Details

analyze288.0ms (4.2%)

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%	74.9%	25.1%	4
12.5%	62.4%	25.1%	5
31.2%	31.2%	37.6%	6
37.5%	25%	37.6%	7
40.6%	15.6%	43.8%	8
42.9%	11.7%	45.4%	9
44.1%	7.4%	48.5%	10
45.1%	5.7%	49.3%	11
45.6%	3.6%	50.8%	12
46%	2.8%	51.2%	13
46.2%	1.8%	52%	14

Compiler

Compiled 17 to 14 computations (17.6% saved)

sample43.0ms (0.6%)

Algorithm

1×

intervals

Results

28.0ms	256×	body	128	valid
1.0ms	5×	body	128	invalid
0.0ms	2×	body	128	nan

Compiler

Compiled 35 to 29 computations (17.1% saved)

simplify234.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

1205×	`fma-neg_binary64`
900×	`fma-def_binary64`
326×	`associate-/l*_binary64`
318×	`cancel-sign-sub-inv_binary64`
290×	`distribute-rgt-neg-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	28	18
2	68	18
3	145	16
4	257	16
5	411	16
6	861	16
7	1371	16
8	2386	16
9	2493	16
10	2675	16
11	2607	16
12	2581	16
13	2581	16
14	3531	16
15	3364	16
16	3364	16
17	3364	16
18	3364	16
19	3171	16

prune7.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.5b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.7b	(*.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3))
▶	0.7b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))

Compiler

Compiled 85 to 66 computations (22.4% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 y (/.f64 1 (*.f64 x 9)))
✓	0.3b	(*.f64 3 (sqrt.f64 x))
✓	0.3b	(/.f64 1 (*.f64 x 9))
✓	0.5b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))

series85.0ms (1.2%)

Counts

4 → 48

Calls

4 calls:

57.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
15.0ms	(*.f64 3 (sqrt.f64 x))
10.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
3.0ms	(/.f64 1 (*.f64 x 9))

rewrite63.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64`
37×	`add-sqr-sqrt_binary64`
30×	`prod-diff_binary64`
29×	`add-cube-cbrt_binary64`
22×	`add-exp-log_binary64`

Counts

4 → 140

Calls

4 calls:

23.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
8.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
7.0ms	(*.f64 3 (sqrt.f64 x))
7.0ms	(/.f64 1 (*.f64 x 9))

simplify144.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

625×	`times-frac_binary64`
456×	`distribute-rgt-in_binary64`
422×	`distribute-lft-in_binary64`
305×	`fma-def_binary64`
289×	`associate-/l*_binary64`

Counts

188 → 171

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	174	2841
1	412	2251
2	1241	2225
3	5098	2225

prune399.0ms (5.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	158	13	171
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	159	14	173

Error

0.3b

Counts

173 → 14

Alt Table

Status	Error	Program
	1.6b	(.f64 (.f64 (.f64 3 (.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 (sqrt.f64 x)))) (cbrt.f64 (sqrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	20.8b	(.f64 3 (.f64 (-.f64 (*.f64 1/9 (/.f64 1 x)) 1) (sqrt.f64 x)))
	0.7b	(*.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3))
	17.8b	(.f64 (cbrt.f64 (.f64 (.f64 (.f64 3 3) 3) (.f64 (.f64 (sqrt.f64 x) (sqrt.f64 x)) (sqrt.f64 x)))) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.7b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 (/.f64 1 x) 9)) 1))
	25.3b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 y 1))
	1.2b	(.f64 (.f64 (.f64 3 (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
▶	0.6b	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (*.f64 1/3 (sqrt.f64 (/.f64 1 x))))
	0.9b	(.f64 (.f64 (.f64 3 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	1.1b	(.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (sqrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	15.0b	(.f64 (.f64 (.f64 3 (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 y (/.f64 1 (.f64 x 9)))) 1)) (-.f64 (sqrt.f64 (+.f64 y (/.f64 1 (*.f64 x 9)))) 1))
	1.0b	(.f64 (.f64 (sqrt.f64 (.f64 3 (sqrt.f64 x))) (sqrt.f64 (.f64 3 (sqrt.f64 x)))) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	1.5b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 3 (sqrt.f64 x)) (+.f64 (-.f64 (/.f64 1/9 x) 1) y))) (cbrt.f64 (.f64 (.f64 3 (sqrt.f64 x)) (+.f64 (-.f64 (/.f64 1/9 x) 1) y)))) (cbrt.f64 (.f64 (.f64 3 (sqrt.f64 x)) (+.f64 (-.f64 (/.f64 1/9 x) 1) y))))
	0.7b	(.f64 3 (.f64 (sqrt.f64 x) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1)))

