Details

analyze3.5s (11.7%)

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)

sample200.0ms (0.7%)

Algorithm

1×

intervals

Results

31.0ms	176×	body	128	valid
19.0ms	104×	body	128	nan
19.0ms	28×	body	1024	valid
17.0ms	18×	body	2048	valid
17.0ms	30×	body	512	nan
16.0ms	20×	body	2048	nan
16.0ms	24×	body	1024	nan
11.0ms	20×	body	512	valid
4.0ms	14×	body	256	valid
4.0ms	10×	body	256	nan

Compiler

Compiled 81 to 69 computations (14.8% saved)

simplify58.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (52.0ms)

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

51.2b

Counts

2 → 1

Compiler

Compiled 80 to 59 computations (26.3% saved)

localize33.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.8b	(.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)
11.7b	(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))))))
23.0b	(/.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)))
38.0b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))

rewrite1.0s (3.4%)

Algorithm

1×	rewrite-expression-head

Error

51.0b

Rules

66×	`sqrt-div_binary64_2482`
40×	`associate-*r/_binary64_2407`
39×	`*-un-lft-identity_binary64_2465`
36×	`times-frac_binary64_2471`
35×	`add-sqr-sqrt_binary64_2487`
34×	`associate-*l/_binary64_2408`
32×	`add-cube-cbrt_binary64_2500`
25×	`flip3-+_binary64_2468` `flip-+_binary64_2439`
24×	`frac-sub_binary64_2474` `frac-times_binary64_2475`
22×	`flip3--_binary64_2469` `flip--_binary64_2440`
20×	`distribute-neg-frac_binary64_2429` `associate-/l/_binary64_2412`
17×	`pow1_binary64_2526`
16×	`distribute-rgt-neg-in_binary64_2423` `distribute-lft-neg-in_binary64_2422`
15×	`sqrt-prod_binary64_2481`
12×	`associate-/l*_binary64_2410`
8×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
7×	`pow-prod-down_binary64_2536`
5×	`sqrt-pow1_binary64_2483`
4×	`add-log-exp_binary64_2504` `unpow-prod-down_binary64_2544` `neg-mul-1_binary64_2461`
3×	`distribute-lft-out_binary64_2416` `associate-/r_binary64_2409` `associate-l_binary64_2406` `associate-r*_binary64_2405`
2×	`pow1/2_binary64_2545` `associate-/r/_binary64_2411`
1×	`distribute-lft-out--_binary64_2417` `rem-sqrt-square_binary64_2478` `div-exp_binary64_2516` `cbrt-undiv_binary64_2499` `frac-2neg_binary64_2476` `neg-sub0_binary64_2460` `div-sub_binary64_2470` `clear-num_binary64_2464` `div-inv_binary64_2462` `distribute-frac-neg_binary64_2428` `prod-exp_binary64_2514` `cbrt-unprod_binary64_2498` `unswap-sqr_binary64_2433` `*-commutative_binary64_2396`

Counts

4 → 158

Calls

4 calls:

34.0ms	(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))))))
20.0ms	(/.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)))
13.0ms	(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 11876 to 7641 computations (35.7% saved)

series5.6s (18.5%)

Error

30.0b

Counts

4 → 75

Calls

4 calls:

3.1s	(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)))
420.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))
358.0ms	(.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)

Compiler

Compiled 15919 to 11915 computations (25.2% saved)

simplify153.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

233 → 233

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5049	14676

prune974.0ms (3.2%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	216	17	233
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	216	18	234

Error

29.9b

Counts

234 → 18

Compiler

Compiled 15472 to 8151 computations (47.3% saved)

localize10.0ms (0%)

Local error

Found 3 expressions with local error:

