Details

analyze2.9s (10.4%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5334	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%	99.8%	0.2%	7
0%	98.2%	1.8%	8
0%	94.3%	5.7%	9
0.4%	93%	6.6%	10
7.4%	83.3%	9.3%	11
12.4%	75.2%	12.4%	12
14.4%	68.9%	16.7%	13
16.8%	65.4%	17.8%	14

Symmetry

(sort A C)

Compiler

Compiled 41 to 33 computations (19.5% saved)

sample164.0ms (0.6%)

Algorithm

1×

intervals

Results

33.0ms	172×	body	128	valid
18.0ms	24×	body	2048	nan
17.0ms	23×	body	2048	valid
15.0ms	23×	body	1024	valid
13.0ms	94×	body	128	nan
13.0ms	21×	body	1024	nan
11.0ms	26×	body	512	valid
4.0ms	11×	body	512	nan
3.0ms	12×	body	256	valid
3.0ms	10×	body	256	nan

Compiler

Compiled 81 to 69 computations (14.8% saved)

simplify40.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5613	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

55.4b

Counts

2 → 1

Compiler

Compiled 80 to 59 computations (26.3% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

8.3b	(.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)
16.5b	(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))))))
23.9b	(/.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)))
37.3b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))

rewrite815.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Error

53.0b

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`
31×	`flip3-+_binary64_2809` `flip-+_binary64_2780`
24×	`frac-add_binary64_2814` `frac-times_binary64_2816`
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` `flip3--_binary64_2810` `flip--_binary64_2781`
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:

31.0ms	(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))))))
17.0ms	(/.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)))
11.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))
8.0ms	(.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)

Compiler

Compiled 11876 to 7641 computations (35.7% saved)

series7.4s (25.9%)

Error

31.6b

Counts

4 → 77

Calls

4 calls:

3.9s	(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))))))
2.7s	(/.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)))
318.0ms	(.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)
299.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))

Compiler

Compiled 20101 to 14898 computations (25.9% saved)

simplify162.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

235 → 235

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5001	15443

prune819.0ms (2.9%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	214	21	235
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	215	21	236

Error

30.9b

Counts

236 → 21

Compiler

Compiled 16164 to 8484 computations (47.5% saved)

localize8.0ms (0%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 -1/2 (/.f64 F A))
0.4b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A))))
14.4b	(sqrt.f64 (*.f64 -1/2 (/.f64 F A)))

rewrite106.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

30.7b

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:

9.0ms	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A))))
7.0ms	(*.f64 -1/2 (/.f64 F A))
4.0ms	(sqrt.f64 (*.f64 -1/2 (/.f64 F A)))

Compiler

Compiled 1174 to 824 computations (29.8% saved)

series174.0ms (0.6%)

Error

30.9b

Counts

3 → 18

Calls

3 calls:

60.0ms	(*.f64 -1/2 (/.f64 F A))
58.0ms	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A))))
45.0ms	(sqrt.f64 (*.f64 -1/2 (/.f64 F A)))

Compiler

Compiled 674 to 676 computations (-0.3% saved)

simplify79.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4948	1045
1	4948	1045

prune130.0ms (0.5%)

Pruning

29 alts after pruning (28 fresh and 1 done)

	Pruned	Kept	Total
New	82	8	90
Fresh	0	20	20
Picked	0	1	1
Done	0	0	0
Total	82	29	111

Error

30.7b

Counts

111 → 29

Compiler

Compiled 2200 to 1566 computations (28.8% saved)

localize5.0ms (0%)

Local error

Found 1 expressions with local error:

14.4b

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

rewrite44.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Error

28.0b

Rules

30×	`sqrt-prod_binary64_2822`
18×	`times-frac_binary64_2812`
17×	`add-sqr-sqrt_binary64_2828`
16×	`add-cube-cbrt_binary64_2841` `*-un-lft-identity_binary64_2806`
13×	`distribute-rgt-neg-in_binary64_2764` `distribute-lft-neg-in_binary64_2763`
2×	`pow1_binary64_2867` `div-inv_binary64_2803`
1×	`pow1/2_binary64_2886` `add-log-exp_binary64_2845` `add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842` `sqrt-pow1_binary64_2824` `distribute-neg-frac_binary64_2770` `sqrt-div_binary64_2823` `neg-mul-1_binary64_2802` `rem-sqrt-square_binary64_2819`

Counts

1 → 41

Calls

1 calls:

4.0ms

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

Compiler

Compiled 547 to 221 computations (59.6% saved)

series37.0ms (0.1%)

Error

30.7b

Counts

1 → 6

Calls

1 calls:

