Details

analyze3.6s (11.2%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4978	427
1	4978	427
0	4	4
1	4	4

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	98.2%	1.8%	7
0%	92%	8%	8
0%	91.2%	8.8%	9
0.4%	89.3%	10.3%	10
7.1%	79.2%	13.6%	11
11.9%	70.2%	17.9%	12
13.8%	67.4%	18.7%	13
16.6%	63.3%	20.1%	14

Symmetry

(sort A C)

Compiler

Compiled 41 to 33 computations (19.5% saved)

sample187.0ms (0.6%)

Algorithm

1×

intervals

Results

36.0ms	185×	body	128	valid
24.0ms	20×	body	2048	nan
23.0ms	29×	body	1024	valid
19.0ms	25×	body	1024	nan
15.0ms	18×	body	2048	valid
13.0ms	83×	body	128	nan
10.0ms	19×	body	512	valid
5.0ms	11×	body	512	nan
3.0ms	9×	body	256	nan
2.0ms	5×	body	256	valid

Compiler

Compiled 81 to 69 computations (14.8% saved)

simplify61.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5390	61

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

51.9b

Counts

2 → 1

Compiler

Compiled 80 to 59 computations (26.3% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.7b	(.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)
16.2b	(sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))
22.8b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)))
34.3b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))

rewrite1.1s (3.3%)

Algorithm

1×	rewrite-expression-head

Error

51.6b

Rules

66×	`sqrt-div_binary64_2823`
40×	`associate-*r/_binary64_2748`
39×	`*-un-lft-identity_binary64_2806`
36×	`times-frac_binary64_2812`
35×	`add-sqr-sqrt_binary64_2828`
34×	`associate-*l/_binary64_2749`
32×	`add-cube-cbrt_binary64_2841`
25×	`flip3-+_binary64_2809` `flip-+_binary64_2780`
24×	`frac-sub_binary64_2815` `frac-times_binary64_2816`
22×	`flip3--_binary64_2810` `flip--_binary64_2781`
20×	`distribute-neg-frac_binary64_2770` `associate-/l/_binary64_2753`
17×	`pow1_binary64_2867`
16×	`distribute-rgt-neg-in_binary64_2764` `distribute-lft-neg-in_binary64_2763`
15×	`sqrt-prod_binary64_2822`
12×	`associate-/l*_binary64_2751`
8×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842`
7×	`pow-prod-down_binary64_2877`
5×	`sqrt-pow1_binary64_2824`
4×	`add-log-exp_binary64_2845` `unpow-prod-down_binary64_2885` `neg-mul-1_binary64_2802`
3×	`distribute-lft-out_binary64_2757` `associate-/r_binary64_2750` `associate-l_binary64_2747` `associate-r*_binary64_2746`
2×	`pow1/2_binary64_2886` `associate-/r/_binary64_2752`
1×	`distribute-lft-out--_binary64_2758` `rem-sqrt-square_binary64_2819` `div-exp_binary64_2857` `cbrt-undiv_binary64_2840` `frac-2neg_binary64_2817` `neg-sub0_binary64_2801` `div-sub_binary64_2811` `clear-num_binary64_2805` `div-inv_binary64_2803` `distribute-frac-neg_binary64_2769` `prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `unswap-sqr_binary64_2774` `*-commutative_binary64_2737`

Counts

4 → 158

Calls

4 calls:

43.0ms	(sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))
26.0ms	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)))
24.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))
16.0ms	(.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)

Compiler

Compiled 11876 to 7641 computations (35.7% saved)

series6.4s (19.6%)

Error

31.5b

Counts

4 → 75

Calls

4 calls:

3.8s	(sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))
1.5s	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)))
370.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))
352.0ms	(.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)

Compiler

Compiled 16756 to 12473 computations (25.6% saved)

simplify176.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

233 → 233

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5093	14926

prune1.1s (3.3%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	213	20	233
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	214	20	234

