Details

analyze1.0s (12.7%)

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)

sample1.2s (15.5%)

Results

1.1s	8256×	body	128	valid
44.0ms	357×	body	128	invalid

Compiler

Compiled 65 to 41 computations (36.9% saved)

simplify91.0ms (1.2%)

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

7.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	7.5b	(/.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 (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 t z) x)
✓	0.5b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
✓	9.1b	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))

series150.0ms (1.9%)

Counts

3 → 105

Calls

3 calls:

100.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
45.0ms	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))
5.0ms	(-.f64 (*.f64 t z) x)

rewrite29.0ms (0.4%)

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:

13.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
7.0ms	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))
3.0ms	(-.f64 (*.f64 t z) x)

simplify154.0ms (2%)

Algorithm

1×	egg-herbie

Rules

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

Counts

202 → 231

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	401	8044
1	1239	7625
2	4864	7623
3	5291	7623

prune311.0ms (3.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	223	8	231
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	224	8	232

Error

0.0b

Counts

232 → 8

Alt Table

Status	Error	Program
	25.2b	(/.f64 (+.f64 x (neg.f64 (fma.f64 (/.f64 y x) z -1))) (+.f64 x 1))
	20.9b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1))) (/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (*.f64 t z) x))) (sqrt.f64 (+.f64 x 1))))
	7.6b	(/.f64 1 (/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))))
	19.9b	(/.f64 (+.f64 x (/.f64 y t)) (+.f64 x 1))
▶	2.3b	(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)))
	35.4b	(/.f64 (+.f64 x (-.f64 (+.f64 1 (/.f64 (.f64 t z) x)) (+.f64 (/.f64 (.f64 y (.f64 t (pow.f64 z 2))) (pow.f64 x 2)) (/.f64 (.f64 y z) x)))) (+.f64 x 1))
	7.9b	(/.f64 (+.f64 x (.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 (.f64 t z) x)) (cbrt.f64 (-.f64 (.f64 t z) x)))) (/.f64 (-.f64 (.f64 y z) x) (cbrt.f64 (-.f64 (.f64 t z) x))))) (+.f64 x 1))
	8.0b	(/.f64 (+.f64 x (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 z y) x)) (cbrt.f64 (-.f64 (.f64 z y) x))) (/.f64 (cbrt.f64 (-.f64 (.f64 z y) x)) (-.f64 (.f64 t z) x)))) (+.f64 x 1))

Compiler

Compiled 8806 to 3391 computations (61.5% saved)

localize50.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 y (+.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)))
✓	2.4b	(/.f64 x (-.f64 (*.f64 t z) x))
✓	6.8b	(/.f64 z (-.f64 (*.f64 t z) x))

series151.0ms (1.9%)

Counts

4 → 144

Calls

4 calls:

99.0ms	(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)))
21.0ms	(/.f64 x (-.f64 (*.f64 t z) x))
21.0ms	(/.f64 z (-.f64 (*.f64 t z) x))
9.0ms	(/.f64 y (+.f64 x 1))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64`
30×	`times-frac_binary64`
29×	`add-sqr-sqrt_binary64`
29×	`add-cube-cbrt_binary64`
10×	`associate-/r*_binary64`

Counts

4 → 107

Calls

4 calls:

6.0ms	(/.f64 z (-.f64 (*.f64 t z) x))
4.0ms	(/.f64 x (-.f64 (*.f64 t z) x))
3.0ms	(/.f64 y (+.f64 x 1))
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)))

simplify154.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

408×	`times-frac_binary64`
329×	`associate-/l*_binary64`
276×	`fma-neg_binary64`
255×	`associate-/r*_binary64`
250×	`+-commutative_binary64`

Counts

251 → 263

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	398	7626
1	1119	7175
2	4600	7050
3	4982	7050

prune358.0ms (4.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	262	1	263
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	263	8	271

