Details

analyze75.0ms (1.9%)

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)

sample1.2s (29.4%)

Results

1.0s	8256×	body	128	valid
21.0ms	188×	body	128	invalid

Compiler

Compiled 50 to 41 computations (18% saved)

simplify182.0ms (4.6%)

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

prune4.0ms (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

0.3b

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)

localize10.0ms (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))
✓	0.3b	(*.f64 3 (sqrt.f64 x))
✓	0.3b	(/.f64 1 (*.f64 x 9))

series61.0ms (1.5%)

Counts

4 → 48

Calls

4 calls:

42.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
12.0ms	(*.f64 3 (sqrt.f64 x))
5.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
2.0ms	(/.f64 1 (*.f64 x 9))

rewrite238.0ms (6%)

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:

87.0ms	(/.f64 1 (*.f64 x 9))
12.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
4.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
4.0ms	(*.f64 3 (sqrt.f64 x))

simplify83.0ms (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`
290×	`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

prune220.0ms (5.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	163	8	171
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	164	9	173

Error

0.0b

Counts

173 → 9

Alt Table

Status	Error	Program
	24.4b	(.f64 (sqrt.f64 (.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))) (sqrt.f64 (.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))))
	0.8b	(.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (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 1/3 (sqrt.f64 (/.f64 1 x))))
	12.9b	(.f64 (.f64 (.f64 3 (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 y (/.f64 1 (.f64 x 9)))) (sqrt.f64 1))) (-.f64 (sqrt.f64 (+.f64 y (/.f64 1 (*.f64 x 9)))) (sqrt.f64 1)))
	1.4b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))) (cbrt.f64 (.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1)))) (cbrt.f64 (.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))))
	0.6b	(.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))
	19.7b	(.f64 (cbrt.f64 (.f64 (.f64 (.f64 3 (sqrt.f64 x)) (.f64 3 (sqrt.f64 x))) (.f64 3 (sqrt.f64 x)))) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.4b	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 (-.f64 (/.f64 1/9 x) 1) y)))
	0.4b	(*.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3))

Compiler

Compiled 4317 to 3260 computations (24.5% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(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))))
✓	0.4b	(*.f64 1/3 (sqrt.f64 (/.f64 1 x)))

series47.0ms (1.2%)

Counts

4 → 24

Calls

4 calls:

30.0ms	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (*.f64 1/3 (sqrt.f64 (/.f64 1 x))))
9.0ms	(*.f64 1/3 (sqrt.f64 (/.f64 1 x)))
6.0ms	(sqrt.f64 (/.f64 1 x))
2.0ms	(fma.f64 3 y -3)

rewrite23.0ms (0.6%)

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:

15.0ms	(*.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)

simplify71.0ms (1.8%)

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

prune131.0ms (3.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	114	2	116
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	116	9	125

Error

0.0b

Counts

125 → 9

Alt Table

Status	Error	Program
▶	0.4b	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (/.f64 1/3 (sqrt.f64 x)))
	0.6b	(.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	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (*.f64 1/3 (sqrt.f64 (/.f64 1 x))))
	0.5b	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (.f64 (sqrt.f64 (.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (sqrt.f64 (*.f64 1/3 (sqrt.f64 (/.f64 1 x))))))
	0.8b	(.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (sqrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	12.9b	(.f64 (.f64 (.f64 3 (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 y (/.f64 1 (.f64 x 9)))) (sqrt.f64 1))) (-.f64 (sqrt.f64 (+.f64 y (/.f64 1 (*.f64 x 9)))) (sqrt.f64 1)))
	19.7b	(.f64 (cbrt.f64 (.f64 (.f64 (.f64 3 (sqrt.f64 x)) (.f64 3 (sqrt.f64 x))) (.f64 3 (sqrt.f64 x)))) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.4b	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 (-.f64 (/.f64 1/9 x) 1) y)))
	0.4b	(*.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3))

Compiler

Compiled 2503 to 1826 computations (27% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(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))

series77.0ms (2%)

Counts

2 → 12

Calls

2 calls:

41.0ms	(/.f64 1/3 (sqrt.f64 x))
36.0ms	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (/.f64 1/3 (sqrt.f64 x)))

rewrite8.0ms (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:

5.0ms	(/.f64 1/3 (sqrt.f64 x))
0.0ms	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (/.f64 1/3 (sqrt.f64 x)))

simplify96.0ms (2.4%)

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

prune89.0ms (2.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	78	1	79
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	79	9	88

