Details

analyze746.0ms (13.8%)

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
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
28.1%	71.8%	0.1%	9
42.1%	57.7%	0.1%	10
49.1%	50.7%	0.1%	11
57.3%	42.5%	0.1%	12
66.9%	33%	0.1%	13
71.7%	28.2%	0.1%	14

Compiler

Compiled 16 to 10 computations (37.5% saved)

sample32.0ms (0.6%)

Algorithm

1×

intervals

Results

10.0ms

256×

body

128

valid

Compiler

Compiled 34 to 22 computations (35.3% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
3×	`associate-+r+_binary64`
3×	`associate-+l+_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	14	18
2	20	18
3	20	18
4	20	18

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

35.3b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	35.3b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

Compiler

Compiled 30 to 18 computations (40% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
0.0b	(+.f64 (.f64 x x) (.f64 y y))
32.9b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

rewrite44.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

35.3b

Rules

10×	`add-log-exp_binary64`
5×	`add-sqr-sqrt_binary64`
4×	`sum-log_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`

Counts

3 → 39

Calls

3 calls:

7.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
6.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
4.0ms	(+.f64 (.f64 x x) (.f64 y y))

Compiler

Compiled 886 to 154 computations (82.6% saved)

series199.0ms (3.7%)

Error

0.5b

Counts

3 → 53

Calls

3 calls:

93.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
42.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
23.0ms	(+.f64 (.f64 x x) (.f64 y y))

Compiler

Compiled 2334 to 1833 computations (21.5% saved)

simplify549.0ms (10.2%)

Algorithm

1×	egg-herbie

Rules

877×	`associate-/l*_binary64`
392×	`distribute-rgt-in_binary64`
329×	`distribute-lft-in_binary64`
282×	`cancel-sign-sub-inv_binary64`
146×	`sub-neg_binary64`

Counts

92 → 79

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	210	2080
1	571	2015
2	2224	1984
3	5642	1984

prune52.0ms (1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	75	4	79
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	75	5	80

Error

4.0b

Counts

80 → 5

Alt Table

Status	Error	Program
▶	28.5b	(neg.f64 x)
✓	35.3b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
	34.1b	(+.f64 (neg.f64 x) (.f64 -1/2 (+.f64 (/.f64 (.f64 y y) x) (/.f64 (*.f64 z z) x))))
	47.7b	(sqrt.f64 (*.f64 x x))
	38.6b	(+.f64 z (.f64 1/2 (+.f64 (/.f64 (.f64 x x) z) (/.f64 (*.f64 y y) z))))

Compiler

Compiled 1322 to 469 computations (64.5% saved)

localize2.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

4.0b

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

Error: 4.0b
Counts: 0 → 0
Compiler: Compiled 0 to 0 computations (0% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune7.0ms (0.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	3	3
Picked	1	1
Done	1	1
Total	5	5

Error

4.0b

Counts

5 → 5

Alt Table

Status	Error	Program
✓	28.5b	(neg.f64 x)
✓	35.3b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
▶	34.1b	(+.f64 (neg.f64 x) (.f64 -1/2 (+.f64 (/.f64 (.f64 y y) x) (/.f64 (*.f64 z z) x))))
	47.7b	(sqrt.f64 (*.f64 x x))
	38.6b	(+.f64 z (.f64 1/2 (+.f64 (/.f64 (.f64 x x) z) (/.f64 (*.f64 y y) z))))

Compiler

Compiled 108 to 69 computations (36.1% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(.f64 -1/2 (+.f64 (/.f64 (.f64 y y) x) (/.f64 (*.f64 z z) x)))
5.1b	(/.f64 (*.f64 z z) x)
9.2b	(/.f64 (*.f64 y y) x)

rewrite114.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

3.9b

Rules

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

Counts

3 → 67

Calls

3 calls:

17.0ms	(.f64 -1/2 (+.f64 (/.f64 (.f64 y y) x) (/.f64 (*.f64 z z) x)))
9.0ms	(/.f64 (*.f64 z z) x)
8.0ms	(/.f64 (*.f64 y y) x)

Compiler

Compiled 1505 to 451 computations (70% saved)

series164.0ms (3%)

Error

4.0b

Counts

3 → 27

Calls

3 calls:

92.0ms	(.f64 -1/2 (+.f64 (/.f64 (.f64 y y) x) (/.f64 (*.f64 z z) x)))
33.0ms	(/.f64 (*.f64 z z) x)
28.0ms	(/.f64 (*.f64 y y) x)

Compiler

Compiled 1022 to 739 computations (27.7% saved)

simplify175.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

488×	`associate-*l/_binary64`
440×	`associate-l_binary64`
435×	`associate-/l*_binary64`
415×	`associate-*r/_binary64`
352×	`times-frac_binary64`

Counts

94 → 59

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	143	1319
1	363	1216
2	1087	1216
3	4333	1216
4	4856	1216
5	4998	1216
6	4927	1216

prune44.0ms (0.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	56	3	59
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	57	7	64

