Details

analyze236.0ms (5.3%)

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)

sample20.0ms (0.4%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
0.0ms	6×	body	128	nan
0.0ms	4×	body	128	invalid

Compiler

Compiled 35 to 29 computations (17.1% saved)

simplify155.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

326×	`associate-/l*_binary64`
318×	`cancel-sign-sub-inv_binary64`
290×	`distribute-rgt-neg-in_binary64`
248×	`distribute-rgt-in_binary64`
231×	`unsub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	28	18
2	68	18
3	137	18
4	197	18
5	297	18
6	671	18
7	1065	18
8	1544	18
9	1657	18
10	1839	18
11	1771	18
12	1745	18
13	1745	18
14	1943	18
15	1776	18
16	1776	18
17	1776	18
18	1583	18

prune6.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.3b

Counts

2 → 2

Alt Table

Status	Error	Program
▶	0.3b	(.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 1/9 x) (+.f64 y -1)))

Compiler

Compiled 74 to 59 computations (20.3% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1)
0.3b	(.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))

rewrite178.0ms (4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

29×	`*-un-lft-identity_binary64`
25×	`add-sqr-sqrt_binary64`
22×	`add-exp-log_binary64`
16×	`add-cbrt-cube_binary64`
15×	`associate-r_binary64`

Counts

4 → 108

Calls

4 calls:

14.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
8.0ms	(-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1)
5.0ms	(*.f64 3 (sqrt.f64 x))
5.0ms	(/.f64 1 (*.f64 x 9))

Compiler

Compiled 2017 to 1510 computations (25.1% saved)

series78.0ms (1.8%)

Error

0.1b

Counts

4 → 27

Calls

4 calls:

33.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
22.0ms	(-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1)
7.0ms	(*.f64 3 (sqrt.f64 x))
6.0ms	(/.f64 1 (*.f64 x 9))

Compiler

Compiled 828 to 645 computations (22.1% saved)

simplify99.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

507×	`times-frac_binary64`
499×	`distribute-rgt-in_binary64`
481×	`distribute-lft-in_binary64`
282×	`associate-/l*_binary64`
197×	`associate-/r*_binary64`

Counts

135 → 100

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	168	2001
1	387	1603
2	1242	1595
3	4780	1595
4	4939	1595

prune82.0ms (1.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	91	9	100
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	92	10	102

Error

0.0b

Counts

102 → 10

Alt Table

Status	Error	Program
	1.3b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 3 (sqrt.f64 x)) (+.f64 y (-.f64 (/.f64 1/9 x) 1)))) (cbrt.f64 (.f64 (.f64 3 (sqrt.f64 x)) (+.f64 y (-.f64 (/.f64 1/9 x) 1))))) (cbrt.f64 (.f64 (.f64 3 (sqrt.f64 x)) (+.f64 y (-.f64 (/.f64 1/9 x) 1)))))
	0.7b	(.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 x) (sqrt.f64 3))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
✓	0.3b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.4b	(+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (.f64 3 (.f64 (sqrt.f64 x) (-.f64 (/.f64 1/9 x) 1))))
	33.9b	(cbrt.f64 (pow.f64 (.f64 (.f64 3 (sqrt.f64 x)) (+.f64 y (-.f64 (/.f64 1/9 x) 1))) 3))
	19.6b	(.f64 (cbrt.f64 (pow.f64 (.f64 3 (sqrt.f64 x)) 3)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	28.5b	(.f64 (sqrt.f64 (.f64 (.f64 3 (sqrt.f64 x)) (+.f64 y (-.f64 (/.f64 1/9 x) 1)))) (sqrt.f64 (.f64 (*.f64 3 (sqrt.f64 x)) (+.f64 y (-.f64 (/.f64 1/9 x) 1)))))
	1.0b	(.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	(+.f64 (.f64 1/3 (sqrt.f64 (/.f64 1 x))) (.f64 (*.f64 3 (sqrt.f64 x)) (-.f64 y 1)))
	28.5b	(.f64 (.f64 (.f64 3 (sqrt.f64 x)) (sqrt.f64 (+.f64 y (-.f64 (/.f64 1/9 x) 1)))) (sqrt.f64 (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1)))