0.2b	(*.f64 -1/2 (/.f64 F C))
0.4b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F C))))
12.2b	(sqrt.f64 (*.f64 -1/2 (/.f64 F C)))

rewrite132.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

26.8b

Rules

23×	`add-sqr-sqrt_binary64_2487`
17×	`associate-r_binary64_2405`
15×	`pow1_binary64_2526`
14×	`add-cube-cbrt_binary64_2500` `*-un-lft-identity_binary64_2465`
10×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `times-frac_binary64_2471`
9×	`associate-l_binary64_2406`
7×	`pow-prod-down_binary64_2536`
6×	`sqrt-pow1_binary64_2483` `sqrt-prod_binary64_2481`
4×	`associate-*r/_binary64_2407` `unswap-sqr_binary64_2433`
3×	`pow1/2_binary64_2545` `add-log-exp_binary64_2504` `prod-exp_binary64_2514` `cbrt-unprod_binary64_2498`
2×	`sqrt-div_binary64_2482` `*-commutative_binary64_2396`
1×	`sqrt-unprod_binary64_2485` `div-exp_binary64_2516` `cbrt-undiv_binary64_2499` `div-inv_binary64_2462`

Counts

3 → 72

Calls

3 calls:

17.0ms	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F C))))
11.0ms	(*.f64 -1/2 (/.f64 F C))
8.0ms	(sqrt.f64 (*.f64 -1/2 (/.f64 F C)))

Compiler

Compiled 1174 to 824 computations (29.8% saved)

series278.0ms (0.9%)

Error

29.9b

Counts

3 → 18

Calls

3 calls:

114.0ms	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F C))))
78.0ms	(*.f64 -1/2 (/.f64 F C))
60.0ms	(sqrt.f64 (*.f64 -1/2 (/.f64 F C)))

Compiler

Compiled 674 to 676 computations (-0.3% saved)

simplify107.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4948	1045
1	4948	1045

prune143.0ms (0.5%)

Pruning

26 alts after pruning (25 fresh and 1 done)

	Pruned	Kept	Total
New	78	12	90
Fresh	3	13	16
Picked	1	0	1
Done	0	1	1
Total	82	26	108

Error

26.8b

Counts

108 → 26

Compiler

Compiled 1951 to 1405 computations (28% saved)

localize17.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.3b	(/.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)))

rewrite101.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

26.8b

Rules

13×	`add-sqr-sqrt_binary64_2487`
11×	`sqrt-prod_binary64_2481`
9×	`pow1_binary64_2526` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `add-cube-cbrt_binary64_2500` `*-un-lft-identity_binary64_2465`
6×	`associate-l_binary64_2406` `times-frac_binary64_2471` `associate-/r*_binary64_2409`
5×	`pow-prod-down_binary64_2536`
4×	`sqrt-pow1_binary64_2483` `associate-r_binary64_2405`
2×	`pow1/2_binary64_2545` `prod-exp_binary64_2514` `add-log-exp_binary64_2504` `cbrt-unprod_binary64_2498` `sqrt-unprod_binary64_2485` `unswap-sqr_binary64_2433` `div-exp_binary64_2516` `cbrt-undiv_binary64_2499`
1×	`-commutative_binary64_2396` `sqrt-undiv_binary64_2486` `frac-2neg_binary64_2476` `clear-num_binary64_2464` `div-inv_binary64_2462` `associate-/l_binary64_2410`

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 953 to 713 computations (25.2% saved)

series127.0ms (0.4%)

Error

26.8b

Counts

2 → 9

Calls

2 calls:

94.0ms	(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 F -1/2))) (sqrt.f64 C))
28.0ms	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 F -1/2)))

Compiler

Compiled 399 to 405 computations (-1.5% saved)

simplify97.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	5152	969

prune134.0ms (0.4%)

Pruning

30 alts after pruning (29 fresh and 1 done)

	Pruned	Kept	Total
New	55	9	64
Fresh	4	20	24
Picked	1	0	1
Done	0	1	1
Total	60	30	90

Error

26.8b

Counts

90 → 30

Compiler

Compiled 1717 to 1321 computations (23.1% saved)

localize8.0ms (0%)

Local error

Found 2 expressions with local error:

0.3b	(/.f64 (sqrt.f64 (*.f64 F -1/2)) (sqrt.f64 C))
0.3b	(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 F -1/2)) (sqrt.f64 C)))

rewrite175.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

26.8b

Rules

52×	`add-sqr-sqrt_binary64_2487` `times-frac_binary64_2471`
48×	`sqrt-prod_binary64_2481`
36×	`add-cube-cbrt_binary64_2500` `*-un-lft-identity_binary64_2465`
28×	`associate-r_binary64_2405`
9×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
6×	`unswap-sqr_binary64_2433` `associate-l_binary64_2406` `associate-/r*_binary64_2409`
4×	`pow1_binary64_2526` `associate-/l*_binary64_2410`
2×	`div-exp_binary64_2516` `prod-exp_binary64_2514` `add-log-exp_binary64_2504` `cbrt-unprod_binary64_2498` `cbrt-undiv_binary64_2499` `sqrt-undiv_binary64_2486` `div-inv_binary64_2462`
1×	`pow-prod-down_binary64_2536` `sqrt-unprod_binary64_2485` `associate-r/_binary64_2407` `-commutative_binary64_2396` `frac-2neg_binary64_2476` `clear-num_binary64_2464`

Counts

2 → 102

Calls

2 calls:

25.0ms	(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 F -1/2)) (sqrt.f64 C)))
6.0ms	(/.f64 (sqrt.f64 (*.f64 F -1/2)) (sqrt.f64 C))

Compiler

Compiled 2073 to 1432 computations (30.9% saved)

series164.0ms (0.5%)

Error

26.8b

Counts

2 → 12

Calls

2 calls:

83.0ms	(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 F -1/2)) (sqrt.f64 C)))
66.0ms	(/.f64 (sqrt.f64 (*.f64 F -1/2)) (sqrt.f64 C))

Compiler

Compiled 542 to 547 computations (-0.9% saved)

simplify115.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	5025	2172

prune152.0ms (0.5%)

Pruning

32 alts after pruning (30 fresh and 2 done)

	Pruned	Kept	Total
New	110	4	114
Fresh	2	26	28
Picked	0	1	1
Done	0	1	1
Total	112	32	144

Error

26.8b

Counts

144 → 32

Compiler

Compiled 2020 to 1411 computations (30.1% saved)

regimes4.8s (15.8%)

Accuracy

Total 4.4b remaining (13.9%)

Threshold costs 0b (0%)

Compiler

Compiled 40228 to 31623 computations (21.4% saved)

bsearch22.0ms (0.1%)

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

simplify53.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	608	413
1	608	413

Compiler

Compiled 536 to 362 computations (32.5% saved)

end0.0ms (0%)

sample12.0s (39.8%)

Algorithm

1×

intervals

Results

1.0s	5511×	body	128	valid
640.0ms	853×	body	1024	nan
635.0ms	873×	body	1024	valid
623.0ms	635×	body	2048	valid
556.0ms	604×	body	2048	nan
435.0ms	2499×	body	128	nan
317.0ms	595×	body	512	valid
290.0ms	550×	body	512	nan
141.0ms	385×	body	256	valid
119.0ms	339×	body	256	nan
1.0ms	1×	body	4096	valid

Compiler

Compiled 6308 to 4900 computations (22.3% saved)

Details

analyze3.5s (11.7%)

sample200.0ms (0.7%)

simplify58.0ms (0.2%)

prune5.0ms (0%)

localize33.0ms (0.1%)

rewrite1.0s (3.4%)

series5.6s (18.5%)

simplify153.0ms (0.5%)

prune974.0ms (3.2%)

localize10.0ms (0%)

rewrite132.0ms (0.4%)

series278.0ms (0.9%)

simplify107.0ms (0.4%)

prune143.0ms (0.5%)

localize17.0ms (0.1%)

rewrite101.0ms (0.3%)

series127.0ms (0.4%)

simplify97.0ms (0.3%)

prune134.0ms (0.4%)

localize8.0ms (0%)

rewrite175.0ms (0.6%)

series164.0ms (0.5%)

simplify115.0ms (0.4%)

prune152.0ms (0.5%)

regimes4.8s (15.8%)

bsearch22.0ms (0.1%)

simplify53.0ms (0.2%)

end0.0ms (0%)

sample12.0s (39.8%)

Profiling