Details

analyze686.0ms (23.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
9.4%	90.5%	0.1%	7
14%	85.8%	0.1%	8
21.1%	78%	0.9%	9
37.3%	60.3%	2.5%	10
39.7%	56.1%	4.2%	11
45.6%	48.7%	5.7%	12
55.9%	35.1%	8.9%	13
57.6%	32.1%	10.3%	14

Compiler

Compiled 13 to 8 computations (38.5% saved)

sample1.2s (40.8%)

Results

924.0ms	8256×	body	128	valid
126.0ms	1134×	body	128	invalid

Compiler

Compiled 38 to 23 computations (39.5% saved)

simplify114.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

2064×	`fma-neg_binary64`
381×	`div-sub_binary64`
365×	`associate-/l*_binary64`
334×	`distribute-neg-frac_binary64`
322×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	12	11
2	25	11
3	47	11
4	82	11
5	143	11
6	228	11
7	442	11
8	1041	11
9	2472	11
10	2805	11
11	2944	11
12	3273	11
13	3441	11
14	3513	11
15	4986	11

prune3.0ms (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

11.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	11.1b	(/.f64 (fma.f64 y (-.f64 z x) x) z)

Compiler

Compiled 42 to 21 computations (50% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	10.3b	(/.f64 (fma.f64 y (-.f64 z x) x) z)

series13.0ms (0.4%)

Counts

1 → 36

Calls

1 calls:

13.0ms

(/.f64 (fma.f64 y (-.f64 z x) x) z)

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
9×	`times-frac_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
3×	`associate-/r*_binary64`

Counts

1 → 29

Calls

1 calls:

2.0ms

(/.f64 (fma.f64 y (-.f64 z x) x) z)

simplify84.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

595×	`neg-mul-1_binary64`
446×	`div-sub_binary64`
418×	`distribute-rgt-neg-out_binary64`
374×	`fma-neg_binary64`
271×	`fma-def_binary64`

Counts

65 → 44

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	76	987
1	150	941
2	357	885
3	807	885
4	2783	885
5	4648	885
6	5195	885

prune25.0ms (0.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	39	5	44
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	39	6	45

Error

0.0b

Counts

45 → 6

Alt Table

Status	Error	Program
	40.2b	(*.f64 (sqrt.f64 (/.f64 (fma.f64 y (-.f64 z x) x) z)) (sqrt.f64 (/.f64 (fma.f64 y (-.f64 z x) x) z)))
	23.9b	(-.f64 y (*.f64 (/.f64 x z) y))
	11.3b	(/.f64 1 (/.f64 z (fma.f64 y (-.f64 z x) x)))
▶	3.1b	(*.f64 1 (fma.f64 x (/.f64 (-.f64 1 y) z) y))
✓	11.1b	(/.f64 (fma.f64 y (-.f64 z x) x) z)
	12.4b	(.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 y (-.f64 z x) x)) (cbrt.f64 (fma.f64 y (-.f64 z x) x))) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (cbrt.f64 (fma.f64 y (-.f64 z x) x)) (cbrt.f64 z)))

Compiler

Compiled 826 to 227 computations (72.5% saved)

localize9.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 1 y) z)
✓	2.9b	(fma.f64 x (/.f64 (-.f64 1 y) z) y)

series17.0ms (0.6%)

Counts

2 → 52

Calls

2 calls:

12.0ms	(fma.f64 x (/.f64 (-.f64 1 y) z) y)
5.0ms	(/.f64 (-.f64 1 y) z)

rewrite8.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`*-un-lft-identity_binary64`
25×	`add-sqr-sqrt_binary64`
18×	`times-frac_binary64`
13×	`add-cube-cbrt_binary64`
8×	`difference-of-squares_binary64`

Counts

2 → 54

Calls

2 calls:

5.0ms	(/.f64 (-.f64 1 y) z)
0.0ms	(fma.f64 x (/.f64 (-.f64 1 y) z) y)

simplify80.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

880×	`fma-def_binary64`
424×	`neg-mul-1_binary64`
416×	`associate-/l/_binary64`
289×	`distribute-rgt-neg-out_binary64`
263×	`fma-neg_binary64`

Counts

106 → 80

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	107	1312
1	225	1203
2	575	1199
3	1752	1199
4	4030	1199
5	5018	1199

prune60.0ms (2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	78	2	80
Fresh	2	2	4
Picked	0	1	1
Done	1	0	1
Total	81	5	86

Error

Counts

86 → 5

Alt Table

Status	Error	Program
	11.3b	(/.f64 1 (/.f64 z (fma.f64 y (-.f64 z x) x)))
▶	0.1b	(*.f64 1 (fma.f64 (/.f64 x z) (-.f64 1 y) y))
	40.2b	(*.f64 (sqrt.f64 (/.f64 (fma.f64 y (-.f64 z x) x) z)) (sqrt.f64 (/.f64 (fma.f64 y (-.f64 z x) x) z)))
	25.6b	(*.f64 1 (fma.f64 x (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 y) z) 3)) y))
✓	3.1b	(*.f64 1 (fma.f64 x (/.f64 (-.f64 1 y) z) y))

