Details

analyze69.0ms (1.6%)

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)

sample1.1s (25.5%)

Results

947.0ms	8256×	body	128	valid
19.0ms	191×	body	128	invalid

Compiler

Compiled 50 to 41 computations (18% saved)

simplify181.0ms (4.2%)

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

prune3.0ms (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

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.4b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.4b	(*.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3))

Compiler

Compiled 85 to 66 computations (22.4% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 y (/.f64 1 (*.f64 x 9)))
✓	0.2b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
✓	0.2b	(/.f64 1 (*.f64 x 9))
✓	0.3b	(*.f64 3 (sqrt.f64 x))

series44.0ms (1%)

Counts

4 → 48

Calls

4 calls:

27.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
10.0ms	(*.f64 3 (sqrt.f64 x))
4.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
2.0ms	(/.f64 1 (*.f64 x 9))

rewrite33.0ms (0.8%)

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:

14.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
4.0ms	(*.f64 3 (sqrt.f64 x))
4.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
3.0ms	(/.f64 1 (*.f64 x 9))

simplify78.0ms (1.8%)

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

prune193.0ms (4.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	161	10	171
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	163	10	173

Error

0.0b

Counts

173 → 10

Alt Table

Status	Error	Program
	0.9b	(.f64 (.f64 (.f64 3 (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
▶	0.3b	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (*.f64 1/3 (sqrt.f64 (/.f64 1 x))))
	0.4b	(.f64 3 (.f64 (sqrt.f64 x) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1)))
	1.4b	(.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))))
	0.6b	(.f64 (.f64 (.f64 3 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	1.4b	(.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))
	0.7b	(.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (sqrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	0.9b	(.f64 (.f64 (.f64 3 (sqrt.f64 x)) (.f64 (cbrt.f64 (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1)) (cbrt.f64 (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1)))) (cbrt.f64 (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1)))
	0.7b	(.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))
	0.4b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (.f64 (sqrt.f64 (/.f64 1 (.f64 x 9))) (sqrt.f64 (/.f64 1 (*.f64 x 9))))) 1))

Compiler

Compiled 4363 to 3288 computations (24.6% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 3 y -3)
✓	0.1b	(sqrt.f64 (/.f64 1 x))
✓	0.2b	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (*.f64 1/3 (sqrt.f64 (/.f64 1 x))))
✓	0.3b	(*.f64 1/3 (sqrt.f64 (/.f64 1 x)))

series37.0ms (0.9%)

Counts

4 → 24

Calls

4 calls:

24.0ms	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (*.f64 1/3 (sqrt.f64 (/.f64 1 x))))
6.0ms	(*.f64 1/3 (sqrt.f64 (/.f64 1 x)))
5.0ms	(sqrt.f64 (/.f64 1 x))
2.0ms	(fma.f64 3 y -3)

rewrite11.0ms (0.3%)

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:

5.0ms	(*.f64 1/3 (sqrt.f64 (/.f64 1 x)))
2.0ms	(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)

simplify72.0ms (1.7%)

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

prune146.0ms (3.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	113	3	116
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	116	10	126

Error

Counts

126 → 10

Alt Table

Status	Error	Program
	20.7b	(fma.f64 (sqrt.f64 x) (cbrt.f64 (pow.f64 (fma.f64 3 y -3) 3)) (*.f64 1/3 (sqrt.f64 (/.f64 1 x))))
	0.6b	(.f64 (.f64 (.f64 3 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
▶	0.3b	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (/.f64 1/3 (sqrt.f64 x)))
	0.7b	(.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (sqrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	0.4b	(.f64 3 (.f64 (sqrt.f64 x) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1)))
	1.4b	(.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))))
✓	0.3b	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (*.f64 1/3 (sqrt.f64 (/.f64 1 x))))
	0.4b	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (.f64 (.f64 1/3 (sqrt.f64 (/.f64 1 (*.f64 (cbrt.f64 x) (cbrt.f64 x))))) (sqrt.f64 (/.f64 1 (cbrt.f64 x)))))
	0.9b	(.f64 (.f64 (.f64 3 (sqrt.f64 x)) (.f64 (cbrt.f64 (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1)) (cbrt.f64 (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1)))) (cbrt.f64 (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1)))
	0.7b	(.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))

Compiler

Compiled 2611 to 1904 computations (27.1% saved)

localize6.0ms (0.1%)

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)))
✓	0.3b	(/.f64 1/3 (sqrt.f64 x))

series40.0ms (0.9%)

Counts

2 → 12

Calls

2 calls:

27.0ms	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (/.f64 1/3 (sqrt.f64 x)))
13.0ms	(/.f64 1/3 (sqrt.f64 x))

rewrite5.0ms (0.1%)

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:

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

simplify89.0ms (2.1%)

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

prune86.0ms (2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	76	3	79
Fresh	3	5	8
Picked	1	0	1
Done	1	0	1
Total	81	8	89