Error

31.5b

Counts

234 → 20

Compiler

Compiled 15942 to 8425 computations (47.2% saved)

localize8.0ms (0%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 -1/2 (/.f64 F C))
0.4b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F C))))
11.5b	(sqrt.f64 (*.f64 -1/2 (/.f64 F C)))

rewrite150.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

28.6b

Rules

23×	`add-sqr-sqrt_binary64_2828`
17×	`associate-r_binary64_2746`
15×	`pow1_binary64_2867`
14×	`add-cube-cbrt_binary64_2841` `*-un-lft-identity_binary64_2806`
10×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842` `times-frac_binary64_2812`
9×	`associate-l_binary64_2747`
7×	`pow-prod-down_binary64_2877`
6×	`sqrt-pow1_binary64_2824` `sqrt-prod_binary64_2822`
4×	`associate-*r/_binary64_2748` `unswap-sqr_binary64_2774`
3×	`pow1/2_binary64_2886` `add-log-exp_binary64_2845` `prod-exp_binary64_2855` `cbrt-unprod_binary64_2839`
2×	`sqrt-div_binary64_2823` `*-commutative_binary64_2737`
1×	`sqrt-unprod_binary64_2826` `div-exp_binary64_2857` `cbrt-undiv_binary64_2840` `div-inv_binary64_2803`

Counts

3 → 72

Calls

3 calls:

16.0ms	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F C))))
15.0ms	(*.f64 -1/2 (/.f64 F C))
4.0ms	(sqrt.f64 (*.f64 -1/2 (/.f64 F C)))

Compiler

Compiled 1174 to 824 computations (29.8% saved)

series205.0ms (0.6%)

Error

31.5b

Counts

3 → 18

Calls

3 calls:

74.0ms	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F C))))
60.0ms	(*.f64 -1/2 (/.f64 F C))
58.0ms	(sqrt.f64 (*.f64 -1/2 (/.f64 F C)))

Compiler

Compiled 674 to 676 computations (-0.3% saved)

simplify85.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4948	1045
1	4948	1045

prune160.0ms (0.5%)

Pruning

29 alts after pruning (29 fresh and 0 done)

	Pruned	Kept	Total
New	79	11	90
Fresh	1	18	19
Picked	1	0	1
Done	0	0	0
Total	81	29	110

Error

28.6b

Counts

110 → 29

Compiler

Compiled 2325 to 1646 computations (29.2% saved)

localize8.0ms (0%)

Local error

Found 2 expressions with local error:

0.2b	(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 F -1/2))) (sqrt.f64 C))
0.4b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 F -1/2)))

rewrite131.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

28.6b

Rules

13×	`add-sqr-sqrt_binary64_2828`
11×	`sqrt-prod_binary64_2822`
9×	`pow1_binary64_2867` `add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842` `add-cube-cbrt_binary64_2841` `*-un-lft-identity_binary64_2806`
6×	`associate-l_binary64_2747` `times-frac_binary64_2812` `associate-/r*_binary64_2750`
5×	`pow-prod-down_binary64_2877`
4×	`sqrt-pow1_binary64_2824` `associate-r_binary64_2746`
2×	`pow1/2_binary64_2886` `prod-exp_binary64_2855` `add-log-exp_binary64_2845` `cbrt-unprod_binary64_2839` `sqrt-unprod_binary64_2826` `unswap-sqr_binary64_2774` `div-exp_binary64_2857` `cbrt-undiv_binary64_2840`
1×	`-commutative_binary64_2737` `sqrt-undiv_binary64_2827` `frac-2neg_binary64_2817` `clear-num_binary64_2805` `div-inv_binary64_2803` `associate-/l_binary64_2751`

Counts

2 → 55

Calls

2 calls:

21.0ms	(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 F -1/2))) (sqrt.f64 C))
11.0ms	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 F -1/2)))

Compiler

Compiled 953 to 713 computations (25.2% saved)

series112.0ms (0.3%)

Error

28.6b

Counts

2 → 9

Calls

2 calls:

75.0ms	(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 F -1/2))) (sqrt.f64 C))
25.0ms	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 F -1/2)))

Compiler

Compiled 399 to 405 computations (-1.5% saved)

simplify76.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5152	969

prune130.0ms (0.4%)

Pruning

31 alts after pruning (31 fresh and 0 done)

	Pruned	Kept	Total
New	58	6	64
Fresh	3	25	28
Picked	1	0	1
Done	0	0	0
Total	62	31	93