Compiler

Compiled 4453 to 3356 computations (24.6% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 3 y -3)
✓	0.2b	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (*.f64 1/3 (sqrt.f64 (/.f64 1 x))))
✓	0.4b	(sqrt.f64 (/.f64 1 x))
✓	0.4b	(*.f64 1/3 (sqrt.f64 (/.f64 1 x)))

series52.0ms (0.8%)

Counts

4 → 24

Calls

4 calls:

36.0ms	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (*.f64 1/3 (sqrt.f64 (/.f64 1 x))))
8.0ms	(*.f64 1/3 (sqrt.f64 (/.f64 1 x)))
6.0ms	(sqrt.f64 (/.f64 1 x))
2.0ms	(fma.f64 3 y -3)

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64`
29×	`sqrt-prod_binary64`
22×	`times-frac_binary64`
22×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`

Counts

4 → 87

Calls

4 calls:

6.0ms	(*.f64 1/3 (sqrt.f64 (/.f64 1 x)))
3.0ms	(sqrt.f64 (/.f64 1 x))
0.0ms	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (*.f64 1/3 (sqrt.f64 (/.f64 1 x))))
0.0ms	(fma.f64 3 y -3)

simplify76.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

853×	`associate-+l+_binary64`
393×	`distribute-lft-in_binary64`
393×	`distribute-rgt-in_binary64`
288×	`associate-l_binary64`
263×	`distribute-rgt-out_binary64`

Counts

111 → 116

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	102	1378
1	155	1248
2	265	1247
3	574	1247
4	2181	1247
5	5373	1247

prune221.0ms (3.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	113	3	116
Fresh	6	7	13
Picked	1	0	1
Done	0	0	0
Total	120	10	130

Error

0.0b

Counts

130 → 10

Alt Table

Status	Error	Program
	0.4b	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (*.f64 1/3 (pow.f64 x -1/2)))
	15.0b	(.f64 (.f64 (.f64 3 (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 y (/.f64 1 (.f64 x 9)))) 1)) (-.f64 (sqrt.f64 (+.f64 y (/.f64 1 (*.f64 x 9)))) 1))
	0.7b	(*.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3))
▶	0.4b	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (/.f64 1/3 (sqrt.f64 x)))
	0.9b	(.f64 (.f64 (.f64 3 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	1.1b	(.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (sqrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	20.3b	(fma.f64 (sqrt.f64 x) (cbrt.f64 (pow.f64 (fma.f64 3 y -3) 3)) (*.f64 1/3 (sqrt.f64 (/.f64 1 x))))
	0.7b	(.f64 3 (.f64 (sqrt.f64 x) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1)))
	0.7b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 (/.f64 1 x) 9)) 1))
	1.2b	(.f64 (.f64 (.f64 3 (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))

Compiler

Compiled 2520 to 1838 computations (27.1% saved)

localize14.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 3 y -3)
✓	0.2b	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (/.f64 1/3 (sqrt.f64 x)))
✓	0.4b	(/.f64 1/3 (sqrt.f64 x))

series102.0ms (1.5%)

Counts

2 → 12

Calls

2 calls:

69.0ms	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (/.f64 1/3 (sqrt.f64 x)))
32.0ms	(/.f64 1/3 (sqrt.f64 x))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`times-frac_binary64`
17×	`*-un-lft-identity_binary64`
17×	`add-sqr-sqrt_binary64`
17×	`add-cube-cbrt_binary64`
12×	`sqrt-prod_binary64`

Counts

2 → 51

Calls

2 calls:

6.0ms	(/.f64 1/3 (sqrt.f64 x))
3.0ms	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (/.f64 1/3 (sqrt.f64 x)))

simplify135.0ms (2%)

Algorithm

1×	egg-herbie

Rules

708×	`div-sub_binary64`
349×	`distribute-rgt-out_binary64`
299×	`associate-+r+_binary64`
280×	`associate-+l+_binary64`
257×	`*-commutative_binary64`

Counts

63 → 64

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	94	1035
1	149	911
2	259	911
3	460	911
4	1411	911
5	2863	911
6	4652	911
7	5715	911

prune152.0ms (2.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	77	2	79
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	80	9	89

Error

0.0b

Counts

89 → 9

Alt Table

Status	Error	Program
	0.7b	(*.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3))
✓	0.4b	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (/.f64 1/3 (sqrt.f64 x)))
	1.1b	(.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (sqrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	15.0b	(.f64 (.f64 (.f64 3 (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 y (/.f64 1 (.f64 x 9)))) 1)) (-.f64 (sqrt.f64 (+.f64 y (/.f64 1 (*.f64 x 9)))) 1))
	20.0b	(fma.f64 (sqrt.f64 x) (cbrt.f64 (pow.f64 (fma.f64 3 y -3) 3)) (/.f64 1/3 (sqrt.f64 x)))
▶	0.6b	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (/.f64 (/.f64 1/3 (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))))
	0.7b	(.f64 3 (.f64 (sqrt.f64 x) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1)))
	0.7b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 (/.f64 1 x) 9)) 1))
	1.2b	(.f64 (.f64 (.f64 3 (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))