Error

Counts

89 → 8

Alt Table

Status	Error	Program
	0.6b	(.f64 (.f64 (.f64 3 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
▶	0.4b	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (/.f64 (/.f64 1/3 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))))
	0.7b	(.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (sqrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	0.9b	(.f64 (.f64 (.f64 3 (sqrt.f64 x)) (.f64 (cbrt.f64 (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1)) (cbrt.f64 (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1)))) (cbrt.f64 (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1)))
	0.4b	(.f64 3 (.f64 (sqrt.f64 x) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1)))
	0.7b	(.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))
	20.7b	(fma.f64 (sqrt.f64 x) (cbrt.f64 (pow.f64 (fma.f64 3 y -3) 3)) (/.f64 1/3 (sqrt.f64 x)))
	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (/.f64 1/3 (sqrt.f64 x)))) (cbrt.f64 (fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (/.f64 1/3 (sqrt.f64 x))))) (cbrt.f64 (fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (/.f64 1/3 (sqrt.f64 x)))))

Compiler

Compiled 1685 to 1070 computations (36.5% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(sqrt.f64 (sqrt.f64 x))
✓	0.2b	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (/.f64 (/.f64 1/3 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))))
✓	0.3b	(/.f64 (/.f64 1/3 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))
✓	0.4b	(/.f64 1/3 (sqrt.f64 (sqrt.f64 x)))

series77.0ms (1.8%)

Counts

4 → 28

Calls

4 calls:

24.0ms	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (/.f64 (/.f64 1/3 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))))
24.0ms	(/.f64 1/3 (sqrt.f64 (sqrt.f64 x)))
17.0ms	(sqrt.f64 (sqrt.f64 x))
13.0ms	(/.f64 (/.f64 1/3 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))

rewrite70.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

604×	`sqrt-prod_binary64`
576×	`times-frac_binary64`
316×	`add-sqr-sqrt_binary64`
314×	`*-un-lft-identity_binary64`
314×	`add-cube-cbrt_binary64`

Counts

4 → 420

Calls

4 calls:

11.0ms	(/.f64 (/.f64 1/3 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))
3.0ms	(/.f64 1/3 (sqrt.f64 (sqrt.f64 x)))
1.0ms	(sqrt.f64 (sqrt.f64 x))
0.0ms	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (/.f64 (/.f64 1/3 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))))

simplify417.0ms (9.7%)

Algorithm

1×	egg-herbie

Rules

605×	`associate-/l/_binary64`
420×	`*-commutative_binary64`
359×	`times-frac_binary64`
329×	`associate-/r*_binary64`
274×	`fma-neg_binary64`

Counts

448 → 419

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	323	11984
1	653	11524
2	1115	10916
3	2410	10808
4	3742	10793
5	4892	10793
6	4914	10793

prune460.0ms (10.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	441	0	441
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	441	8	449

Error

Counts

449 → 8

Alt Table

Status	Error	Program
	0.6b	(.f64 (.f64 (.f64 3 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
✓	0.4b	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (/.f64 (/.f64 1/3 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))))
	0.7b	(.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (sqrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	0.9b	(.f64 (.f64 (.f64 3 (sqrt.f64 x)) (.f64 (cbrt.f64 (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1)) (cbrt.f64 (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1)))) (cbrt.f64 (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1)))
	0.4b	(.f64 3 (.f64 (sqrt.f64 x) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1)))
	0.7b	(.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))
	20.7b	(fma.f64 (sqrt.f64 x) (cbrt.f64 (pow.f64 (fma.f64 3 y -3) 3)) (/.f64 1/3 (sqrt.f64 x)))
	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (/.f64 1/3 (sqrt.f64 x)))) (cbrt.f64 (fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (/.f64 1/3 (sqrt.f64 x))))) (cbrt.f64 (fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (/.f64 1/3 (sqrt.f64 x)))))

Compiler

Compiled 12086 to 5720 computations (52.7% saved)

regimes927.0ms (21.5%)

Accuracy

Total 0.4b remaining (91.8%)

Threshold costs 0.4b (91.8%)

Counts

245 → 1

Compiler

Compiled 17631 to 12761 computations (27.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	10	16

end134.0ms (3.1%)

Compiler: Compiled 219 to 162 computations (26% saved)

Details

analyze69.0ms (1.6%)

sample1.1s (25.5%)

simplify181.0ms (4.2%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

series44.0ms (1%)

rewrite33.0ms (0.8%)

simplify78.0ms (1.8%)

prune193.0ms (4.5%)

localize8.0ms (0.2%)

series37.0ms (0.9%)

rewrite11.0ms (0.3%)

simplify72.0ms (1.7%)

prune146.0ms (3.4%)

localize6.0ms (0.1%)

series40.0ms (0.9%)

rewrite5.0ms (0.1%)

simplify89.0ms (2.1%)

prune86.0ms (2%)

localize8.0ms (0.2%)

series77.0ms (1.8%)

rewrite70.0ms (1.6%)

simplify417.0ms (9.7%)

prune460.0ms (10.7%)

regimes927.0ms (21.5%)

simplify2.0ms (0%)

end134.0ms (3.1%)

Profiling