Details

analyze272.0ms (4.5%)

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 (0.6%)

Algorithm

1×

intervals

Results

9.0ms	93×	body	256	valid
9.0ms	283×	pre	128	true
8.0ms	163×	body	128	valid
1.0ms	27×	body	128	nan

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify399.0ms (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

44.3b

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))
39.9b	(-.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)
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series268.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

111.0ms	(/.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)
58.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
34.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify92.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4899	1979
1	4899	1979

prune104.0ms (1.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	81	5	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	5	87

Error

0.2b

Counts

87 → 5

Compiler

Compiled 2097 to 1244 computations (40.7% 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))
0.2b	(/.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))

series454.0ms (7.6%)

Counts

4 → 12

Calls

4 calls:

205.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
151.0ms	(/.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))))
37.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify61.0ms (1%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4982	3037
1	4982	3037

prune162.0ms (2.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	102	9	111
Fresh	4	0	4
Picked	1	0	1
Done	0	0	0
Total	107	9	116

Error

Counts

116 → 9

Compiler

Compiled 3339 to 2062 computations (38.2% 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 (.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))))))

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))))

series330.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

177.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
61.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
59.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
33.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify80.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4905	1972
1	4905	1972

prune108.0ms (1.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	85	8	93

Error

Counts

93 → 8

Compiler

Compiled 2360 to 1470 computations (37.7% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite48.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`times-frac_binary64_2471`
96×	`*-un-lft-identity_binary64_2465`
62×	`add-cube-cbrt_binary64_2500` `add-sqr-sqrt_binary64_2487`
19×	`associate-/r*_binary64_2409`
17×	`add-exp-log_binary64_2503` `distribute-lft-out_binary64_2416`
11×	`add-cbrt-cube_binary64_2501`
8×	`add-log-exp_binary64_2504` `div-exp_binary64_2516`
7×	`associate-/l*_binary64_2410`
6×	`div-inv_binary64_2462`
5×	`pow1_binary64_2526`
4×	`cbrt-undiv_binary64_2499`
2×	`flip3-+_binary64_2468` `associate-/l/_binary64_2412` `flip-+_binary64_2439` `rec-exp_binary64_2515` `clear-num_binary64_2464` `frac-2neg_binary64_2476` `1-exp_binary64_2509`
1×	`+-commutative_binary64_2395` `flip--_binary64_2440` `sum-log_binary64_2556` `inv-pow_binary64_2550` `pow-flip_binary64_2539` `sub-neg_binary64_2458` `cancel-sign-sub-inv_binary64_2431` `diff-log_binary64_2557` `associate-/r/_binary64_2411` `flip3--_binary64_2469`

Counts

4 → 145

Calls

4 calls:

12.0ms	(/.f64 1 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))) c))
8.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))) c)
7.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))

series489.0ms (8.2%)

Counts

4 → 12

Calls

4 calls:

325.0ms	(/.f64 1 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))) c))
72.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))) c)
60.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
32.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify108.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5148	4909

prune216.0ms (3.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	157	0	157
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	157	8	165

Error

Counts

165 → 8

Compiler

Compiled 4701 to 2935 computations (37.6% saved)

regimes409.0ms (6.8%)

Accuracy

Total 0.2b remaining (99.8%)

Threshold costs 0.2b (99.8%)

Compiler

Compiled 5800 to 4346 computations (25.1% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	63	24
1	63	24

end0.0ms (0%)

sample2.2s (36.5%)

Algorithm

1×

intervals

Results

293.0ms	2902×	body	256	valid
275.0ms	8894×	pre	128	true
260.0ms	5098×	body	128	valid
42.0ms	894×	body	128	nan

Compiler

Compiled 1486 to 1115 computations (25% saved)

Details

analyze272.0ms (4.5%)

sample37.0ms (0.6%)

simplify399.0ms (6.7%)

prune4.0ms (0.1%)

localize14.0ms (0.2%)

rewrite35.0ms (0.6%)

series268.0ms (4.5%)

simplify92.0ms (1.5%)

prune104.0ms (1.7%)

localize14.0ms (0.2%)

rewrite46.0ms (0.8%)

series454.0ms (7.6%)

simplify61.0ms (1%)

prune162.0ms (2.7%)

localize13.0ms (0.2%)

rewrite29.0ms (0.5%)

series330.0ms (5.5%)

simplify80.0ms (1.3%)

prune108.0ms (1.8%)

localize13.0ms (0.2%)

rewrite48.0ms (0.8%)

series489.0ms (8.2%)

simplify108.0ms (1.8%)

prune216.0ms (3.6%)

regimes409.0ms (6.8%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.2s (36.5%)

Profiling