Error

Counts

271 → 8

Alt Table

Status	Error	Program
	7.6b	(/.f64 1 (/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))))
	19.9b	(/.f64 (+.f64 x (/.f64 y t)) (+.f64 x 1))
✓	2.3b	(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)))
▶	2.5b	(fma.f64 (.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))) (/.f64 (cbrt.f64 y) (cbrt.f64 (+.f64 x 1)))) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (*.f64 t z) x))) (+.f64 x 1)))
	35.4b	(/.f64 (+.f64 x (-.f64 (+.f64 1 (/.f64 (.f64 t z) x)) (+.f64 (/.f64 (.f64 y (.f64 t (pow.f64 z 2))) (pow.f64 x 2)) (/.f64 (.f64 y z) x)))) (+.f64 x 1))
	20.9b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1))) (/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (*.f64 t z) x))) (sqrt.f64 (+.f64 x 1))))
	7.9b	(/.f64 (+.f64 x (.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 (.f64 t z) x)) (cbrt.f64 (-.f64 (.f64 t z) x)))) (/.f64 (-.f64 (.f64 y z) x) (cbrt.f64 (-.f64 (.f64 t z) x))))) (+.f64 x 1))
	8.0b	(/.f64 (+.f64 x (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 z y) x)) (cbrt.f64 (-.f64 (.f64 z y) x))) (/.f64 (cbrt.f64 (-.f64 (.f64 z y) x)) (-.f64 (.f64 t z) x)))) (+.f64 x 1))

Compiler

Compiled 10490 to 4052 computations (61.4% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
✓	0.5b	(cbrt.f64 y)
	2.4b	(/.f64 x (-.f64 (*.f64 t z) x))
	6.8b	(/.f64 z (-.f64 (*.f64 t z) x))

series72.0ms (0.9%)

Counts

2 → 24

Calls

2 calls:

36.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
35.0ms	(cbrt.f64 y)

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`
9×	`pow1_binary64`

Counts

2 → 55

Calls

2 calls:

4.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
1.0ms	(cbrt.f64 y)

simplify70.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

577×	`distribute-rgt-in_binary64`
561×	`log-prod_binary64`
538×	`distribute-lft-in_binary64`
525×	`unswap-sqr_binary64`
384×	`fma-def_binary64`

Counts

79 → 74

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	58	610
1	98	554
2	296	516
3	769	502
4	1799	410
5	4642	410
6	4805	410

prune377.0ms (4.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	252	0	252
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	252	8	260

Error

Counts

260 → 8

Alt Table

Status	Error	Program
▶	7.6b	(/.f64 1 (/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))))
	19.9b	(/.f64 (+.f64 x (/.f64 y t)) (+.f64 x 1))
✓	2.3b	(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)))
✓	2.5b	(fma.f64 (.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))) (/.f64 (cbrt.f64 y) (cbrt.f64 (+.f64 x 1)))) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (*.f64 t z) x))) (+.f64 x 1)))
	35.4b	(/.f64 (+.f64 x (-.f64 (+.f64 1 (/.f64 (.f64 t z) x)) (+.f64 (/.f64 (.f64 y (.f64 t (pow.f64 z 2))) (pow.f64 x 2)) (/.f64 (.f64 y z) x)))) (+.f64 x 1))
	20.9b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1))) (/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (*.f64 t z) x))) (sqrt.f64 (+.f64 x 1))))
	7.9b	(/.f64 (+.f64 x (.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 (.f64 t z) x)) (cbrt.f64 (-.f64 (.f64 t z) x)))) (/.f64 (-.f64 (.f64 y z) x) (cbrt.f64 (-.f64 (.f64 t z) x))))) (+.f64 x 1))
	8.0b	(/.f64 (+.f64 x (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 z y) x)) (cbrt.f64 (-.f64 (.f64 z y) x))) (/.f64 (cbrt.f64 (-.f64 (.f64 z y) x)) (-.f64 (.f64 t z) x)))) (+.f64 x 1))

Compiler

Compiled 13320 to 5518 computations (58.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (*.f64 t z) x)
✓	0.1b	(/.f64 1 (/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))))
✓	0.6b	(/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))))
	9.1b	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))

series746.0ms (9.5%)

