Details

analyze685.0ms (11.2%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5132	96
0	3	3
1	3	3

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample45.0ms (0.7%)

Algorithm

1×

intervals

Results

9.0ms	161×	body	128	valid
8.0ms	33×	body	2048	valid
7.0ms	14×	body	4096	valid
5.0ms	26×	body	1024	valid
2.0ms	12×	body	512	valid
1.0ms	25×	body	128	nan
1.0ms	10×	body	256	valid
1.0ms	10×	body	128	invalid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify337.0ms (5.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (332.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune5.0ms (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

34.7b

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	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
20.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite39.0ms (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:

15.0ms	(/.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	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series273.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

112.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
63.0ms	(-.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)))
35.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify101.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4899	1979
1	4899	1979

prune115.0ms (1.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	79	7	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	7	87

Error

4.3b

Counts

87 → 7

Compiler

Compiled 2086 to 1245 computations (40.3% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.7b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
4.4b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
8.0b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
20.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite49.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
22×	`times-frac_binary64_2471`
21×	`*-un-lft-identity_binary64_2465`
17×	`cbrt-undiv_binary64_2499` `div-exp_binary64_2516`
13×	`prod-exp_binary64_2514` `cbrt-unprod_binary64_2498`
12×	`add-sqr-sqrt_binary64_2487`
11×	`add-cube-cbrt_binary64_2500` `associate-/l*_binary64_2410`
6×	`add-log-exp_binary64_2504` `associate-/r/_binary64_2411`
5×	`associate-/r*_binary64_2409` `pow1_binary64_2526` `distribute-lft-out_binary64_2416`
4×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `div-inv_binary64_2462`
3×	`sqrt-prod_binary64_2481`
2×	`clear-num_binary64_2464` `frac-2neg_binary64_2476` `sqrt-div_binary64_2482`
1×	`+-commutative_binary64_2395` `flip--_binary64_2440` `sum-log_binary64_2556` `pow1/2_binary64_2545` `associate-/l/_binary64_2412` `rem-sqrt-square_binary64_2478` `flip3--_binary64_2469` `sqrt-pow1_binary64_2483`

Counts

4 → 102

Calls

4 calls:

15.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
12.0ms	(/.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	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series495.0ms (8.1%)

Counts

4 → 12

Calls

4 calls:

207.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
162.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
68.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
59.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify107.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4956	3121
1	4956	3121

prune147.0ms (2.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	114	7	121

Error

4.2b

Counts

121 → 7

Compiler

Compiled 3228 to 1983 computations (38.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.7b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
20.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite30.0ms (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 (*.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))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series333.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

172.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
67.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
61.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
33.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify86.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4891	1972
1	4891	1972

prune100.0ms (1.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	84	7	91

Error

4.2b

Counts

91 → 7

Compiler

Compiled 2226 to 1380 computations (38% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
20.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite43.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64_2487`
18×	`*-un-lft-identity_binary64_2465`
14×	`add-cube-cbrt_binary64_2500`
13×	`associate-r_binary64_2405`
10×	`times-frac_binary64_2471`
9×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
8×	`add-log-exp_binary64_2504`
7×	`pow1_binary64_2526`
6×	`associate-l_binary64_2406`
5×	`sqrt-prod_binary64_2481` `flip--_binary64_2440` `flip3--_binary64_2469`
4×	`difference-of-squares_binary64_2434` `cancel-sign-sub-inv_binary64_2431`
2×	`associate-*l/_binary64_2408` `frac-times_binary64_2475` `distribute-lft-out--_binary64_2417` `sub-neg_binary64_2458` `unswap-sqr_binary64_2433` `diff-log_binary64_2557` `prod-exp_binary64_2514` `sqrt-div_binary64_2482` `cbrt-unprod_binary64_2498`
1×	`-commutative_binary64_2396` `pow1/2_binary64_2545` `associate-r/_binary64_2407` `cbrt-undiv_binary64_2499` `div-exp_binary64_2516` `div-inv_binary64_2462` `rem-sqrt-square_binary64_2478` `pow-prod-down_binary64_2536` `sqrt-pow1_binary64_2483`

Counts

4 → 83

Calls

4 calls:

16.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
7.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series279.0ms (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 1/2 a))
66.0ms	(-.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)))
38.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify100.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	5360	2202

prune101.0ms (1.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	95	7	102

Error

4.2b

Counts

102 → 7

Compiler

Compiled 2191 to 1291 computations (41.1% saved)

regimes524.0ms (8.5%)

Accuracy

Total 1.0b remaining (14.8%)

Threshold costs 1.0b (14.8%)

Compiler

Compiled 3136 to 2504 computations (20.2% saved)

bsearch108.0ms (1.8%)

Steps

Iters	Range	Point
7	1.8515760575460165e+108	7.079746839452132e+109	9.806096002062306e+108
9	3.471655958753961e-308	1.338164201957951e-301	7.151073671652035e-308
9	-3.203657050301464e+105	-6.409993448757428e+99	-3.161255245507665e+105

Iters

Range

Point

1.8515760575460165e+108

7.079746839452132e+109

9.806096002062306e+108

3.471655958753961e-308

1.338164201957951e-301

7.151073671652035e-308

-3.203657050301464e+105

-6.409993448757428e+99

-3.161255245507665e+105

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	105	82
1	105	82

end0.0ms (0%)

sample2.0s (32.2%)

Algorithm

1×

intervals

Results

295.0ms	5228×	body	128	valid
280.0ms	1110×	body	2048	valid
150.0ms	748×	body	1024	valid
128.0ms	390×	body	4096	valid
49.0ms	332×	body	512	valid
35.0ms	639×	body	128	nan
22.0ms	192×	body	256	valid
20.0ms	359×	body	128	invalid

Compiler

Compiled 876 to 684 computations (21.9% saved)

Details

analyze685.0ms (11.2%)

sample45.0ms (0.7%)

simplify337.0ms (5.5%)

prune5.0ms (0.1%)

localize11.0ms (0.2%)

rewrite39.0ms (0.6%)

series273.0ms (4.5%)

simplify101.0ms (1.6%)

prune115.0ms (1.9%)

localize17.0ms (0.3%)

rewrite49.0ms (0.8%)

series495.0ms (8.1%)

simplify107.0ms (1.7%)

prune147.0ms (2.4%)

localize13.0ms (0.2%)

rewrite30.0ms (0.5%)

series333.0ms (5.4%)

simplify86.0ms (1.4%)

prune100.0ms (1.6%)

localize12.0ms (0.2%)

rewrite43.0ms (0.7%)

series279.0ms (4.5%)

simplify100.0ms (1.6%)

prune101.0ms (1.6%)

regimes524.0ms (8.5%)

bsearch108.0ms (1.8%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.0s (32.2%)

Profiling