Compiler

Compiled 1323 to 989 computations (25.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (/.f64 1 x))
0.1b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 y 1))
0.3b	(*.f64 3 (sqrt.f64 x))
0.4b	(*.f64 1/3 (sqrt.f64 (/.f64 1 x)))

rewrite212.0ms (4.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

47×	`add-sqr-sqrt_binary64`
33×	`sqrt-prod_binary64`
31×	`*-un-lft-identity_binary64`
29×	`associate-r_binary64`
26×	`add-cube-cbrt_binary64`

Counts

4 → 117

Calls

4 calls:

9.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 y 1))
8.0ms	(*.f64 1/3 (sqrt.f64 (/.f64 1 x)))
5.0ms	(*.f64 3 (sqrt.f64 x))
3.0ms	(sqrt.f64 (/.f64 1 x))

Compiler

Compiled 2258 to 1677 computations (25.7% saved)

series55.0ms (1.2%)

Error

0.0b

Counts

4 → 18

Calls

4 calls:

27.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 y 1))
8.0ms	(*.f64 1/3 (sqrt.f64 (/.f64 1 x)))
8.0ms	(*.f64 3 (sqrt.f64 x))
7.0ms	(sqrt.f64 (/.f64 1 x))

Compiler

Compiled 741 to 590 computations (20.4% saved)

simplify132.0ms (3%)

Algorithm

1×	egg-herbie

Rules

498×	`unsub-neg_binary64`
330×	`*-commutative_binary64`
232×	`exp-prod_binary64`
223×	`associate-/l*_binary64`
214×	`times-frac_binary64`

Counts

135 → 82

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	174	1574
1	357	1468
2	917	1464
3	1819	1464
4	3258	1464
5	4721	1464
6	4973	1464

prune82.0ms (1.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	78	4	82
Fresh	3	5	8
Picked	1	0	1
Done	0	1	1
Total	82	10	92

Error

0.0b

Counts

92 → 10

Alt Table

Status	Error	Program
	1.3b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 3 (sqrt.f64 x)) (+.f64 y (-.f64 (/.f64 1/9 x) 1)))) (cbrt.f64 (.f64 (.f64 3 (sqrt.f64 x)) (+.f64 y (-.f64 (/.f64 1/9 x) 1))))) (cbrt.f64 (.f64 (.f64 3 (sqrt.f64 x)) (+.f64 y (-.f64 (/.f64 1/9 x) 1)))))
	0.7b	(.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 x) (sqrt.f64 3))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
✓	0.3b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.6b	(+.f64 (.f64 1/3 (sqrt.f64 (/.f64 1 x))) (.f64 (.f64 (.f64 3 (sqrt.f64 x)) (*.f64 (cbrt.f64 (+.f64 y -1)) (cbrt.f64 (+.f64 y -1)))) (cbrt.f64 (-.f64 y 1))))
	25.3b	(+.f64 (.f64 1/3 (sqrt.f64 (/.f64 1 x))) (cbrt.f64 (.f64 27 (pow.f64 (*.f64 (sqrt.f64 x) (+.f64 y -1)) 3))))
	0.3b	(+.f64 (/.f64 1/3 (sqrt.f64 x)) (.f64 (.f64 3 (sqrt.f64 x)) (-.f64 y 1)))
	19.6b	(.f64 (cbrt.f64 (pow.f64 (.f64 3 (sqrt.f64 x)) 3)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
▶	0.3b	(+.f64 (.f64 1/3 (sqrt.f64 (/.f64 1 x))) (.f64 3 (*.f64 (sqrt.f64 x) (+.f64 y -1))))
	1.0b	(.f64 (.f64 (.f64 3 (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	28.5b	(.f64 (.f64 (.f64 3 (sqrt.f64 x)) (sqrt.f64 (+.f64 y (-.f64 (/.f64 1/9 x) 1)))) (sqrt.f64 (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1)))

Compiler

Compiled 1319 to 999 computations (24.3% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (/.f64 1 x))
0.1b	(*.f64 (sqrt.f64 x) (+.f64 y -1))
0.3b	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 y -1)))
0.4b	(*.f64 1/3 (sqrt.f64 (/.f64 1 x)))

rewrite193.0ms (4.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

42×	`add-sqr-sqrt_binary64`
33×	`sqrt-prod_binary64`
28×	`*-un-lft-identity_binary64`
24×	`add-cube-cbrt_binary64`
22×	`times-frac_binary64` `associate-r_binary64`

Counts

4 → 115

Calls

4 calls:

8.0ms	(*.f64 1/3 (sqrt.f64 (/.f64 1 x)))
8.0ms	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 y -1)))
7.0ms	(*.f64 (sqrt.f64 x) (+.f64 y -1))
3.0ms	(sqrt.f64 (/.f64 1 x))

Compiler

Compiled 2210 to 1625 computations (26.5% saved)

series72.0ms (1.6%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

28.0ms	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 y -1)))
22.0ms	(*.f64 (sqrt.f64 x) (+.f64 y -1))
9.0ms	(sqrt.f64 (/.f64 1 x))
8.0ms	(*.f64 1/3 (sqrt.f64 (/.f64 1 x)))

Compiler

Compiled 945 to 730 computations (22.8% saved)

simplify113.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

451×	`distribute-rgt-in_binary64`
433×	`distribute-lft-in_binary64`
364×	`times-frac_binary64`
307×	`*-commutative_binary64`
254×	`+-commutative_binary64`

Counts

139 → 86

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	176	1662
1	369	1548
2	1018	1541
3	2454	1541
4	4352	1541
5	4993	1541

prune94.0ms (2.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	83	3	86
Fresh	2	6	8
Picked	1	0	1
Done	0	1	1
Total	86	10	96

Error

0.0b

Counts

96 → 10

Alt Table

Status	Error	Program
	1.3b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 3 (sqrt.f64 x)) (+.f64 y (-.f64 (/.f64 1/9 x) 1)))) (cbrt.f64 (.f64 (.f64 3 (sqrt.f64 x)) (+.f64 y (-.f64 (/.f64 1/9 x) 1))))) (cbrt.f64 (.f64 (.f64 3 (sqrt.f64 x)) (+.f64 y (-.f64 (/.f64 1/9 x) 1)))))
✓	0.3b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.6b	(+.f64 (.f64 1/3 (sqrt.f64 (/.f64 1 x))) (.f64 (.f64 (.f64 3 (sqrt.f64 x)) (*.f64 (cbrt.f64 (+.f64 y -1)) (cbrt.f64 (+.f64 y -1)))) (cbrt.f64 (-.f64 y 1))))
▶	0.3b	(+.f64 (/.f64 1/3 (sqrt.f64 x)) (.f64 (.f64 3 (sqrt.f64 x)) (-.f64 y 1)))
	19.6b	(.f64 (cbrt.f64 (pow.f64 (.f64 3 (sqrt.f64 x)) 3)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.6b	(+.f64 (.f64 1/3 (sqrt.f64 (/.f64 1 x))) (.f64 (sqrt.f64 x) (+.f64 -3 (*.f64 3 y))))
	1.0b	(.f64 (.f64 (.f64 3 (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	0.8b	(+.f64 (.f64 1/3 (sqrt.f64 (/.f64 1 x))) (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 x) (.f64 (+.f64 y -1) (sqrt.f64 3)))))
	28.5b	(.f64 (.f64 (.f64 3 (sqrt.f64 x)) (sqrt.f64 (+.f64 y (-.f64 (/.f64 1/9 x) 1)))) (sqrt.f64 (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1)))
	0.5b	(+.f64 (.f64 1/3 (sqrt.f64 (/.f64 1 x))) (.f64 3 (.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (+.f64 y -1) (sqrt.f64 (sqrt.f64 x))))))

Compiler

Compiled 1416 to 1054 computations (25.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 1/3 (sqrt.f64 x)) (.f64 (.f64 3 (sqrt.f64 x)) (-.f64 y 1)))
0.1b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 y 1))
0.3b	(*.f64 3 (sqrt.f64 x))
0.4b	(/.f64 1/3 (sqrt.f64 x))

rewrite191.0ms (4.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

35×	`add-sqr-sqrt_binary64`
30×	`*-un-lft-identity_binary64`
27×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`
16×	`sqrt-prod_binary64`

Counts

4 → 114

Calls

4 calls:

12.0ms	(+.f64 (/.f64 1/3 (sqrt.f64 x)) (.f64 (.f64 3 (sqrt.f64 x)) (-.f64 y 1)))
9.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 y 1))
5.0ms	(*.f64 3 (sqrt.f64 x))
4.0ms	(/.f64 1/3 (sqrt.f64 x))

