Details

analyze14.0ms (0.5%)

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
49.9%	49.9%	0.1%	5
74.9%	25%	0.1%	6
87.4%	12.5%	0.1%	7
93.6%	6.2%	0.1%	8
96.7%	3.1%	0.1%	9
98.3%	1.6%	0.1%	10
99.1%	0.8%	0.1%	11
99.5%	0.4%	0.1%	12
99.7%	0.2%	0.1%	13
99.8%	0.1%	0.1%	14

Compiler

Compiled 15 to 12 computations (20% saved)

sample19.0ms (0.6%)

Algorithm

1×

intervals

Results

11.0ms

256×

body

valid

Compiler

Compiled 29 to 26 computations (10.3% saved)

simplify12.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	22	21
1	22	21

prune8.0ms (0.3%)

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: 35.6b

Counts

2 → 1

Compiler

Compiled 28 to 22 computations (21.4% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.1b	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3)
33.1b	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))

rewrite23.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
19×	`times-frac_binary64`
18×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
13×	`sqrt-prod_binary64`
5×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`pow1_binary64`
3×	`associate-/r_binary64` `associate-/l_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `flip-+_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `+-commutative_binary64` `sqrt-div_binary64` `sum-log_binary64`

Counts

3 → 65

Calls

3 calls:

10.0ms	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3)
7.0ms	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))
5.0ms	(+.f64 (.f64 x x) (.f64 y y))

series52.0ms (1.7%)

Counts

3 → 9

Calls

3 calls:

31.0ms	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))
15.0ms	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3)
6.0ms	(+.f64 (.f64 x x) (.f64 y y))

simplify82.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5216	1857

prune74.0ms (2.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	68	6	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	6	75

Merged error: 17.8b

Counts

75 → 6

Compiler

Compiled 1740 to 546 computations (68.6% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.4b	(.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z))) (sqrt.f64 1/3))
33.1b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

rewrite26.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
13×	`sqrt-prod_binary64`
8×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
6×	`associate-r_binary64` `associate-l_binary64`
5×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`unswap-sqr_binary64` `sqrt-div_binary64`
3×	`pow-prod-down_binary64` `flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `flip-+_binary64`
2×	`associate-*l/_binary64`
1×	`cbrt-unprod_binary64` `sqrt-unprod_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

3 → 58

Calls

3 calls:

12.0ms	(.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z))) (sqrt.f64 1/3))
8.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
5.0ms	(+.f64 (.f64 x x) (.f64 y y))

series59.0ms (2%)

Counts

3 → 9

Calls

3 calls:

31.0ms	(.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z))) (sqrt.f64 1/3))
22.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
6.0ms	(+.f64 (.f64 x x) (.f64 y y))

simplify99.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4950	1486
1	4950	1486

prune47.0ms (1.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	66	1	67
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	66	7	73

Merged error: 17.8b

Counts

73 → 7

Compiler

Compiled 1564 to 493 computations (68.5% saved)

localize12.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.4b	(/.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) (sqrt.f64 3))
33.1b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

rewrite25.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`sqrt-prod_binary64`
36×	`times-frac_binary64`
33×	`add-sqr-sqrt_binary64`
32×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`associate-/r_binary64` `associate-/l_binary64`
5×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`pow1_binary64` `sqrt-div_binary64`
3×	`flip3-+_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

3 → 89

Calls

3 calls:

11.0ms	(/.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) (sqrt.f64 3))
6.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
5.0ms	(+.f64 (.f64 x x) (.f64 y y))

series67.0ms (2.2%)

Counts

3 → 9

Calls

3 calls:

38.0ms	(/.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) (sqrt.f64 3))
23.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
7.0ms	(+.f64 (.f64 x x) (.f64 y y))

simplify94.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5130	3024

prune74.0ms (2.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	95	3	98
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	95	10	105

Merged error: 17.7b

Counts

105 → 10

Compiler

Compiled 2555 to 760 computations (70.3% saved)

localize16.0ms (0.5%)

Local error

Found 4 expressions with local error:

18.9b	(sqrt.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z))) (cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))) (sqrt.f64 3)))
34.1b	(cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
34.1b	(cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
34.1b	(cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

rewrite36.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`sqrt-prod_binary64`
13×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`cbrt-prod_binary64`
8×	`times-frac_binary64`
6×	`cbrt-div_binary64`
5×	`pow1_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`flip3-+_binary64` `pow1/3_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `div-inv_binary64` `sqrt-div_binary64`

Counts

4 → 62

Calls

4 calls:

13.0ms	(sqrt.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z))) (cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))) (sqrt.f64 3)))
8.0ms	(cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
7.0ms	(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)))

series162.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

61.0ms	(sqrt.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z))) (cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))) (sqrt.f64 3)))
36.0ms	(cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
33.0ms	(cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
32.0ms	(cbrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

simplify78.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5384	2338

prune58.0ms (1.9%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	74	10	84

Merged error: 17.7b

Counts

84 → 10

Compiler

Compiled 3946 to 962 computations (75.6% saved)

regimes571.0ms (19%)

Compiler: Compiled 1466 to 1152 computations (21.4% saved)

bsearch31.0ms (1%)

Steps

Iters	Range		Point
7	8.287372697218046e+142	3.119550877101529e+144	2.926732043878023e+143
10	-3.8685841581220905e+118	-2.037343040940111e+105	-3.825103058543913e+118

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	49
1	42	49

end0.0ms (0%)

sample1.2s (41.3%)

Algorithm

1×

intervals

Results

363.0ms

8000×

body

valid

Compiler

Compiled 198 to 160 computations (19.2% saved)

Details

analyze14.0ms (0.5%)

sample19.0ms (0.6%)

simplify12.0ms (0.4%)

prune8.0ms (0.3%)

localize9.0ms (0.3%)

rewrite23.0ms (0.8%)

series52.0ms (1.7%)

simplify82.0ms (2.7%)

prune74.0ms (2.5%)

localize10.0ms (0.3%)

rewrite26.0ms (0.9%)

series59.0ms (2%)

simplify99.0ms (3.3%)

prune47.0ms (1.6%)

localize12.0ms (0.4%)

rewrite25.0ms (0.8%)

series67.0ms (2.2%)

simplify94.0ms (3.1%)

prune74.0ms (2.5%)

localize16.0ms (0.5%)

rewrite36.0ms (1.2%)

series162.0ms (5.4%)

simplify78.0ms (2.6%)

prune58.0ms (1.9%)

regimes571.0ms (19%)

bsearch31.0ms (1%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.2s (41.3%)

Profiling