Details

analyze570.0ms (12.9%)

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%	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)

sample17.0ms (0.4%)

Algorithm

1×

intervals

Results

9.0ms

256×

body

128

valid

Compiler

Compiled 25 to 22 computations (12% saved)

simplify128.0ms (2.9%)

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: 41.5b

Counts

2 → 1

Compiler

Compiled 24 to 18 computations (25% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))
38.7b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

rewrite12.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-sqr-sqrt_binary64_17832` `add-log-exp_binary64_17849`
3×	`sqrt-prod_binary64_17826` `*-un-lft-identity_binary64_17810` `add-cube-cbrt_binary64_17845` `pow1_binary64_17871`
2×	`sqrt-div_binary64_17827` `flip-+_binary64_17784` `add-exp-log_binary64_17848` `flip3-+_binary64_17813` `add-cbrt-cube_binary64_17846`
1×	`sum-log_binary64_17901` `sqrt-pow1_binary64_17828` `+-commutative_binary64_17740` `rem-sqrt-square_binary64_17823` `pow1/2_binary64_17890`

Counts

2 → 26

Calls

2 calls:

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

series102.0ms (2.3%)

Counts

2 → 6

Calls

2 calls:

82.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
20.0ms	(+.f64 (.f64 x x) (.f64 y y))

simplify75.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5150	566

prune32.0ms (0.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	28	4	32
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	28	5	33

Merged error: 22.2b

Counts

33 → 5

Compiler

Compiled 601 to 136 computations (77.4% saved)

localize21.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))))
38.7b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
38.7b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
38.7b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

rewrite33.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`sqrt-prod_binary64_17826` `add-sqr-sqrt_binary64_17832`
9×	`*-un-lft-identity_binary64_17810` `add-cube-cbrt_binary64_17845`
8×	`sqrt-div_binary64_17827`
7×	`pow1_binary64_17871`
6×	`cbrt-prod_binary64_17841`
4×	`flip-+_binary64_17784` `add-exp-log_binary64_17848` `flip3-+_binary64_17813` `add-log-exp_binary64_17849` `add-cbrt-cube_binary64_17846`
3×	`sqrt-pow1_binary64_17828` `rem-sqrt-square_binary64_17823` `pow1/2_binary64_17890`
2×	`cbrt-div_binary64_17842`
1×	`pow1/3_binary64_17892`

Counts

4 → 61

Calls

4 calls:

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

series397.0ms (9%)

Counts

4 → 12

Calls

4 calls:

117.0ms	(cbrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))))
97.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
93.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
90.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

simplify62.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4826	1597
1	4826	1597

prune91.0ms (2.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	72	1	73
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	73	5	78

Merged error: 22.2b

Counts

78 → 5

Compiler

Compiled 3477 to 340 computations (90.2% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

5.4b	(pow.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) 1/3)
38.7b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
38.7b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
38.7b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

rewrite46.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_17832`
12×	`sqrt-prod_binary64_17826`
10×	`*-un-lft-identity_binary64_17810` `add-cube-cbrt_binary64_17845`
9×	`pow1_binary64_17871`
6×	`sqrt-div_binary64_17827` `unpow-prod-down_binary64_17889`
5×	`add-exp-log_binary64_17848`
4×	`sqrt-pow1_binary64_17828` `add-log-exp_binary64_17849` `add-cbrt-cube_binary64_17846` `pow1/2_binary64_17890`
3×	`flip-+_binary64_17784` `pow-unpow_binary64_17887` `flip3-+_binary64_17813` `pow-pow_binary64_17882` `rem-sqrt-square_binary64_17823`
1×	`pow-exp_binary64_17878` `sqr-pow_binary64_17782` `unpow1/3_binary64_17877` `pow-to-exp_binary64_17879` `sqrt-pow2_binary64_17829`

Counts

4 → 69

Calls

4 calls:

