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary64`
6×	`*-commutative_binary64`
5×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	89
1	44	89
2	53	89
3	57	89
4	59	89
5	58	89

end150.0ms (2.1%)

Compiler: Compiled 307 to 167 computations (45.6% saved)

Details

analyze1.0s (13.8%)

sample1.3s (17.3%)

simplify95.0ms (1.3%)

prune2.0ms (0%)

localize11.0ms (0.2%)

series138.0ms (1.9%)

rewrite34.0ms (0.5%)

simplify165.0ms (2.3%)

prune236.0ms (3.3%)

localize13.0ms (0.2%)

series131.0ms (1.8%)

rewrite12.0ms (0.2%)

simplify167.0ms (2.3%)

prune214.0ms (3%)

localize12.0ms (0.2%)

series148.0ms (2.1%)

rewrite30.0ms (0.4%)

simplify181.0ms (2.5%)

prune335.0ms (4.6%)

localize16.0ms (0.2%)

series62.0ms (0.9%)

rewrite105.0ms (1.5%)

simplify186.0ms (2.6%)

prune562.0ms (7.8%)

regimes2.0s (27.1%)

bsearch11.0ms (0.2%)

simplify4.0ms (0%)

end150.0ms (2.1%)

Profiling