Counts

2 → 96

Calls

2 calls:

668.0ms	(/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))))
77.0ms	(/.f64 1 (/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))))

rewrite63.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

155×	`*-un-lft-identity_binary64`
146×	`times-frac_binary64`
71×	`add-sqr-sqrt_binary64`
71×	`add-cube-cbrt_binary64`
42×	`distribute-lft-out_binary64`

Counts

2 → 156

Calls

2 calls:

25.0ms	(/.f64 1 (/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))))
12.0ms	(/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))))

simplify317.0ms (4%)

Algorithm

1×	egg-herbie

Rules

868×	`fma-def_binary64`
514×	`+-commutative_binary64`
450×	`associate-+r+_binary64`
275×	`*-commutative_binary64`
221×	`associate-/r*_binary64`

Counts

252 → 264

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1257	25754
1	4648	25408
2	5344	25408

prune952.0ms (12.1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	385	1	386
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	386	8	394

Error

Counts

394 → 8

Alt Table

Status	Error	Program
✓	7.6b	(/.f64 1 (/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))))
	19.9b	(/.f64 (+.f64 x (/.f64 y t)) (+.f64 x 1))
✓	2.3b	(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)))
✓	2.5b	(fma.f64 (.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))) (/.f64 (cbrt.f64 y) (cbrt.f64 (+.f64 x 1)))) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (*.f64 t z) x))) (+.f64 x 1)))
	7.6b	(/.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))))
	35.4b	(/.f64 (+.f64 x (-.f64 (+.f64 1 (/.f64 (.f64 t z) x)) (+.f64 (/.f64 (.f64 y (.f64 t (pow.f64 z 2))) (pow.f64 x 2)) (/.f64 (.f64 y z) x)))) (+.f64 x 1))
	7.9b	(/.f64 (+.f64 x (.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 (.f64 t z) x)) (cbrt.f64 (-.f64 (.f64 t z) x)))) (/.f64 (-.f64 (.f64 y z) x) (cbrt.f64 (-.f64 (.f64 t z) x))))) (+.f64 x 1))
	8.0b	(/.f64 (+.f64 x (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 z y) x)) (cbrt.f64 (-.f64 (.f64 z y) x))) (/.f64 (cbrt.f64 (-.f64 (.f64 z y) x)) (-.f64 (.f64 t z) x)))) (+.f64 x 1))

Compiler

Compiled 32157 to 15327 computations (52.3% saved)

regimes1.4s (17.7%)

Accuracy

Total 0.6b remaining (96.9%)

Threshold costs 0.6b (96.9%)

Counts

184 → 2

Compiler

Compiled 26645 to 15872 computations (40.4% saved)

bsearch8.0ms (0.1%)

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

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
5×	`sub-neg_binary64`
4×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	84
1	40	84
2	49	84
3	53	84
4	55	84
5	54	84

end143.0ms (1.8%)

Compiler: Compiled 370 to 208 computations (43.8% saved)

Details

analyze1.0s (12.7%)

sample1.2s (15.5%)

simplify91.0ms (1.2%)

prune2.0ms (0%)

localize10.0ms (0.1%)

series150.0ms (1.9%)

rewrite29.0ms (0.4%)

simplify154.0ms (2%)

prune311.0ms (3.9%)

localize50.0ms (0.6%)

series151.0ms (1.9%)

rewrite19.0ms (0.2%)

simplify154.0ms (1.9%)

prune358.0ms (4.5%)

localize20.0ms (0.3%)

series72.0ms (0.9%)

rewrite7.0ms (0.1%)

simplify70.0ms (0.9%)

prune377.0ms (4.8%)

localize11.0ms (0.1%)

series746.0ms (9.5%)

rewrite63.0ms (0.8%)

simplify317.0ms (4%)

prune952.0ms (12.1%)

regimes1.4s (17.7%)

bsearch8.0ms (0.1%)

simplify4.0ms (0%)

end143.0ms (1.8%)

Profiling