Details

analyze230.0ms (3.2%)

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
49.9%	49.9%	0.1%	3
49.9%	49.9%	0.1%	4
49.9%	49.9%	0.1%	5
74.9%	25%	0.1%	6
74.9%	25%	0.1%	7
74.9%	25%	0.1%	8
87.4%	12.5%	0.1%	9
87.4%	12.5%	0.1%	10
87.4%	12.5%	0.1%	11
93.6%	6.2%	0.1%	12
93.6%	6.2%	0.1%	13
93.6%	6.2%	0.1%	14

Compiler

Compiled 24 to 21 computations (12.5% saved)

sample75.0ms (1%)

Algorithm

1×

intervals

Results

24.0ms	33×	body	4096	valid
17.0ms	170×	body	128	valid
12.0ms	22×	body	2048	valid
7.0ms	18×	body	1024	valid
2.0ms	8×	body	512	valid
1.0ms	5×	body	256	valid

Compiler

Compiled 47 to 44 computations (6.4% saved)

simplify169.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4970	33
1	4970	33

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

29.8b

Counts

2 → 1

Compiler

Compiled 42 to 34 computations (19% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))) B)
0.0b	(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))) B)) PI.f64)
0.7b	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
36.7b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

rewrite67.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

53×	`*-un-lft-identity_binary64_2806`
49×	`add-sqr-sqrt_binary64_2828`
30×	`times-frac_binary64_2812`
28×	`add-cube-cbrt_binary64_2841`
15×	`distribute-lft-out--_binary64_2758`
11×	`sqrt-prod_binary64_2822`
10×	`sqrt-div_binary64_2823` `difference-of-squares_binary64_2775` `associate-/l*_binary64_2751`
9×	`cancel-sign-sub-inv_binary64_2772` `add-log-exp_binary64_2845`
8×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842` `frac-sub_binary64_2815`
6×	`associate-/l/_binary64_2753` `flip3--_binary64_2810` `associate-/r*_binary64_2750` `flip--_binary64_2781`
5×	`flip-+_binary64_2780` `flip3-+_binary64_2809` `pow1_binary64_2867`
4×	`associate--l+_binary64_2743`
3×	`diff-log_binary64_2898`
2×	`div-inv_binary64_2803` `div-exp_binary64_2857` `cbrt-undiv_binary64_2840` `sub-neg_binary64_2799` `clear-num_binary64_2805` `frac-2neg_binary64_2817`
1×	`pow1/2_binary64_2886` `sqrt-pow1_binary64_2824` `div-sub_binary64_2811` `associate--l-_binary64_2744` `rem-sqrt-square_binary64_2819`

Counts

4 → 123

Calls

4 calls:

20.0ms	(/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))) B)
17.0ms	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
5.0ms	(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))) B)) PI.f64)

series343.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

109.0ms	(/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))) B)
87.0ms	(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))) B)) PI.f64)
77.0ms	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
69.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

simplify94.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4957	4636
1	4957	4636

prune221.0ms (3.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	126	9	135
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	127	9	136

Error

11.8b

Counts

136 → 9

Compiler

Compiled 4779 to 2373 computations (50.3% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B)))) (sqrt.f64 (cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))))
10.3b	(-.f64 (-.f64 C A) (.f64 (fabs.f64 (cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B)))) (sqrt.f64 (cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))))
37.8b	(cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
37.8b	(cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

rewrite53.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64_2828`
11×	`*-un-lft-identity_binary64_2806` `add-cube-cbrt_binary64_2841`
10×	`cbrt-div_binary64_2838` `cbrt-prod_binary64_2837`
9×	`add-log-exp_binary64_2845` `associate-r_binary64_2746`
8×	`sqrt-prod_binary64_2822`
6×	`sqrt-div_binary64_2823` `add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842` `associate-*r/_binary64_2748` `pow1_binary64_2867`
5×	`flip-+_binary64_2780` `flip3-+_binary64_2809`
4×	`cancel-sign-sub-inv_binary64_2772` `associate--l+_binary64_2743` `frac-sub_binary64_2815`
3×	`associate-l_binary64_2747` `flip3--_binary64_2810` `diff-log_binary64_2898` `flip--_binary64_2781` `unswap-sqr_binary64_2774`
2×	`pow1/3_binary64_2888` `sub-neg_binary64_2799`
1×	`*-commutative_binary64_2737` `associate--l-_binary64_2744` `prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `pow-prod-down_binary64_2877`

Counts

4 → 76

Calls

4 calls:

15.0ms	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B)))) (sqrt.f64 (cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))))
9.0ms	(-.f64 (-.f64 C A) (.f64 (fabs.f64 (cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B)))) (sqrt.f64 (cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))))
8.0ms	(cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
8.0ms	(cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

series760.0ms (10.5%)

Counts

4 → 12

Calls

4 calls:

314.0ms	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B)))) (sqrt.f64 (cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))))
155.0ms	(-.f64 (-.f64 C A) (.f64 (fabs.f64 (cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B)))) (sqrt.f64 (cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))))
150.0ms	(cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
141.0ms	(cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

simplify107.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	5468	3524

prune182.0ms (2.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	88	9	97

Error

11.8b

Counts

97 → 9

Compiler

Compiled 4250 to 2289 computations (46.1% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.0b	(sqrt.f64 PI.f64)
36.7b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
36.7b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
36.7b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

rewrite38.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_2828` `sqrt-prod_binary64_2822`
8×	`*-un-lft-identity_binary64_2806` `add-cube-cbrt_binary64_2841` `pow1_binary64_2867`
6×	`sqrt-div_binary64_2823`
4×	`pow1/2_binary64_2886` `add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842` `sqrt-pow1_binary64_2824` `rem-sqrt-square_binary64_2819` `add-log-exp_binary64_2845`
3×	`flip-+_binary64_2780` `flip3-+_binary64_2809`

Counts

4 → 58

Calls

4 calls:

8.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
1.0ms	(sqrt.f64 PI.f64)

series220.0ms (3%)

Counts

4 → 10

Calls

4 calls:

76.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
72.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
71.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
0.0ms	(sqrt.f64 PI.f64)

simplify99.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4895	1103
1	4895	1103

prune188.0ms (2.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	68	9	77

Error

11.8b

Counts

77 → 9

Compiler

Compiled 4835 to 2357 computations (51.3% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.7b	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
36.7b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
36.7b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
36.7b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

rewrite59.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64_2828`
15×	`*-un-lft-identity_binary64_2806`
13×	`sqrt-prod_binary64_2822`
10×	`sqrt-div_binary64_2823` `add-cube-cbrt_binary64_2841`
9×	`cancel-sign-sub-inv_binary64_2772` `add-log-exp_binary64_2845`
7×	`pow1_binary64_2867`
5×	`flip-+_binary64_2780` `flip3-+_binary64_2809`
4×	`add-exp-log_binary64_2844` `associate--l+_binary64_2743` `add-cbrt-cube_binary64_2842` `frac-sub_binary64_2815`
3×	`pow1/2_binary64_2886` `flip3--_binary64_2810` `sqrt-pow1_binary64_2824` `distribute-lft-out--_binary64_2758` `diff-log_binary64_2898` `rem-sqrt-square_binary64_2819` `flip--_binary64_2781`
2×	`sub-neg_binary64_2799` `difference-of-squares_binary64_2775`
1×	`associate--l-_binary64_2744`

Counts

4 → 76

Calls

4 calls:

22.0ms	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

series290.0ms (4%)

Counts

4 → 12

Calls

4 calls:

77.0ms	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
72.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
71.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
69.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

simplify79.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5018	1969

prune251.0ms (3.5%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	88	9	97

Error

11.8b

Counts

97 → 9

Compiler

Compiled 5849 to 2876 computations (50.8% saved)

regimes523.0ms (7.3%)

Accuracy

Total 10.3b remaining (45%)

Threshold costs 0b (0%)

Compiler

Compiled 5607 to 4069 computations (27.4% saved)

bsearch59.0ms (0.8%)

Steps

Iters	Range		Point
10	1.0252717731345001e-91	1.5205765053144617e-78	2.2313699524667266e-79

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	67	69
1	67	69

end0.0ms (0%)

sample3.0s (41.9%)

Algorithm

1×

intervals

Results

710.0ms	890×	body	4096	valid
542.0ms	5348×	body	128	valid
528.0ms	906×	body	2048	valid
223.0ms	507×	body	1024	valid
72.0ms	222×	body	512	valid
26.0ms	127×	body	256	valid

Compiler

Compiled 845 to 617 computations (27% saved)

Details

analyze230.0ms (3.2%)

sample75.0ms (1%)

simplify169.0ms (2.3%)

prune4.0ms (0.1%)

localize14.0ms (0.2%)

rewrite67.0ms (0.9%)

series343.0ms (4.7%)

simplify94.0ms (1.3%)

prune221.0ms (3.1%)

localize18.0ms (0.3%)

rewrite53.0ms (0.7%)

series760.0ms (10.5%)

simplify107.0ms (1.5%)

prune182.0ms (2.5%)

localize23.0ms (0.3%)

rewrite38.0ms (0.5%)

series220.0ms (3%)

simplify99.0ms (1.4%)

prune188.0ms (2.6%)

localize20.0ms (0.3%)

rewrite59.0ms (0.8%)

series290.0ms (4%)

simplify79.0ms (1.1%)

prune251.0ms (3.5%)

regimes523.0ms (7.3%)

bsearch59.0ms (0.8%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.0s (41.9%)

Profiling