Details

analyze279.0ms (4.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 30 to 24 computations (20% saved)

sample38.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms	290×	pre	128	true
8.0ms	173×	body	128	valid
8.0ms	83×	body	256	valid
2.0ms	34×	body	128	nan

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify405.0ms (6.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (306.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

40.7b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.2b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
36.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite34.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_2487`
14×	`*-un-lft-identity_binary64_2465`
9×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
8×	`add-log-exp_binary64_2504` `add-cube-cbrt_binary64_2500`
6×	`difference-of-squares_binary64_2434` `times-frac_binary64_2471` `sqrt-prod_binary64_2481` `associate-/l*_binary64_2410`
5×	`pow1_binary64_2526`
4×	`flip--_binary64_2440` `cancel-sign-sub-inv_binary64_2431` `flip3--_binary64_2469`
3×	`distribute-lft-out--_binary64_2417`
2×	`associate-/l/_binary64_2412` `cbrt-undiv_binary64_2499` `sub-neg_binary64_2458` `div-exp_binary64_2516` `diff-log_binary64_2557` `sqrt-div_binary64_2482`
1×	`associate-/r*_binary64_2409` `pow1/2_binary64_2545` `clear-num_binary64_2464` `div-sub_binary64_2470` `div-inv_binary64_2462` `rem-sqrt-square_binary64_2478` `prod-exp_binary64_2514` `frac-2neg_binary64_2476` `sqrt-pow1_binary64_2483` `cbrt-unprod_binary64_2498`

Counts

4 → 74

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series264.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

105.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
64.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
63.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
32.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify92.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4899	1979
1	4899	1979

prune103.0ms (1.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	81	5	86
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	81	6	87

Error

0.2b

Counts

87 → 6

Compiler

Compiled 2080 to 1238 computations (40.5% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.3b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
0.4b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

rewrite46.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
22×	`times-frac_binary64_2471`
20×	`*-un-lft-identity_binary64_2465`
17×	`cbrt-undiv_binary64_2499` `div-exp_binary64_2516`
13×	`prod-exp_binary64_2514` `cbrt-unprod_binary64_2498`
11×	`associate-/l*_binary64_2410`
10×	`add-cube-cbrt_binary64_2500` `add-sqr-sqrt_binary64_2487`
8×	`add-log-exp_binary64_2504`
6×	`associate-/r/_binary64_2411`
5×	`associate-/r*_binary64_2409` `distribute-lft-out_binary64_2416`
4×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `div-inv_binary64_2462` `pow1_binary64_2526`
2×	`clear-num_binary64_2464` `frac-2neg_binary64_2476`
1×	`+-commutative_binary64_2395` `flip--_binary64_2440` `sum-log_binary64_2556` `associate-/l/_binary64_2412` `sub-neg_binary64_2458` `cancel-sign-sub-inv_binary64_2431` `diff-log_binary64_2557` `flip3--_binary64_2469`

Counts

4 → 99

Calls

4 calls:

14.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
11.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series465.0ms (7.7%)

Counts

4 → 12

Calls

4 calls:

210.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
159.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
60.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
35.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify67.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4982	3037
1	4982	3037

prune155.0ms (2.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	103	8	111
Fresh	4	0	4
Picked	1	0	1
Done	1	0	1
Total	109	8	117

Error

0.0b

Counts

117 → 8

Compiler

Compiled 3285 to 2026 computations (38.3% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
0.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
0.2b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
0.2b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

rewrite28.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_2465`
15×	`add-sqr-sqrt_binary64_2487`
14×	`add-cube-cbrt_binary64_2500`
12×	`times-frac_binary64_2471`
8×	`add-log-exp_binary64_2504`
6×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
5×	`pow1_binary64_2526` `distribute-lft-out_binary64_2416`
4×	`associate-/r*_binary64_2409`
3×	`sqrt-prod_binary64_2481` `associate-/l*_binary64_2410`
2×	`flip3-+_binary64_2468` `flip--_binary64_2440` `flip-+_binary64_2439` `associate-/r/_binary64_2411` `sqrt-div_binary64_2482` `flip3--_binary64_2469`
1×	`+-commutative_binary64_2395` `sum-log_binary64_2556` `pow1/2_binary64_2545` `clear-num_binary64_2464` `cbrt-undiv_binary64_2499` `sub-neg_binary64_2458` `cancel-sign-sub-inv_binary64_2431` `div-exp_binary64_2516` `div-inv_binary64_2462` `rem-sqrt-square_binary64_2478` `diff-log_binary64_2557` `frac-2neg_binary64_2476` `sqrt-pow1_binary64_2483`

Counts

4 → 72

Calls

4 calls:

8.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
4.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))

series323.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

170.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
60.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
59.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
33.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify79.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4905	1972
1	4905	1972

prune110.0ms (1.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	85	7	92

Error

0.0b

Counts

92 → 7

Compiler

Compiled 2382 to 1484 computations (37.7% saved)

localize23.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 c (+.f64 b (sqrt.f64 (/.f64 (-.f64 (pow.f64 b 4) (.f64 a (.f64 c (.f64 (.f64 c a) 16)))) (+.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
0.3b	(.f64 c (.f64 (*.f64 c a) 16))
0.3b	(.f64 a (.f64 c (.f64 (.f64 c a) 16)))
0.4b	(/.f64 (-.f64 (pow.f64 b 4) (.f64 a (.f64 c (.f64 (.f64 c a) 16)))) (+.f64 (.f64 b b) (.f64 c (*.f64 a 4))))

rewrite58.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`*-un-lft-identity_binary64_2465` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
27×	`pow1_binary64_2526`
23×	`add-cube-cbrt_binary64_2500` `add-sqr-sqrt_binary64_2487`
21×	`times-frac_binary64_2471`
16×	`prod-exp_binary64_2514` `pow-prod-down_binary64_2536` `cbrt-unprod_binary64_2498`
7×	`associate-/r*_binary64_2409`
6×	`associate-/l_binary64_2410` `associate-l*_binary64_2406`
4×	`add-log-exp_binary64_2504` `associate-/r/_binary64_2411` `distribute-lft-out_binary64_2416`
2×	`flip3-+_binary64_2468` `-commutative_binary64_2396` `associate-/l/_binary64_2412` `flip-+_binary64_2439` `clear-num_binary64_2464` `cbrt-undiv_binary64_2499` `div-exp_binary64_2516` `div-inv_binary64_2462` `frac-2neg_binary64_2476` `associate-r*_binary64_2405`
1×	`flip--_binary64_2440` `div-sub_binary64_2470` `flip3--_binary64_2469`

Counts

4 → 110

Calls

4 calls:

15.0ms	(/.f64 c (+.f64 b (sqrt.f64 (/.f64 (-.f64 (pow.f64 b 4) (.f64 a (.f64 c (.f64 (.f64 c a) 16)))) (+.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
11.0ms	(/.f64 (-.f64 (pow.f64 b 4) (.f64 a (.f64 c (.f64 (.f64 c a) 16)))) (+.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
10.0ms	(.f64 a (.f64 c (.f64 (.f64 c a) 16)))
7.0ms	(.f64 c (.f64 (*.f64 c a) 16))

series359.0ms (6%)

Counts

4 → 12

Calls

4 calls:

229.0ms	(/.f64 c (+.f64 b (sqrt.f64 (/.f64 (-.f64 (pow.f64 b 4) (.f64 a (.f64 c (.f64 (.f64 c a) 16)))) (+.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
77.0ms	(/.f64 (-.f64 (pow.f64 b 4) (.f64 a (.f64 c (.f64 (.f64 c a) 16)))) (+.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
34.0ms	(.f64 a (.f64 c (.f64 (.f64 c a) 16)))
19.0ms	(.f64 c (.f64 (*.f64 c a) 16))

simplify76.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5380	4088

prune215.0ms (3.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	120	2	122
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	122	7	129

Error

Counts

129 → 7

Compiler

Compiled 5083 to 2966 computations (41.6% saved)

regimes438.0ms (7.3%)

Accuracy

Total 0.2b remaining (99.2%)

Threshold costs 0.2b (99.2%)

Compiler

Compiled 5928 to 4422 computations (25.4% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	63	24
1	63	24

end0.0ms (0%)

sample2.3s (38.2%)

Algorithm

1×

intervals

Results

285.0ms	8927×	pre	128	true
280.0ms	2927×	body	256	valid
260.0ms	5071×	body	128	valid
51.0ms	927×	body	128	nan
0.0ms	2×	body	512	valid

Compiler

Compiled 1518 to 1134 computations (25.3% saved)

Details

analyze279.0ms (4.7%)

sample38.0ms (0.6%)

simplify405.0ms (6.7%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite34.0ms (0.6%)

series264.0ms (4.4%)

simplify92.0ms (1.5%)

prune103.0ms (1.7%)

localize14.0ms (0.2%)

rewrite46.0ms (0.8%)

series465.0ms (7.7%)

simplify67.0ms (1.1%)

prune155.0ms (2.6%)

localize16.0ms (0.3%)

rewrite28.0ms (0.5%)

series323.0ms (5.4%)

simplify79.0ms (1.3%)

prune110.0ms (1.8%)

localize23.0ms (0.4%)

rewrite58.0ms (1%)

series359.0ms (6%)

simplify76.0ms (1.3%)

prune215.0ms (3.6%)

regimes438.0ms (7.3%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample2.3s (38.2%)

Profiling