Details

analyze452.0ms (10.5%)

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 13 to 10 computations (23.1% saved)

sample18.0ms (0.4%)

Algorithm

1×

intervals

Results

10.0ms

256×

body

128

valid

Compiler

Compiled 25 to 22 computations (12% saved)

simplify92.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	18
1	20	18

prune3.0ms (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

36.4b

Counts

2 → 1

Compiler

Compiled 24 to 18 computations (25% saved)

localize13.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.0b	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
33.8b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

rewrite19.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-log-exp_binary64_17167`
5×	`add-sqr-sqrt_binary64_17150`
4×	`add-cube-cbrt_binary64_17163` `pow1_binary64_17189` `*-un-lft-identity_binary64_17128` `sum-log_binary64_17219`
3×	`flip-+_binary64_17102` `add-cbrt-cube_binary64_17164` `add-exp-log_binary64_17166` `sqrt-prod_binary64_17144` `flip3-+_binary64_17131`
2×	`sqrt-div_binary64_17145` `+-commutative_binary64_17058`
1×	`sqrt-pow1_binary64_17146` `pow1/2_binary64_17208` `associate-+l+_binary64_17061` `rem-sqrt-square_binary64_17141`

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))

series119.0ms (2.8%)

Counts

3 → 9

Calls

3 calls:

67.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
33.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
19.0ms	(+.f64 (.f64 x x) (.f64 y y))

simplify83.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4954	904
1	4954	904

prune40.0ms (0.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	43	5	48
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	43	6	49

Error

17.3b

Counts

49 → 6

Compiler

Compiled 895 to 187 computations (79.1% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.5b	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)))) (sqrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))))
33.8b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
33.8b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

rewrite56.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`sqrt-prod_binary64_17144`
58×	`add-sqr-sqrt_binary64_17150`
34×	`sqrt-pow1_binary64_17146`
29×	`pow1_binary64_17189`
28×	`sqrt-div_binary64_17145`
18×	`add-cube-cbrt_binary64_17163` `*-un-lft-identity_binary64_17128` `pow1/2_binary64_17208`
15×	`swap-sqr_binary64_17095`
10×	`rem-sqrt-square_binary64_17141`
9×	`associate-r_binary64_17068` `flip-+_binary64_17102` `unswap-sqr_binary64_17096` `associate-l_binary64_17069` `flip3-+_binary64_17131` `pow-prod-up_binary64_17198`
6×	`add-cbrt-cube_binary64_17164` `add-exp-log_binary64_17166` `add-log-exp_binary64_17167`
5×	`pow-sqr_binary64_17101` `pow-prod-down_binary64_17199`
4×	`frac-times_binary64_17138` `sqr-abs_binary64_17143`
2×	`associate-r/_binary64_17070` `associate-l/_binary64_17071`
1×	`cbrt-unprod_binary64_17161` `rem-square-sqrt_binary64_17140` `prod-exp_binary64_17177` `+-commutative_binary64_17058` `*-commutative_binary64_17059` `sum-log_binary64_17219` `pow2_binary64_17209` `pow-plus_binary64_17191` `sqrt-unprod_binary64_17148`

Counts

4 → 128

Calls

4 calls:

25.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)))) (sqrt.f64 (sqrt.f64 (+.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)))
5.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
4.0ms	(+.f64 (.f64 x x) (.f64 y y))

series245.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

84.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)))) (sqrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))))
71.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
70.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
19.0ms	(+.f64 (.f64 x x) (.f64 y y))

simplify93.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4942	3154
1	4942	3154

prune111.0ms (2.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	140	6	146

Error

17.3b

Counts

146 → 6

Compiler

Compiled 3937 to 475 computations (87.9% saved)

localize12.0ms (0.3%)

Local error

Found 4 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))
5.9b	(exp.f64 (log.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))))
33.8b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

rewrite30.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-log-exp_binary64_17167`
9×	`add-sqr-sqrt_binary64_17150`
8×	`add-cube-cbrt_binary64_17163` `*-un-lft-identity_binary64_17128`
7×	`pow1_binary64_17189`
6×	`sqrt-prod_binary64_17144` `exp-sum_binary64_17174` `exp-prod_binary64_17180` `log-prod_binary64_17214`
4×	`sqrt-div_binary64_17145` `flip-+_binary64_17102` `add-cbrt-cube_binary64_17164` `add-exp-log_binary64_17166` `sum-log_binary64_17219` `flip3-+_binary64_17131`
3×	`log-pow_binary64_17217`
2×	`exp-diff_binary64_17176` `log-div_binary64_17215` `sqrt-pow1_binary64_17146` `+-commutative_binary64_17058` `pow1/2_binary64_17208`
1×	`rem-exp-log_binary64_17168` `associate-+l+_binary64_17061` `rem-sqrt-square_binary64_17141`

