Details

analyze2.3s (12.2%)

Algorithm

1×

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

Compiler

Compiled 41 to 33 computations (19.5% saved)

sample130.0ms (0.7%)

Algorithm

1×

intervals

Results

25.0ms	182×	body	128	valid
14.0ms	26×	body	1024	valid
13.0ms	25×	body	1024	nan
13.0ms	19×	body	2048	nan
11.0ms	82×	body	128	nan
9.0ms	13×	body	2048	valid
8.0ms	20×	body	512	nan
8.0ms	19×	body	512	valid
7.0ms	9×	body	256	nan
4.0ms	16×	body	256	valid

Compiler

Compiled 81 to 69 computations (14.8% saved)

simplify149.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (47.0ms)

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

Merged error: 51.8b

Counts

2 → 1

Compiler

Compiled 80 to 59 computations (26.3% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

7.7b	(.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)
15.0b	(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))))))
22.6b	(/.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)))
35.9b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))

rewrite101.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

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-times_binary64_2475` `frac-sub_binary64_2474`
22×	`flip--_binary64_2440` `flip3--_binary64_2469`
20×	`associate-/l/_binary64_2412` `distribute-neg-frac_binary64_2429`
17×	`pow1_binary64_2526`
16×	`distribute-lft-neg-in_binary64_2422` `distribute-rgt-neg-in_binary64_2423`
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×	`associate-/r_binary64_2409` `associate-r_binary64_2405` `distribute-lft-out_binary64_2416` `associate-l*_binary64_2406`
2×	`pow1/2_binary64_2545` `associate-/r/_binary64_2411`
1×	`*-commutative_binary64_2396` `clear-num_binary64_2464` `cbrt-undiv_binary64_2499` `div-sub_binary64_2470` `distribute-lft-out--_binary64_2417` `unswap-sqr_binary64_2433` `div-exp_binary64_2516` `div-inv_binary64_2462` `rem-sqrt-square_binary64_2478` `prod-exp_binary64_2514` `frac-2neg_binary64_2476` `distribute-frac-neg_binary64_2428` `neg-sub0_binary64_2460` `cbrt-unprod_binary64_2498`

Counts

4 → 158

Calls

4 calls:

32.0ms	(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)))
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)

series856.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

366.0ms	(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))))))
365.0ms	(/.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)))
64.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))
61.0ms	(.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)

simplify150.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4948	11070
1	4948	11070

prune612.0ms (3.3%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	153	17	170
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	154	17	171

Merged error: 46.6b

Counts

171 → 17

Compiler

Compiled 12188 to 6910 computations (43.3% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

7.7b	(.f64 (-.f64 (.f64 B B) (.f64 C (.f64 A 4))) F)
15.0b	(sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 C (.f64 A 4))) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))))
22.3b	(/.f64 (-.f64 (.f64 B B) (.f64 C (.f64 A 4))) (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 C (.f64 A 4))) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B)))))))
35.9b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

rewrite96.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`sqrt-div_binary64_2482`
40×	`associate-*r/_binary64_2407`
34×	`associate-*l/_binary64_2408`
25×	`flip3-+_binary64_2468` `flip-+_binary64_2439`
24×	`frac-times_binary64_2475` `frac-sub_binary64_2474`
22×	`flip--_binary64_2440` `flip3--_binary64_2469`
20×	`associate-/r/_binary64_2411`
19×	`add-sqr-sqrt_binary64_2487`
17×	`pow1_binary64_2526`
16×	`*-un-lft-identity_binary64_2465` `add-cube-cbrt_binary64_2500`
12×	`times-frac_binary64_2471`
8×	`sqrt-prod_binary64_2481` `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` `associate-/r*_binary64_2409`
3×	`associate-r_binary64_2405` `associate-/l_binary64_2410` `associate-l*_binary64_2406`
2×	`pow1/2_binary64_2545` `associate-/l/_binary64_2412`
1×	`*-commutative_binary64_2396` `clear-num_binary64_2464` `cbrt-undiv_binary64_2499` `div-sub_binary64_2470` `unswap-sqr_binary64_2433` `div-exp_binary64_2516` `div-inv_binary64_2462` `rem-sqrt-square_binary64_2478` `prod-exp_binary64_2514` `frac-2neg_binary64_2476` `cbrt-unprod_binary64_2498`

Counts

4 → 122

Calls

4 calls:

29.0ms	(/.f64 (-.f64 (.f64 B B) (.f64 C (.f64 A 4))) (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 C (.f64 A 4))) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B)))))))
22.0ms	(sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 C (.f64 A 4))) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))))
7.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
7.0ms	(.f64 (-.f64 (.f64 B B) (.f64 C (.f64 A 4))) F)

series1.1s (5.7%)

Counts

4 → 12

Calls

4 calls:

573.0ms	(/.f64 (-.f64 (.f64 B B) (.f64 C (.f64 A 4))) (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 C (.f64 A 4))) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B)))))))
366.0ms	(sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 C (.f64 A 4))) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))))
67.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
64.0ms	(.f64 (-.f64 (.f64 B B) (.f64 C (.f64 A 4))) F)

simplify110.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5274	8210

prune385.0ms (2.1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	132	2	134
Fresh	3	13	16
Picked	1	0	1
Done	0	0	0
Total	136	15	151

Merged error: 46.6b

Counts

151 → 15

Compiler

Compiled 9597 to 5064 computations (47.2% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