Error

3.9b

Counts

64 → 7

Alt Table

Status	Error	Program
✓	28.5b	(neg.f64 x)
✓	35.3b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
	32.4b	(+.f64 (neg.f64 x) (.f64 -1/2 (+.f64 (/.f64 (.f64 y y) x) (/.f64 (.f64 (/.f64 z (.f64 (cbrt.f64 x) (cbrt.f64 x))) z) (cbrt.f64 x)))))
	32.4b	(+.f64 (neg.f64 x) (.f64 -1/2 (+.f64 (/.f64 (.f64 y y) x) (*.f64 z (/.f64 z x)))))
	47.7b	(sqrt.f64 (*.f64 x x))
	38.6b	(+.f64 z (.f64 1/2 (+.f64 (/.f64 (.f64 x x) z) (/.f64 (*.f64 y y) z))))
▶	30.5b	(+.f64 (neg.f64 x) (.f64 -1/2 (+.f64 (.f64 y (/.f64 y x)) (/.f64 (*.f64 z z) x))))

Compiler

Compiled 661 to 288 computations (56.4% saved)

localize15.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(.f64 -1/2 (+.f64 (.f64 y (/.f64 y x)) (/.f64 (*.f64 z z) x)))
0.1b	(*.f64 y (/.f64 y x))
5.1b	(/.f64 (*.f64 z z) x)

rewrite140.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

3.9b

Rules

22×	`add-sqr-sqrt_binary64`
16×	`associate-r_binary64`
15×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`
15×	`add-cbrt-cube_binary64`

Counts

3 → 76

Calls

3 calls:

14.0ms	(.f64 -1/2 (+.f64 (.f64 y (/.f64 y x)) (/.f64 (*.f64 z z) x)))
13.0ms	(*.f64 y (/.f64 y x))
6.0ms	(/.f64 (*.f64 z z) x)

Compiler

Compiled 1733 to 521 computations (69.9% saved)

series130.0ms (2.4%)

Error

3.9b

Counts

3 → 27

Calls

3 calls:

66.0ms	(.f64 -1/2 (+.f64 (.f64 y (/.f64 y x)) (/.f64 (*.f64 z z) x)))
30.0ms	(*.f64 y (/.f64 y x))
29.0ms	(/.f64 (*.f64 z z) x)

Compiler

Compiled 1022 to 739 computations (27.7% saved)

simplify129.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

499×	`associate-*l/_binary64`
468×	`associate-/l*_binary64`
433×	`associate-*r/_binary64`
387×	`times-frac_binary64`
240×	`distribute-rgt-in_binary64`

Counts

103 → 78

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	162	1450
1	418	1329
2	1322	1326
3	4390	1318
4	4928	1318
5	4997	1318
6	4933	1318

prune41.0ms (0.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	78	7	85

Error

3.9b

Counts

85 → 7

Alt Table

Status	Error	Program
	28.5b	(neg.f64 x)
	35.3b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
	32.4b	(+.f64 (neg.f64 x) (.f64 -1/2 (+.f64 (/.f64 (.f64 y y) x) (/.f64 (.f64 (/.f64 z (.f64 (cbrt.f64 x) (cbrt.f64 x))) z) (cbrt.f64 x)))))
	32.4b	(+.f64 (neg.f64 x) (.f64 -1/2 (+.f64 (/.f64 (.f64 y y) x) (*.f64 z (/.f64 z x)))))
	47.7b	(sqrt.f64 (*.f64 x x))
	38.6b	(+.f64 z (.f64 1/2 (+.f64 (/.f64 (.f64 x x) z) (/.f64 (*.f64 y y) z))))
	30.5b	(+.f64 (neg.f64 x) (.f64 -1/2 (+.f64 (.f64 y (/.f64 y x)) (/.f64 (*.f64 z z) x))))

Compiler

Compiled 1056 to 366 computations (65.3% saved)

regimes1.2s (22.6%)

Accuracy

Total 5.7b remaining (53%)

Threshold costs 0b (0%)

Compiler

Compiled 6463 to 4287 computations (33.7% saved)

bsearch61.0ms (1.1%)

Steps

Iters	Range		Point
8	3.81854460665572e+146	1.9447331195050446e+149	4.6936553999927715e+146
6	2.3297348762896703e+43	2.9250099537376085e+44	2.392365744457182e+43
6	8.723736205411303	136.07900477509125	132.10635457596226
2	4.325482253372271e-112	4.952763135801352e-112	4.403892363675905e-112

Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
4×	`*-commutative_binary64`
2×	`unsub-neg_binary64`
1×	`sub-neg_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	42	103
1	56	99
2	60	99
3	61	99
4	61	99

end17.0ms (0.3%)

Compiler: Compiled 210 to 120 computations (42.9% saved)

sample1.5s (27%)

Algorithm

1×

intervals

Results

389.0ms

8000×

body

128

valid

Compiler

Compiled 198 to 121 computations (38.9% saved)

Details

analyze746.0ms (13.8%)

sample32.0ms (0.6%)

simplify9.0ms (0.2%)

prune2.0ms (0%)

localize13.0ms (0.2%)

rewrite44.0ms (0.8%)

series199.0ms (3.7%)

simplify549.0ms (10.2%)

prune52.0ms (1%)

localize2.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify8.0ms (0.1%)

prune7.0ms (0.1%)

localize13.0ms (0.2%)

rewrite114.0ms (2.1%)

series164.0ms (3%)

simplify175.0ms (3.2%)

prune44.0ms (0.8%)

localize15.0ms (0.3%)

rewrite140.0ms (2.6%)

series130.0ms (2.4%)

simplify129.0ms (2.4%)

prune41.0ms (0.8%)

regimes1.2s (22.6%)

bsearch61.0ms (1.1%)

simplify6.0ms (0.1%)

end17.0ms (0.3%)

sample1.5s (27%)

Profiling