Details

analyze457.0ms (15.4%)

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 (0.6%)

Algorithm

1×

intervals

Results

10.0ms

256×

body

128

valid

Compiler

Compiled 25 to 22 computations (12% saved)

simplify94.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	18
1	20	18

prune2.0ms (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

Merged error: 39.1b

Counts

2 → 1

Compiler

Compiled 24 to 18 computations (25% saved)

localize8.0ms (0.3%)

Local error

Found 1 expressions with local error:

36.3b

(sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)))

rewrite8.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-sqr-sqrt_binary64_19537` `sqrt-prod_binary64_19531`
2×	`add-cube-cbrt_binary64_19550` `pow1_binary64_19576` `*-un-lft-identity_binary64_19515` `sqrt-div_binary64_19532`
1×	`flip-+_binary64_19489` `add-log-exp_binary64_19554` `sqrt-pow1_binary64_19533` `add-cbrt-cube_binary64_19551` `pow1/2_binary64_19595` `rem-sqrt-square_binary64_19528` `flip3-+_binary64_19518` `add-exp-log_binary64_19553`

Counts

1 → 15

Calls

1 calls:

6.0ms

(sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)))

series70.0ms (2.3%)

Counts

1 → 3

Calls

1 calls:

69.0ms

(sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)))

simplify60.0ms (2%)

Algorithm

1×	egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4939	373
1	4939	373

prune23.0ms (0.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	13	5	18
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	13	6	19

Merged error: 19.8b

Counts

19 → 6

Compiler

Compiled 368 to 91 computations (75.3% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))))
0.3b	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)))) (sqrt.f64 (cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))))
37.5b	(cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
37.5b	(cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

rewrite37.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_19537`
14×	`cbrt-prod_binary64_19546` `sqrt-prod_binary64_19531`
12×	`add-cube-cbrt_binary64_19550` `*-un-lft-identity_binary64_19515`
9×	`associate-r_binary64_19455`
8×	`cbrt-div_binary64_19547`
7×	`pow1_binary64_19576`
6×	`add-cbrt-cube_binary64_19551` `add-exp-log_binary64_19553`
4×	`flip-+_binary64_19489` `add-log-exp_binary64_19554` `sqrt-div_binary64_19532` `flip3-+_binary64_19518`
3×	`pow1/3_binary64_19597` `associate-l_binary64_19456` `unswap-sqr_binary64_19483`
2×	`associate-*r/_binary64_19457` `sqrt-pow1_binary64_19533` `rem-sqrt-square_binary64_19528`
1×	`cbrt-unprod_binary64_19548` `pow1/2_binary64_19595` `*-commutative_binary64_19446` `prod-exp_binary64_19564` `pow-prod-down_binary64_19586`

Counts

4 → 74

Calls

4 calls:

12.0ms	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)))) (sqrt.f64 (cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))))
6.0ms	(sqrt.f64 (cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))))
6.0ms	(cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
5.0ms	(cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

series494.0ms (16.7%)

Counts

4 → 12

Calls

4 calls:

185.0ms	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)))) (sqrt.f64 (cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))))
108.0ms	(cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
101.0ms	(sqrt.f64 (cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))))
99.0ms	(cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

simplify57.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5185	2828

prune85.0ms (2.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	86	6	92

Merged error: 19.8b

Counts

92 → 6

Compiler

Compiled 3187 to 396 computations (87.6% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b

(pow.f64 (sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z))) 3)

36.3b

(sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)))

46.5b

(cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z))) 3))

rewrite32.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`cbrt-prod_binary64_19546`
15×	`add-sqr-sqrt_binary64_19537` `sqrt-prod_binary64_19531`
14×	`add-cube-cbrt_binary64_19550` `*-un-lft-identity_binary64_19515`
12×	`unpow-prod-down_binary64_19594` `cube-prod_binary64_19543`
6×	`pow1_binary64_19576` `sqrt-div_binary64_19532`
4×	`add-cbrt-cube_binary64_19551` `cube-div_binary64_19544` `add-exp-log_binary64_19553`
3×	`pow-unpow_binary64_19592` `flip-+_binary64_19489` `add-log-exp_binary64_19554` `pow-pow_binary64_19587` `flip3-+_binary64_19518`
2×	`cube-mult_binary64_19545` `unpow3_binary64_19581` `sqrt-pow1_binary64_19533` `sqr-pow_binary64_19487` `pow1/2_binary64_19595` `cbrt-div_binary64_19547`
1×	`pow1/3_binary64_19597` `pow-to-exp_binary64_19584` `rem-cube-cbrt_binary64_19538` `sqrt-pow2_binary64_19534` `pow-exp_binary64_19583` `rem-sqrt-square_binary64_19528` `rem-cbrt-cube_binary64_19539`

Counts

3 → 78

Calls

3 calls:

8.0ms

(cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z))) 3))

8.0ms

(pow.f64 (sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z))) 3)

6.0ms

(sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)))

series308.0ms (10.4%)

Counts

3 → 9

Calls

3 calls:

175.0ms

(pow.f64 (sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z))) 3)

69.0ms

(cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z))) 3))

64.0ms

(sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)))

simplify71.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5003	2168

prune71.0ms (2.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	84	3	87
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	84	9	93

Merged error: 19.8b

Counts

93 → 9

Compiler

Compiled 1882 to 384 computations (79.6% saved)

localize3.0ms (0.1%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify9.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune1.0ms (0%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	5	5
Picked	1	1
Done	3	3
Total	9	9

Merged error: 19.8b

Counts

9 → 9

Compiler

Compiled 0 to 0 computations (0% saved)

regimes314.0ms (10.6%)

Compiler: Compiled 1398 to 1055 computations (24.5% saved)

bsearch38.0ms (1.3%)

Steps

Iters	Range		Point
10	9.15334201943951e+118	2.4364122440679375e+135	7.704060870309131e+133
10	-8.600402313932862e+154	-4.605328941081082e+141	-1.983993386737577e+145

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	34
1	27	34

end0.0ms (0%)

sample679.0ms (22.9%)

Algorithm

1×

intervals

Results

309.0ms

8000×

body

128

valid

Compiler

Compiled 156 to 119 computations (23.7% saved)

Details

analyze457.0ms (15.4%)

sample18.0ms (0.6%)

simplify94.0ms (3.2%)

prune2.0ms (0.1%)

localize8.0ms (0.3%)

rewrite8.0ms (0.3%)

series70.0ms (2.3%)

simplify60.0ms (2%)

prune23.0ms (0.8%)

localize11.0ms (0.4%)

rewrite37.0ms (1.3%)

series494.0ms (16.7%)

simplify57.0ms (1.9%)

prune85.0ms (2.9%)

localize10.0ms (0.3%)

rewrite32.0ms (1.1%)

series308.0ms (10.4%)

simplify71.0ms (2.4%)

prune71.0ms (2.4%)

localize3.0ms (0.1%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify9.0ms (0.3%)

prune1.0ms (0%)

regimes314.0ms (10.6%)

bsearch38.0ms (1.3%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample679.0ms (22.9%)

Profiling