Error

28.6b

Counts

93 → 31

Compiler

Compiled 2024 to 1501 computations (25.8% saved)

localize6.0ms (0%)

Local error

Found 1 expressions with local error:

0.2b	(/.f64 (sqrt.f64 (neg.f64 F)) (sqrt.f64 C))

rewrite145.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

28.6b

Rules

112×	`sqrt-prod_binary64_2822`
78×	`times-frac_binary64_2812`
57×	`add-cube-cbrt_binary64_2841` `add-sqr-sqrt_binary64_2828` `*-un-lft-identity_binary64_2806`
21×	`distribute-rgt-neg-in_binary64_2764` `distribute-lft-neg-in_binary64_2763`
13×	`associate-/l*_binary64_2751`
7×	`neg-mul-1_binary64_2802`
6×	`associate-/r*_binary64_2750`
3×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842`
1×	`pow1_binary64_2867` `div-exp_binary64_2857` `add-log-exp_binary64_2845` `cbrt-undiv_binary64_2840` `sqrt-undiv_binary64_2827` `frac-2neg_binary64_2817` `clear-num_binary64_2805` `div-inv_binary64_2803`

Counts

1 → 110

Calls

1 calls:

8.0ms

(/.f64 (sqrt.f64 (neg.f64 F)) (sqrt.f64 C))

Compiler

Compiled 1794 to 475 computations (73.5% saved)

series69.0ms (0.2%)

Error

28.6b

Counts

1 → 6

Calls

1 calls:

66.0ms

(/.f64 (sqrt.f64 (neg.f64 F)) (sqrt.f64 C))

Compiler

Compiled 184 to 178 computations (3.3% saved)

simplify136.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (110.0ms)

Iter	Nodes	Cost
0	4713	2256
1	4713	2256

prune102.0ms (0.3%)

Pruning

33 alts after pruning (32 fresh and 1 done)

	Pruned	Kept	Total
New	110	6	116
Fresh	4	26	30
Picked	0	1	1
Done	0	0	0
Total	114	33	147

Error

28.6b

Counts

147 → 33

Compiler

Compiled 1637 to 381 computations (76.7% saved)

regimes5.0s (15.3%)

Accuracy

Total 3.6b remaining (11.7%)

Threshold costs 0b (0%)

Compiler

Compiled 43659 to 33789 computations (22.6% saved)

bsearch16.0ms (0%)

Compiler: Compiled 40 to 32 computations (20% saved)

simplify104.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	891	402
1	891	402

Compiler

Compiled 522 to 352 computations (32.6% saved)

end0.0ms (0%)

sample13.3s (40.9%)

Algorithm

1×

intervals

Results

1.0s	5554×	body	128	valid
648.0ms	886×	body	1024	nan
647.0ms	865×	body	1024	valid
622.0ms	629×	body	2048	valid
582.0ms	597×	body	2048	nan
479.0ms	2580×	body	128	nan
347.0ms	615×	body	512	valid
307.0ms	573×	body	512	nan
119.0ms	343×	body	256	nan
117.0ms	336×	body	256	valid
2.0ms	1×	body	4096	valid

Compiler

Compiled 7515 to 5790 computations (23% saved)

Details

analyze3.6s (11.2%)

sample187.0ms (0.6%)

simplify61.0ms (0.2%)

prune4.0ms (0%)

localize26.0ms (0.1%)

rewrite1.1s (3.3%)

series6.4s (19.6%)

simplify176.0ms (0.5%)

prune1.1s (3.3%)

localize8.0ms (0%)

rewrite150.0ms (0.5%)

series205.0ms (0.6%)

simplify85.0ms (0.3%)

prune160.0ms (0.5%)

localize8.0ms (0%)

rewrite131.0ms (0.4%)

series112.0ms (0.3%)

simplify76.0ms (0.2%)

prune130.0ms (0.4%)

localize6.0ms (0%)

rewrite145.0ms (0.4%)

series69.0ms (0.2%)

simplify136.0ms (0.4%)

prune102.0ms (0.3%)

regimes5.0s (15.3%)

bsearch16.0ms (0%)

simplify104.0ms (0.3%)

end0.0ms (0%)

sample13.3s (40.9%)

Profiling