12.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
9.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
8.0ms	(pow.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) 1/3)
6.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

series326.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

102.0ms	(pow.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) 1/3)
84.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
77.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
63.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

simplify70.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5018	1628

prune106.0ms (2.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	80	1	81
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	81	5	86

Merged error: 22.2b

Counts

86 → 5

Compiler

Compiled 3844 to 477 computations (87.6% saved)

localize25.0ms (0.6%)

Local error

Found 4 expressions with local error:

5.6b	(pow.f64 (pow.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z))) (.f64 (cbrt.f64 1/3) (cbrt.f64 1/3))) (cbrt.f64 1/3))
38.7b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
38.7b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
38.7b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

rewrite59.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`unpow-prod-down_binary64_17889`
15×	`add-sqr-sqrt_binary64_17832`
12×	`sqrt-prod_binary64_17826` `*-un-lft-identity_binary64_17810` `add-cube-cbrt_binary64_17845`
7×	`pow1_binary64_17871`
6×	`sqrt-div_binary64_17827` `pow-unpow_binary64_17887` `add-exp-log_binary64_17848`
4×	`pow-exp_binary64_17878` `add-log-exp_binary64_17849` `add-cbrt-cube_binary64_17846`
3×	`sqrt-pow1_binary64_17828` `flip-+_binary64_17784` `flip3-+_binary64_17813` `cbrt-prod_binary64_17841` `rem-sqrt-square_binary64_17823` `pow1/2_binary64_17890`
2×	`sqr-pow_binary64_17782` `pow-to-exp_binary64_17879`
1×	`pow-pow_binary64_17882`

Counts

4 → 74

Calls

4 calls:

17.0ms	(pow.f64 (pow.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z))) (.f64 (cbrt.f64 1/3) (cbrt.f64 1/3))) (cbrt.f64 1/3))
12.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
9.0ms	(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)))

series679.0ms (15.4%)

Counts

4 → 12

Calls

4 calls:

435.0ms	(pow.f64 (pow.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z))) (.f64 (cbrt.f64 1/3) (cbrt.f64 1/3))) (cbrt.f64 1/3))
89.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
84.0ms	(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)))

simplify83.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5115	2370

prune144.0ms (3.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	86	5	91

Merged error: 22.2b

Counts

91 → 5

Compiler

Compiled 4763 to 1124 computations (76.4% saved)

regimes452.0ms (10.3%)

Compiler: Compiled 3767 to 1625 computations (56.9% saved)

bsearch33.0ms (0.8%)

Steps

Iters	Range		Point
9	1.2124735833772275e+81	2.814636941475208e+90	2.8403577741388615e+85
9	-1.7012109344729206e+83	-3.2006161138958354e+76	-1.6747749261665936e+83

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	34
1	27	34

end0.0ms (0%)

sample805.0ms (18.3%)

Algorithm

1×

intervals

Results

346.0ms

8000×

body

128

valid

Compiler

Compiled 318 to 153 computations (51.9% saved)

Details

analyze570.0ms (12.9%)

sample17.0ms (0.4%)

simplify128.0ms (2.9%)

prune2.0ms (0.1%)

localize8.0ms (0.2%)

rewrite12.0ms (0.3%)

series102.0ms (2.3%)

simplify75.0ms (1.7%)

prune32.0ms (0.7%)

localize21.0ms (0.5%)

rewrite33.0ms (0.7%)

series397.0ms (9%)

simplify62.0ms (1.4%)

prune91.0ms (2.1%)

localize18.0ms (0.4%)

rewrite46.0ms (1.1%)

series326.0ms (7.4%)

simplify70.0ms (1.6%)

prune106.0ms (2.4%)

localize25.0ms (0.6%)

rewrite59.0ms (1.4%)

series679.0ms (15.4%)

simplify83.0ms (1.9%)

prune144.0ms (3.3%)

regimes452.0ms (10.3%)

bsearch33.0ms (0.8%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample805.0ms (18.3%)

Profiling