Counts

4 → 61

Calls

4 calls:

8.0ms	(exp.f64 (log.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))))
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))

series223.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

99.0ms	(exp.f64 (log.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))))
72.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
33.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
19.0ms	(+.f64 (.f64 x x) (.f64 y y))

simplify70.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5068	1422

prune56.0ms (1.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	69	4	73
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	70	9	79

Error

17.3b

Counts

79 → 9

Compiler

Compiled 1485 to 320 computations (78.5% saved)

localize21.0ms (0.5%)

Local error

Found 4 expressions with local error:

6.0b	(pow.f64 (exp.f64 (.f64 (cbrt.f64 (log.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z))))) (cbrt.f64 (log.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z))))))) (cbrt.f64 (log.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z))))))
33.8b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
33.8b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
33.8b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

rewrite31.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_17150`
10×	`add-cube-cbrt_binary64_17163` `pow1_binary64_17189` `*-un-lft-identity_binary64_17128`
9×	`pow-unpow_binary64_17205` `sqrt-prod_binary64_17144`
6×	`sqrt-div_binary64_17145` `cbrt-prod_binary64_17159`
5×	`add-log-exp_binary64_17167`
4×	`add-cbrt-cube_binary64_17164` `add-exp-log_binary64_17166` `sqrt-pow1_binary64_17146` `pow1/2_binary64_17208`
3×	`unpow-prod-down_binary64_17207` `flip-+_binary64_17102` `pow-pow_binary64_17200` `log-pow_binary64_17217` `flip3-+_binary64_17131` `rem-sqrt-square_binary64_17141`
1×	`sqr-pow_binary64_17100` `exp-to-pow_binary64_17190` `exp-prod_binary64_17180` `pow-exp_binary64_17196` `pow-to-exp_binary64_17197`

Counts

4 → 70

Calls

4 calls:

6.0ms	(sqrt.f64 (+.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)))
6.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
4.0ms	(pow.f64 (exp.f64 (.f64 (cbrt.f64 (log.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z))))) (cbrt.f64 (log.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z))))))) (cbrt.f64 (log.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z))))))

series1.0s (23.9%)

Counts

4 → 12

Calls

4 calls:

829.0ms	(pow.f64 (exp.f64 (.f64 (cbrt.f64 (log.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z))))) (cbrt.f64 (log.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z))))))) (cbrt.f64 (log.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z))))))
68.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
66.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
62.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

simplify92.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4914	3052
1	4914	3052

prune112.0ms (2.6%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	78	4	82
Fresh	0	6	6
Picked	1	0	1
Done	0	2	2
Total	79	12	91

Error

17.3b

Counts

91 → 12

Compiler

Compiled 4257 to 391 computations (90.8% saved)

regimes436.0ms (10.1%)

Accuracy

Total 6.7b remaining (26.9%)

Threshold costs 0b (0%)

Compiler

Compiled 3058 to 1979 computations (35.3% saved)

bsearch33.0ms (0.8%)

Steps

Iters	Range		Point
6	1.726639105268989e+133	2.2301182389592457e+134	1.8617496421280384e+134
9	-4.168970572222628e+123	-4.2582851755946696e+117	-1.7691170303226253e+120

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	34
1	27	34

end0.0ms (0%)

sample798.0ms (18.6%)

Algorithm

1×

intervals

Results

318.0ms

8000×

body

128

valid

Compiler

Compiled 284 to 194 computations (31.7% saved)

Details

analyze452.0ms (10.5%)

sample18.0ms (0.4%)

simplify92.0ms (2.2%)

prune3.0ms (0.1%)

localize13.0ms (0.3%)

rewrite19.0ms (0.4%)

series119.0ms (2.8%)

simplify83.0ms (1.9%)

prune40.0ms (0.9%)

localize11.0ms (0.3%)

rewrite56.0ms (1.3%)

series245.0ms (5.7%)

simplify93.0ms (2.2%)

prune111.0ms (2.6%)

localize12.0ms (0.3%)

rewrite30.0ms (0.7%)

series223.0ms (5.2%)

simplify70.0ms (1.6%)

prune56.0ms (1.3%)

localize21.0ms (0.5%)

rewrite31.0ms (0.7%)

series1.0s (23.9%)

simplify92.0ms (2.1%)

prune112.0ms (2.6%)

regimes436.0ms (10.1%)

bsearch33.0ms (0.8%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample798.0ms (18.6%)

Profiling