Compiler

Compiled 1397 to 849 computations (39.2% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (/.f64 x z) (-.f64 1 y) y)

series13.0ms (0.4%)

Counts

1 → 36

Calls

1 calls:

13.0ms

(fma.f64 (/.f64 x z) (-.f64 1 y) y)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 (/.f64 x z) (-.f64 1 y) y)

simplify68.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

705×	`distribute-rgt-neg-out_binary64`
469×	`distribute-neg-out_binary64`
368×	`unsub-neg_binary64`
332×	`distribute-rgt-in_binary64`
326×	`distribute-lft-in_binary64`

Counts

46 → 23

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	37	586
1	78	509
2	194	497
3	424	497
4	2300	497
5	4502	497
6	5263	497

prune14.0ms (0.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	23	0	23
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	23	5	28

Error

Counts

28 → 5

Alt Table

Status	Error	Program
▶	11.3b	(/.f64 1 (/.f64 z (fma.f64 y (-.f64 z x) x)))
✓	0.1b	(*.f64 1 (fma.f64 (/.f64 x z) (-.f64 1 y) y))
	40.2b	(*.f64 (sqrt.f64 (/.f64 (fma.f64 y (-.f64 z x) x) z)) (sqrt.f64 (/.f64 (fma.f64 y (-.f64 z x) x) z)))
	25.6b	(*.f64 1 (fma.f64 x (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 y) z) 3)) y))
✓	3.1b	(*.f64 1 (fma.f64 x (/.f64 (-.f64 1 y) z) y))

Compiler

Compiled 421 to 238 computations (43.5% saved)

localize10.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1 (/.f64 z (fma.f64 y (-.f64 z x) x)))
✓	10.3b	(/.f64 z (fma.f64 y (-.f64 z x) x))

series56.0ms (1.9%)

Counts

2 → 72

Calls

2 calls:

42.0ms	(/.f64 z (fma.f64 y (-.f64 z x) x))
14.0ms	(/.f64 1 (/.f64 z (fma.f64 y (-.f64 z x) x)))

rewrite18.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
52×	`*-un-lft-identity_binary64`
52×	`add-sqr-sqrt_binary64`
52×	`add-cube-cbrt_binary64`
16×	`associate-/r*_binary64`

Counts

2 → 107

Calls

2 calls:

5.0ms	(/.f64 1 (/.f64 z (fma.f64 y (-.f64 z x) x)))
2.0ms	(/.f64 z (fma.f64 y (-.f64 z x) x))

simplify116.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

741×	`fma-def_binary64`
326×	`cancel-sign-sub-inv_binary64`
284×	`times-frac_binary64`
261×	`unswap-sqr_binary64`
227×	`associate-/r*_binary64`

Counts

179 → 197

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	284	4778
1	794	4499
2	3346	4307
3	5187	4307

prune99.0ms (3.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	197	0	197
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	197	5	202

Error

Counts

202 → 5

Alt Table

Status	Error	Program
✓	11.3b	(/.f64 1 (/.f64 z (fma.f64 y (-.f64 z x) x)))
✓	0.1b	(*.f64 1 (fma.f64 (/.f64 x z) (-.f64 1 y) y))
	40.2b	(*.f64 (sqrt.f64 (/.f64 (fma.f64 y (-.f64 z x) x) z)) (sqrt.f64 (/.f64 (fma.f64 y (-.f64 z x) x) z)))
	25.6b	(*.f64 1 (fma.f64 x (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 y) z) 3)) y))
✓	3.1b	(*.f64 1 (fma.f64 x (/.f64 (-.f64 1 y) z) y))

Compiler

Compiled 4829 to 1766 computations (63.4% saved)

regimes161.0ms (5.4%)

Accuracy

Total 0.0b remaining (84.3%)

Threshold costs 0.0b (84.3%)

Counts

46 → 1

Compiler

Compiled 2516 to 1552 computations (38.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-lft-identity_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	14	11
2	18	11
3	20	11
4	21	11
5	20	11

end78.0ms (2.6%)

Compiler: Compiled 99 to 60 computations (39.4% saved)

Details

analyze686.0ms (23.2%)

sample1.2s (40.8%)

simplify114.0ms (3.8%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series13.0ms (0.4%)

rewrite4.0ms (0.1%)

simplify84.0ms (2.8%)

prune25.0ms (0.9%)

localize9.0ms (0.3%)

series17.0ms (0.6%)

rewrite8.0ms (0.3%)

simplify80.0ms (2.7%)

prune60.0ms (2%)

localize6.0ms (0.2%)

series13.0ms (0.4%)

rewrite1.0ms (0%)

simplify68.0ms (2.3%)

prune14.0ms (0.5%)

localize10.0ms (0.3%)

series56.0ms (1.9%)

rewrite18.0ms (0.6%)

simplify116.0ms (3.9%)

prune99.0ms (3.3%)

regimes161.0ms (5.4%)

simplify3.0ms (0.1%)

end78.0ms (2.6%)

Profiling