34.0ms

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

Compiler

Compiled 160 to 154 computations (3.8% saved)

simplify152.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 0 (137.0ms)

Iter	Nodes	Cost
0	4604	671
1	4604	671

prune82.0ms (0.3%)

Pruning

30 alts after pruning (29 fresh and 1 done)

	Pruned	Kept	Total
New	40	7	47
Fresh	5	22	27
Picked	0	1	1
Done	1	0	1
Total	46	30	76

Error

28.0b

Counts

76 → 30

Compiler

Compiled 1474 to 892 computations (39.5% saved)

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

0.1b	(sqrt.f64 (/.f64 -1 A))
0.3b	(*.f64 (sqrt.f64 F) (sqrt.f64 (/.f64 -1 A)))

rewrite89.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

28.0b

Rules

36×	`add-sqr-sqrt_binary64_2828` `sqrt-prod_binary64_2822`
21×	`times-frac_binary64_2812`
19×	`add-cube-cbrt_binary64_2841` `*-un-lft-identity_binary64_2806`
16×	`associate-r_binary64_2746`
7×	`pow1_binary64_2867`
6×	`unswap-sqr_binary64_2774` `associate-l_binary64_2747`
4×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842`
3×	`pow1/2_binary64_2886` `pow-prod-down_binary64_2877` `sqrt-pow1_binary64_2824`
2×	`add-log-exp_binary64_2845` `sqrt-div_binary64_2823` `div-inv_binary64_2803` `rem-sqrt-square_binary64_2819`
1×	`prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `sqrt-unprod_binary64_2826` `associate-r/_binary64_2748` `-commutative_binary64_2737`

Counts

2 → 68

Calls

2 calls:

12.0ms	(*.f64 (sqrt.f64 F) (sqrt.f64 (/.f64 -1 A)))
3.0ms	(sqrt.f64 (/.f64 -1 A))

Compiler

Compiled 1023 to 688 computations (32.7% saved)

series64.0ms (0.2%)

Error

28.0b

Counts

2 → 9

Calls

2 calls:

47.0ms	(*.f64 (sqrt.f64 F) (sqrt.f64 (/.f64 -1 A)))
12.0ms	(sqrt.f64 (/.f64 -1 A))

Compiler

Compiled 277 to 270 computations (2.5% saved)

simplify96.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4831	989
1	4831	989

prune63.0ms (0.2%)

Pruning

32 alts after pruning (30 fresh and 2 done)

	Pruned	Kept	Total
New	69	8	77
Fresh	6	22	28
Picked	0	1	1
Done	0	1	1
Total	75	32	107

Error

28.0b

Counts

107 → 32

Compiler

Compiled 993 to 644 computations (35.1% saved)

regimes4.3s (15.1%)

Accuracy

Total 4.5b remaining (14.5%)

Threshold costs 0b (0%)

Compiler

Compiled 46698 to 34784 computations (25.5% saved)

bsearch16.0ms (0.1%)

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

simplify35.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	386	414
1	386	414

Compiler

Compiled 536 to 374 computations (30.2% saved)

end0.0ms (0%)

sample10.6s (37.4%)

Algorithm

1×

intervals

Results

798.0ms	5547×	body	128	valid
524.0ms	671×	body	2048	valid
518.0ms	833×	body	1024	valid
463.0ms	808×	body	1024	nan
446.0ms	571×	body	2048	nan
428.0ms	2897×	body	128	nan
261.0ms	600×	body	512	valid
246.0ms	586×	body	512	nan
99.0ms	348×	body	256	valid
99.0ms	358×	body	256	nan
1.0ms	1×	body	4096	valid

Compiler

Compiled 8015 to 5958 computations (25.7% saved)

Details

analyze2.9s (10.4%)

sample164.0ms (0.6%)

simplify40.0ms (0.1%)

prune4.0ms (0%)

localize20.0ms (0.1%)

rewrite815.0ms (2.9%)

series7.4s (25.9%)

simplify162.0ms (0.6%)

prune819.0ms (2.9%)

localize8.0ms (0%)

rewrite106.0ms (0.4%)

series174.0ms (0.6%)

simplify79.0ms (0.3%)

prune130.0ms (0.5%)

localize5.0ms (0%)

rewrite44.0ms (0.2%)

series37.0ms (0.1%)

simplify152.0ms (0.5%)

prune82.0ms (0.3%)

localize6.0ms (0%)

rewrite89.0ms (0.3%)

series64.0ms (0.2%)

simplify96.0ms (0.3%)

prune63.0ms (0.2%)

regimes4.3s (15.1%)

bsearch16.0ms (0.1%)

simplify35.0ms (0.1%)

end0.0ms (0%)

sample10.6s (37.4%)

Profiling