Compiler

Compiled 1608 to 1025 computations (36.3% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (/.f64 (/.f64 1/3 (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))))
✓	0.4b	(/.f64 (/.f64 1/3 (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x)))
✓	0.4b	(/.f64 1/3 (fabs.f64 (cbrt.f64 x)))
✓	0.6b	(cbrt.f64 x)

series523.0ms (7.6%)

Counts

4 → 49

Calls

4 calls:

219.0ms	(/.f64 (/.f64 1/3 (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x)))
143.0ms	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (/.f64 (/.f64 1/3 (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))))
90.0ms	(/.f64 1/3 (fabs.f64 (cbrt.f64 x)))
71.0ms	(cbrt.f64 x)

rewrite90.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

696×	`times-frac_binary64`
421×	`add-sqr-sqrt_binary64`
353×	`*-un-lft-identity_binary64`
353×	`add-cube-cbrt_binary64`
253×	`cbrt-prod_binary64`

Counts

4 → 480

Calls

4 calls:

16.0ms	(/.f64 (/.f64 1/3 (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x)))
4.0ms	(/.f64 1/3 (fabs.f64 (cbrt.f64 x)))
1.0ms	(cbrt.f64 x)
0.0ms	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (/.f64 (/.f64 1/3 (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))))

simplify1.0s (15.2%)

Algorithm

1×	egg-herbie

Rules

651×	`times-frac_binary64`
459×	`associate-/l*_binary64`
313×	`associate-/r*_binary64`
298×	`associate-l_binary64`
274×	`associate-/l/_binary64`

Counts

529 → 690

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	511	16009
1	1084	14023
2	1571	13434
3	3566	12746
4	4685	12746
5	4993	12746
6	4935	12746

prune999.0ms (14.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	708	0	708
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	708	9	717

Error

0.0b

Counts

717 → 9

Alt Table

Status	Error	Program
	0.7b	(*.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3))
✓	0.4b	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (/.f64 1/3 (sqrt.f64 x)))
	1.1b	(.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (sqrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	15.0b	(.f64 (.f64 (.f64 3 (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 y (/.f64 1 (.f64 x 9)))) 1)) (-.f64 (sqrt.f64 (+.f64 y (/.f64 1 (*.f64 x 9)))) 1))
	20.0b	(fma.f64 (sqrt.f64 x) (cbrt.f64 (pow.f64 (fma.f64 3 y -3) 3)) (/.f64 1/3 (sqrt.f64 x)))
✓	0.6b	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (/.f64 (/.f64 1/3 (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))))
	0.7b	(.f64 3 (.f64 (sqrt.f64 x) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1)))
	0.7b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 (/.f64 1 x) 9)) 1))
	1.2b	(.f64 (.f64 (.f64 3 (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))

Compiler

Compiled 20085 to 10005 computations (50.2% saved)

regimes799.0ms (11.6%)

Accuracy

Total 0.3b remaining (90.3%)

Threshold costs 0.3b (90.3%)

Counts

115 → 1

Compiler

Compiled 8609 to 6914 computations (19.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	10	16

end1.0ms (0%)

Compiler: Compiled 13 to 9 computations (30.8% saved)

sample1.3s (19.3%)

Algorithm

1×

intervals

Results

721.0ms	8000×	body	128	valid
11.0ms	129×	body	128	nan
11.0ms	77×	body	128	invalid

Compiler

Compiled 193 to 151 computations (21.8% saved)

Details

analyze288.0ms (4.2%)

sample43.0ms (0.6%)

simplify234.0ms (3.4%)

prune7.0ms (0.1%)

localize17.0ms (0.2%)

series85.0ms (1.2%)

rewrite63.0ms (0.9%)

simplify144.0ms (2.1%)

prune399.0ms (5.8%)

localize10.0ms (0.1%)

series52.0ms (0.8%)

rewrite13.0ms (0.2%)

simplify76.0ms (1.1%)

prune221.0ms (3.2%)

localize14.0ms (0.2%)

series102.0ms (1.5%)

rewrite13.0ms (0.2%)

simplify135.0ms (2%)

prune152.0ms (2.2%)

localize23.0ms (0.3%)

series523.0ms (7.6%)

rewrite90.0ms (1.3%)

simplify1.0s (15.2%)

prune999.0ms (14.5%)

regimes799.0ms (11.6%)

simplify3.0ms (0%)

end1.0ms (0%)

sample1.3s (19.3%)

Profiling