Compiler

Compiled 2174 to 1405 computations (35.4% saved)

series87.0ms (1.9%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

37.0ms	(+.f64 (/.f64 1/3 (sqrt.f64 x)) (.f64 (.f64 3 (sqrt.f64 x)) (-.f64 y 1)))
26.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 y 1))
8.0ms	(/.f64 1/3 (sqrt.f64 x))
7.0ms	(*.f64 3 (sqrt.f64 x))

Compiler

Compiled 891 to 671 computations (24.7% saved)

simplify142.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

389×	`*-commutative_binary64`
346×	`cancel-sign-sub-inv_binary64`
339×	`distribute-rgt-in_binary64`
314×	`distribute-lft-in_binary64`
285×	`times-frac_binary64`

Counts

138 → 89

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	197	2031
1	453	1943
2	1205	1921
3	2970	1911
4	4029	1911
5	4871	1911

prune84.0ms (1.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	87	2	89
Fresh	3	5	8
Picked	1	0	1
Done	0	1	1
Total	91	8	99

Error

0.0b

Counts

99 → 8

Alt Table

Status	Error	Program
	0.3b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	17.6b	(/.f64 (+.f64 (.f64 1/3 (+.f64 y 1)) (.f64 (+.f64 -1 (.f64 y y)) (.f64 x 3))) (*.f64 (sqrt.f64 x) (+.f64 y 1)))
	19.6b	(.f64 (cbrt.f64 (pow.f64 (.f64 3 (sqrt.f64 x)) 3)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.6b	(+.f64 (.f64 1/3 (sqrt.f64 (/.f64 1 x))) (.f64 (sqrt.f64 x) (+.f64 -3 (*.f64 3 y))))
	0.8b	(+.f64 (.f64 1/3 (sqrt.f64 (/.f64 1 x))) (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 x) (.f64 (+.f64 y -1) (sqrt.f64 3)))))
	28.4b	(.f64 (sqrt.f64 (+.f64 (.f64 3 (.f64 (sqrt.f64 x) (-.f64 y 1))) (/.f64 1/3 (sqrt.f64 x)))) (sqrt.f64 (+.f64 (.f64 3 (*.f64 (sqrt.f64 x) (-.f64 y 1))) (/.f64 1/3 (sqrt.f64 x)))))
	28.5b	(.f64 (.f64 (.f64 3 (sqrt.f64 x)) (sqrt.f64 (+.f64 y (-.f64 (/.f64 1/9 x) 1)))) (sqrt.f64 (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1)))
	0.5b	(+.f64 (.f64 1/3 (sqrt.f64 (/.f64 1 x))) (.f64 3 (.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (+.f64 y -1) (sqrt.f64 (sqrt.f64 x))))))

Compiler

Compiled 1170 to 787 computations (32.7% saved)

regimes1.3s (29.6%)

Accuracy

Total 0.3b remaining (88.3%)

Threshold costs 0.3b (88.3%)

Compiler

Compiled 18779 to 14870 computations (20.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
2×	`+-commutative_binary64`
1×	`1-exp_binary64` `sub-neg_binary64` `*-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	23
1	25	23
2	26	23
3	24	23

end1.0ms (0%)

Compiler: Compiled 17 to 14 computations (17.6% saved)

sample787.0ms (17.6%)

Algorithm

1×

intervals

Results

354.0ms	8000×	body	128	valid
6.0ms	150×	body	128	nan
3.0ms	66×	body	128	invalid

Compiler

Compiled 212 to 168 computations (20.8% saved)

Details

analyze236.0ms (5.3%)

sample20.0ms (0.4%)

simplify155.0ms (3.5%)

prune6.0ms (0.1%)

localize14.0ms (0.3%)

rewrite178.0ms (4%)

series78.0ms (1.8%)

simplify99.0ms (2.2%)

prune82.0ms (1.8%)

localize10.0ms (0.2%)

rewrite212.0ms (4.7%)

series55.0ms (1.2%)

simplify132.0ms (3%)

prune82.0ms (1.8%)

localize11.0ms (0.2%)

rewrite193.0ms (4.3%)

series72.0ms (1.6%)

simplify113.0ms (2.5%)

prune94.0ms (2.1%)

localize10.0ms (0.2%)

rewrite191.0ms (4.3%)

series87.0ms (1.9%)

simplify142.0ms (3.2%)

prune84.0ms (1.9%)

regimes1.3s (29.6%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample787.0ms (17.6%)

Profiling