Details

analyze270.0ms (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)

sample37.0ms (0.7%)

Algorithm

1×

intervals

Results

10.0ms	93×	body	256	valid
9.0ms	277×	pre	128	true
8.0ms	163×	body	128	valid
1.0ms	21×	body	128	nan

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify406.0ms (7.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (313.0ms)

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

Merged error: 44.4b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.1b	(-.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))
38.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite35.0ms (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)
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series268.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

109.0ms	(/.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)
60.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
35.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify90.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4899	1979
1	4899	1979

prune101.0ms (1.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	82	4	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	4	87

Merged error: 0.2b

Counts

87 → 4

Compiler

Compiled 2054 to 1214 computations (40.9% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
0.1b	(-.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))
0.3b	(/.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))

series463.0ms (8.2%)

Counts

4 → 12

Calls

4 calls:

206.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
160.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
62.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
34.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify62.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4982	3037
1	4982	3037

prune160.0ms (2.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	104	7	111
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	107	8	115

Merged error: 0b

Counts

115 → 8

Compiler

Compiled 3270 to 2015 computations (38.4% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite29.0ms (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))))

series334.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

177.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
62.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
62.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
33.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify77.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4905	1972
1	4905	1972

prune106.0ms (1.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	85	7	92

Merged error: 0b

Counts

92 → 7

Compiler

Compiled 2298 to 1429 computations (37.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
0.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
0.1b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
0.3b	(.f64 (.f64 c -4) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))

rewrite43.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64_2465`
24×	`times-frac_binary64_2471`
21×	`add-cube-cbrt_binary64_2500` `add-sqr-sqrt_binary64_2487`
18×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `associate-r_binary64_2405`
9×	`pow1_binary64_2526`
8×	`add-log-exp_binary64_2504` `distribute-lft-out_binary64_2416`
6×	`prod-exp_binary64_2514` `cbrt-unprod_binary64_2498`
4×	`associate-/r*_binary64_2409` `associate-/r/_binary64_2411`
3×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `cbrt-undiv_binary64_2499` `div-exp_binary64_2516` `pow-prod-down_binary64_2536` `associate-/l*_binary64_2410`
2×	`div-inv_binary64_2462`
1×	`-commutative_binary64_2396` `+-commutative_binary64_2395` `flip--_binary64_2440` `sum-log_binary64_2556` `associate-r/_binary64_2407` `clear-num_binary64_2464` `sub-neg_binary64_2458` `cancel-sign-sub-inv_binary64_2431` `diff-log_binary64_2557` `frac-2neg_binary64_2476` `flip3--_binary64_2469` `associate-l_binary64_2406`

Counts

4 → 95

Calls

4 calls:

13.0ms	(.f64 (.f64 c -4) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
7.0ms	(/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
4.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

series384.0ms (6.8%)

Counts

4 → 12

Calls

4 calls:

190.0ms	(.f64 (.f64 c -4) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
101.0ms	(/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
60.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
33.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify81.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4961	2612
1	4961	2612

prune126.0ms (2.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	107	7	114

Merged error: 0b

Counts

114 → 7

Compiler

Compiled 2744 to 1732 computations (36.9% saved)

regimes390.0ms (6.9%)

Compiler: Compiled 5224 to 3942 computations (24.5% 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%)

sample2.1s (37.2%)

Algorithm

1×

intervals

Results

281.0ms	2855×	body	256	valid
272.0ms	8833×	pre	128	true
265.0ms	5144×	body	128	valid
41.0ms	833×	body	128	nan
0.0ms	1×	body	512	valid

Compiler

Compiled 1342 to 1014 computations (24.4% saved)

Details

analyze270.0ms (4.7%)

sample37.0ms (0.7%)

simplify406.0ms (7.1%)

prune4.0ms (0.1%)

localize14.0ms (0.2%)

rewrite35.0ms (0.6%)

series268.0ms (4.7%)

simplify90.0ms (1.6%)

prune101.0ms (1.8%)

localize14.0ms (0.2%)

rewrite46.0ms (0.8%)

series463.0ms (8.2%)

simplify62.0ms (1.1%)

prune160.0ms (2.8%)

localize13.0ms (0.2%)

rewrite29.0ms (0.5%)

series334.0ms (5.9%)

simplify77.0ms (1.4%)

prune106.0ms (1.9%)

localize12.0ms (0.2%)

rewrite43.0ms (0.8%)

series384.0ms (6.8%)

simplify81.0ms (1.4%)

prune126.0ms (2.2%)

regimes390.0ms (6.9%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample2.1s (37.2%)

Profiling