Details

analyze3.0s (11.3%)

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)

sample167.0ms (0.6%)

Algorithm

1×

intervals

Results

28.0ms	188×	body	128	valid
20.0ms	25×	body	2048	nan
19.0ms	31×	body	1024	nan
18.0ms	23×	body	2048	valid
13.0ms	18×	body	512	valid
12.0ms	19×	body	1024	valid
9.0ms	64×	body	128	nan
8.0ms	18×	body	512	nan
5.0ms	16×	body	256	nan
2.0ms	8×	body	256	valid

Compiler

Compiled 81 to 69 computations (14.8% saved)

simplify50.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5390	61

prune5.0ms (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

48.5b

Counts

2 → 1

Compiler

Compiled 80 to 59 computations (26.3% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.8b	(.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)
11.3b	(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))))))
21.9b	(/.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)))
33.7b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))

rewrite907.0ms (3.4%)

Algorithm

1×	rewrite-expression-head

Error

48.1b

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:

33.0ms	(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))))))
18.0ms	(/.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)))
12.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))
9.0ms	(.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)

Compiler

Compiled 11275 to 7235 computations (35.8% saved)

series6.5s (24.6%)

Error

29.3b

Counts

4 → 75

Calls

4 calls:

3.2s	(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))))))
2.3s	(/.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)))
439.0ms	(.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)
370.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))

Compiler

Compiled 13308 to 9984 computations (25% saved)

simplify141.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

233 → 233

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4971	14078
1	4971	14078

prune746.0ms (2.8%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	217	16	233
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	218	16	234

Error

29.2b

Counts

234 → 16

Compiler

Compiled 12963 to 6906 computations (46.7% saved)

localize8.0ms (0%)

Local error

Found 2 expressions with local error:

0.4b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F C))))
12.2b	(sqrt.f64 (*.f64 -1/2 (/.f64 F C)))

rewrite68.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

26.4b

Rules

12×	`pow1_binary64_2867`
9×	`add-sqr-sqrt_binary64_2828`
6×	`pow-prod-down_binary64_2877` `sqrt-pow1_binary64_2824` `sqrt-prod_binary64_2822` `associate-l_binary64_2747`
5×	`add-cube-cbrt_binary64_2841` `*-un-lft-identity_binary64_2806`
4×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842` `associate-r_binary64_2746`
3×	`pow1/2_binary64_2886` `associate-*r/_binary64_2748`
2×	`add-log-exp_binary64_2845` `sqrt-div_binary64_2823` `unswap-sqr_binary64_2774`
1×	`prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `sqrt-unprod_binary64_2826` `*-commutative_binary64_2737`

Counts

2 → 40

Calls

2 calls:

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

Compiler

Compiled 553 to 408 computations (26.2% saved)

series157.0ms (0.6%)

Error

29.2b

Counts

2 → 12

Calls

2 calls:

92.0ms	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F C))))
65.0ms	(sqrt.f64 (*.f64 -1/2 (/.f64 F C)))

Compiler

Compiled 382 to 406 computations (-6.3% saved)

simplify107.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	4850	676
1	4850	676

prune90.0ms (0.3%)

Pruning

24 alts after pruning (23 fresh and 1 done)

	Pruned	Kept	Total
New	44	8	52
Fresh	0	15	15
Picked	0	1	1
Done	0	0	0
Total	44	24	68

Error

26.4b

Counts

68 → 24

Compiler

Compiled 1318 to 964 computations (26.9% saved)

localize9.0ms (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)))

rewrite96.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

26.4b

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:

9.0ms	(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 F -1/2))) (sqrt.f64 C))
8.0ms	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 F -1/2)))

Compiler

Compiled 843 to 633 computations (24.9% saved)

series147.0ms (0.6%)

Error

26.4b

Counts

2 → 9

Calls

2 calls:

109.0ms	(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 F -1/2))) (sqrt.f64 C))
37.0ms	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 F -1/2)))

Compiler

Compiled 306 to 330 computations (-7.8% saved)

simplify79.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5152	969

prune179.0ms (0.7%)

Pruning

24 alts after pruning (23 fresh and 1 done)

	Pruned	Kept	Total
New	58	6	64
Fresh	5	17	22
Picked	1	0	1
Done	0	1	1
Total	64	24	88

Error

26.4b

Counts

88 → 24

Compiler

Compiled 1460 to 1074 computations (26.4% saved)

localize15.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

rewrite197.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

26.4b

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:

14.0ms

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

Compiler

Compiled 1353 to 406 computations (70% saved)

series109.0ms (0.4%)

Error

26.4b

Counts

1 → 6

Calls

1 calls:

108.0ms

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

Compiler

Compiled 144 to 152 computations (-5.6% saved)

simplify205.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (154.0ms)

Iter	Nodes	Cost
0	4713	2256
1	4713	2256

prune120.0ms (0.5%)

Pruning

28 alts after pruning (26 fresh and 2 done)

	Pruned	Kept	Total
New	110	6	116
Fresh	2	20	22
Picked	0	1	1
Done	0	1	1
Total	112	28	140

Error

26.4b

Counts

140 → 28

Compiler

Compiled 911 to 259 computations (71.6% saved)

regimes6.5s (24.6%)

Accuracy

Total 4.3b remaining (13.9%)

Threshold costs 0b (0%)

Compiler

Compiled 41785 to 32289 computations (22.7% saved)

bsearch16.0ms (0.1%)

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

simplify22.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	646	430
1	646	430

end47.0ms (0.2%)

Compiler: Compiled 831 to 558 computations (32.9% saved)

sample6.7s (25.4%)

Algorithm

1×

intervals

Results

958.0ms	5578×	body	128	valid
797.0ms	820×	body	1024	valid
600.0ms	878×	body	1024	nan
592.0ms	652×	body	2048	valid
530.0ms	599×	body	2048	nan
405.0ms	2402×	body	128	nan
315.0ms	597×	body	512	valid
306.0ms	607×	body	512	nan
120.0ms	328×	body	256	nan
115.0ms	352×	body	256	valid
1.0ms	1×	body	4096	valid

Compiler

Compiled 1260 to 924 computations (26.7% saved)

Details

analyze3.0s (11.3%)

sample167.0ms (0.6%)

simplify50.0ms (0.2%)

prune5.0ms (0%)

localize27.0ms (0.1%)

rewrite907.0ms (3.4%)

series6.5s (24.6%)

simplify141.0ms (0.5%)

prune746.0ms (2.8%)

localize8.0ms (0%)

rewrite68.0ms (0.3%)

series157.0ms (0.6%)

simplify107.0ms (0.4%)

prune90.0ms (0.3%)

localize9.0ms (0%)

rewrite96.0ms (0.4%)

series147.0ms (0.6%)

simplify79.0ms (0.3%)

prune179.0ms (0.7%)

localize15.0ms (0.1%)

rewrite197.0ms (0.7%)

series109.0ms (0.4%)

simplify205.0ms (0.8%)

prune120.0ms (0.5%)

regimes6.5s (24.6%)

bsearch16.0ms (0.1%)

simplify22.0ms (0.1%)

end47.0ms (0.2%)

sample6.7s (25.4%)

Profiling