Error

0.0b

Counts

88 → 9

Alt Table

Status	Error	Program
✓	0.4b	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (/.f64 1/3 (sqrt.f64 x)))
	0.6b	(.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	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (*.f64 1/3 (sqrt.f64 (/.f64 1 x))))
	0.5b	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (*.f64 (sqrt.f64 (/.f64 1/3 (sqrt.f64 x))) (sqrt.f64 (/.f64 1/3 (sqrt.f64 x)))))
	0.8b	(.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (sqrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	12.9b	(.f64 (.f64 (.f64 3 (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 y (/.f64 1 (.f64 x 9)))) (sqrt.f64 1))) (-.f64 (sqrt.f64 (+.f64 y (/.f64 1 (*.f64 x 9)))) (sqrt.f64 1)))
	19.7b	(.f64 (cbrt.f64 (.f64 (.f64 (.f64 3 (sqrt.f64 x)) (.f64 3 (sqrt.f64 x))) (.f64 3 (sqrt.f64 x)))) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
▶	0.4b	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 (-.f64 (/.f64 1/9 x) 1) y)))
	0.4b	(*.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3))

Compiler

Compiled 1621 to 1033 computations (36.3% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series71.0ms (1.8%)

Counts

4 → 48

Calls

4 calls:

38.0ms	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 (-.f64 (/.f64 1/9 x) 1) y)))
23.0ms	(*.f64 (sqrt.f64 x) (+.f64 (-.f64 (/.f64 1/9 x) 1) y))
6.0ms	(+.f64 (-.f64 (/.f64 1/9 x) 1) y)
4.0ms	(/.f64 1/9 x)

rewrite54.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`add-sqr-sqrt_binary64`
66×	`*-un-lft-identity_binary64`
52×	`add-cube-cbrt_binary64`
43×	`associate-+l+_binary64`
39×	`prod-diff_binary64`

Counts

4 → 155

Calls

4 calls:

14.0ms	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 (-.f64 (/.f64 1/9 x) 1) y)))
13.0ms	(+.f64 (-.f64 (/.f64 1/9 x) 1) y)
13.0ms	(*.f64 (sqrt.f64 x) (+.f64 (-.f64 (/.f64 1/9 x) 1) y))
2.0ms	(/.f64 1/9 x)

simplify74.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

922×	`distribute-rgt-in_binary64`
905×	`distribute-lft-in_binary64`
285×	`fma-def_binary64`
119×	`associate-l_binary64`
117×	`associate-r_binary64`

Counts

203 → 222

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	178	2465
1	382	2234
2	1227	2200
3	5247	2200

prune282.0ms (7.1%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	220	2	222
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	221	10	231

Error

Counts

231 → 10

Alt Table

Status	Error	Program
✓	0.4b	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (/.f64 1/3 (sqrt.f64 x)))
	0.6b	(.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 (/.f64 1/9 x) 1) y))
✓	0.4b	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 (-.f64 (/.f64 1/9 x) 1) y)))
	0.6b	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (.f64 (sqrt.f64 x) (+.f64 (-.f64 (/.f64 1/9 x) 1) y))))
✓	0.4b	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (*.f64 1/3 (sqrt.f64 (/.f64 1 x))))
	0.5b	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (*.f64 (sqrt.f64 (/.f64 1/3 (sqrt.f64 x))) (sqrt.f64 (/.f64 1/3 (sqrt.f64 x)))))
	0.8b	(.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (sqrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	12.9b	(.f64 (.f64 (.f64 3 (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 y (/.f64 1 (.f64 x 9)))) (sqrt.f64 1))) (-.f64 (sqrt.f64 (+.f64 y (/.f64 1 (*.f64 x 9)))) (sqrt.f64 1)))
	19.7b	(.f64 (cbrt.f64 (.f64 (.f64 (.f64 3 (sqrt.f64 x)) (.f64 3 (sqrt.f64 x))) (.f64 3 (sqrt.f64 x)))) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))

Compiler

Compiled 5153 to 3793 computations (26.4% saved)

regimes706.0ms (17.9%)

Accuracy

Total 0.4b remaining (89.9%)

Threshold costs 0.4b (89.9%)

Counts

179 → 1

Compiler

Compiled 10815 to 8441 computations (22% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	19
1	16	19
2	15	19

end159.0ms (4%)

Compiler: Compiled 227 to 179 computations (21.1% saved)

Details

analyze75.0ms (1.9%)

sample1.2s (29.4%)

simplify182.0ms (4.6%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

series61.0ms (1.5%)

rewrite238.0ms (6%)

simplify83.0ms (2.1%)

prune220.0ms (5.6%)

localize9.0ms (0.2%)

series47.0ms (1.2%)

rewrite23.0ms (0.6%)

simplify71.0ms (1.8%)

prune131.0ms (3.3%)

localize7.0ms (0.2%)

series77.0ms (2%)

rewrite8.0ms (0.2%)

simplify96.0ms (2.4%)

prune89.0ms (2.3%)

localize8.0ms (0.2%)

series71.0ms (1.8%)

rewrite54.0ms (1.4%)

simplify74.0ms (1.9%)

prune282.0ms (7.1%)

regimes706.0ms (17.9%)

simplify5.0ms (0.1%)

end159.0ms (4%)

Profiling