23.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B)))) (cbrt.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B))))) (cbrt.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B))))))))) (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)))
35.9b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
35.9b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
35.9b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

rewrite222.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

494×	`sqrt-div_binary64_2482`
324×	`cbrt-div_binary64_2497`
276×	`frac-times_binary64_2475`
243×	`flip3-+_binary64_2468` `flip-+_binary64_2439`
212×	`associate-*r/_binary64_2407`
196×	`associate-*l/_binary64_2408`
164×	`associate-/l/_binary64_2412` `distribute-neg-frac_binary64_2429`
156×	`frac-sub_binary64_2474`
59×	`flip--_binary64_2440` `flip3--_binary64_2469`
36×	`times-frac_binary64_2471`
35×	`add-sqr-sqrt_binary64_2487`
32×	`*-un-lft-identity_binary64_2465` `add-cube-cbrt_binary64_2500`
17×	`sqrt-prod_binary64_2481`
16×	`distribute-lft-neg-in_binary64_2422` `distribute-rgt-neg-in_binary64_2423`
12×	`associate-/l*_binary64_2410`
7×	`pow1_binary64_2526`
6×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
4×	`add-log-exp_binary64_2504` `neg-mul-1_binary64_2461`
3×	`associate-/r*_binary64_2409` `pow1/2_binary64_2545` `rem-sqrt-square_binary64_2478` `sqrt-pow1_binary64_2483`
2×	`associate-/r/_binary64_2411`
1×	`clear-num_binary64_2464` `cbrt-undiv_binary64_2499` `div-sub_binary64_2470` `div-exp_binary64_2516` `div-inv_binary64_2462` `frac-2neg_binary64_2476` `distribute-frac-neg_binary64_2428` `neg-sub0_binary64_2460`

Counts

4 → 276

Calls

4 calls:

58.0ms	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B)))) (cbrt.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B))))) (cbrt.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B))))))))) (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)))
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)))

series591.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

375.0ms	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B)))) (cbrt.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B))))) (cbrt.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B))))))))) (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)))
76.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
70.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
70.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

simplify224.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

288 → 288

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5241	21545

prune2.7s (14.5%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	281	7	288
Fresh	2	12	14
Picked	1	0	1
Done	0	0	0
Total	284	19	303

Merged error: 46.6b

Counts

303 → 19

Compiler

Compiled 41023 to 20842 computations (49.2% saved)

localize31.0ms (0.2%)

Local error

Found 4 expressions with local error:

35.9b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
35.9b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
35.9b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
37.1b	(cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

rewrite44.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_2487`
9×	`sqrt-prod_binary64_2481`
8×	`*-un-lft-identity_binary64_2465` `add-cube-cbrt_binary64_2500`
7×	`pow1_binary64_2526`
6×	`sqrt-div_binary64_2482`
4×	`flip3-+_binary64_2468` `add-log-exp_binary64_2504` `flip-+_binary64_2439` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
3×	`pow1/2_binary64_2545` `rem-sqrt-square_binary64_2478` `sqrt-pow1_binary64_2483` `cbrt-prod_binary64_2496`
2×	`cbrt-div_binary64_2497`
1×	`pow1/3_binary64_2547`

Counts

4 → 58

Calls

4 calls:

8.0ms	(sqrt.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	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
7.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

series363.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

149.0ms	(cbrt.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)))
71.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

simplify59.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4959	1280
1	4959	1280

prune248.0ms (1.3%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	67	3	70
Fresh	0	18	18
Picked	1	0	1
Done	0	0	0
Total	68	21	89

Merged error: 46.6b

Counts

89 → 21

Compiler

Compiled 5776 to 3268 computations (43.4% saved)

regimes1.5s (7.9%)

Compiler: Compiled 27205 to 17305 computations (36.4% saved)

bsearch8.0ms (0%)

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

simplify19.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (15.0ms)

Iter	Nodes	Cost
0	465	259
1	465	259

end0.0ms (0%)

sample6.7s (35.8%)

Algorithm

1×

intervals

Results

761.0ms	5494×	body	128	valid
490.0ms	902×	body	1024	valid
469.0ms	654×	body	2048	valid
452.0ms	842×	body	1024	nan
390.0ms	546×	body	2048	nan
363.0ms	2610×	body	128	nan
237.0ms	590×	body	512	valid
223.0ms	559×	body	512	nan
102.0ms	356×	body	256	valid
87.0ms	330×	body	256	nan
7.0ms	4×	body	4096	valid

Compiler

Compiled 4709 to 3004 computations (36.2% saved)

Details

analyze2.3s (12.2%)

sample130.0ms (0.7%)

simplify149.0ms (0.8%)

prune4.0ms (0%)

localize20.0ms (0.1%)

rewrite101.0ms (0.5%)

series856.0ms (4.6%)

simplify150.0ms (0.8%)

prune612.0ms (3.3%)

localize24.0ms (0.1%)

rewrite96.0ms (0.5%)

series1.1s (5.7%)

simplify110.0ms (0.6%)

prune385.0ms (2.1%)

localize30.0ms (0.2%)

rewrite222.0ms (1.2%)

series591.0ms (3.1%)

simplify224.0ms (1.2%)

prune2.7s (14.5%)

localize31.0ms (0.2%)

rewrite44.0ms (0.2%)

series363.0ms (1.9%)

simplify59.0ms (0.3%)

prune248.0ms (1.3%)

regimes1.5s (7.9%)

bsearch8.0ms (0%)

simplify19.0ms (0.1%)

end0.0ms (0%)

sample6.7s (35.8%)

Profiling