Details

analyze455.0ms (7.3%)

Algorithm

1×

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)

sample38.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms	174×	body	128	valid
7.0ms	30×	body	2048	valid
5.0ms	18×	body	4096	valid
3.0ms	17×	body	1024	valid
1.0ms	10×	body	512	valid
1.0ms	19×	body	128	nan
1.0ms	7×	body	256	valid
1.0ms	12×	body	128	invalid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify72.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	927	24
1	927	24

prune6.0ms (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: 33.5b

Counts

2 → 1

Compiler

Compiled 65 to 53 computations (18.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
0.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
23.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite41.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64` `add-cube-cbrt_binary64`
6×	`difference-of-squares_binary64` `associate-/l*_binary64` `times-frac_binary64` `sqrt-prod_binary64`
5×	`pow1_binary64`
4×	`flip3--_binary64` `cancel-sign-sub-inv_binary64` `flip--_binary64`
3×	`distribute-lft-out--_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`associate-/r*_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

4 → 74

Calls

4 calls:

13.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
12.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series535.0ms (8.6%)

Counts

4 → 12

Calls

4 calls:

222.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
124.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
124.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
65.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify69.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4888	1979
1	4888	1979

prune324.0ms (5.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	79	7	86
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	79	8	87

Merged error: 5.9b

Counts

87 → 8

Compiler

Compiled 6134 to 4247 computations (30.8% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.9b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
2.7b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 a 2))
8.3b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
23.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite52.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
22×	`times-frac_binary64`
21×	`*-un-lft-identity_binary64`
17×	`cbrt-undiv_binary64` `div-exp_binary64`
13×	`cbrt-unprod_binary64` `prod-exp_binary64`
12×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64` `associate-/l*_binary64`
6×	`add-log-exp_binary64` `associate-/r/_binary64`
5×	`associate-/r*_binary64` `pow1_binary64` `distribute-lft-out_binary64`
4×	`flip3-+_binary64` `div-inv_binary64` `flip-+_binary64`
3×	`sqrt-prod_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64` `sqrt-div_binary64`
1×	`associate-/l/_binary64` `pow1/2_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

4 → 102

Calls

4 calls:

15.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 a 2))
12.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series946.0ms (15.2%)

Counts

4 → 12

Calls

4 calls:

370.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
315.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 a 2))
133.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
127.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify73.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4978	3121
1	4978	3121

prune254.0ms (4.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	112	2	114
Fresh	3	3	6
Picked	1	0	1
Done	0	1	1
Total	116	6	122

Merged error: 5.8b

Counts

122 → 6

Compiler

Compiled 5105 to 3304 computations (35.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
0.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.9b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
23.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite32.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
8×	`add-log-exp_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-lft-out_binary64`
4×	`associate-/r*_binary64`
3×	`associate-/l*_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `cancel-sign-sub-inv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 72

Calls

4 calls:

9.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series639.0ms (10.3%)

Counts

4 → 12

Calls

4 calls:

337.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
122.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
114.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
66.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify67.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5229	1969

prune106.0ms (1.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	84	6	90

Merged error: 5.8b

Counts

90 → 6

Compiler

Compiled 2361 to 1395 computations (40.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 c -4) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
0.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.9b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
23.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite41.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64`
18×	`associate-r_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
10×	`pow1_binary64`
8×	`add-log-exp_binary64`
6×	`cbrt-unprod_binary64` `prod-exp_binary64`
4×	`distribute-lft-out_binary64`
3×	`pow-prod-down_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `div-exp_binary64` `flip--_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `associate-r/_binary64` `associate-l_binary64` `cancel-sign-sub-inv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `+-commutative_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 77

Calls

4 calls:

17.0ms	(.f64 (.f64 c -4) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series682.0ms (11%)

Counts

4 → 12

Calls

4 calls:

376.0ms	(.f64 (.f64 c -4) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
124.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
117.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
65.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify72.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5196	1915

prune114.0ms (1.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	88	7	95

Merged error: 5.8b

Counts

95 → 7

Compiler

Compiled 2385 to 1419 computations (40.5% saved)

regimes86.0ms (1.4%)

Compiler: Compiled 282 to 252 computations (10.6% saved)

bsearch104.0ms (1.7%)

Steps

Iters	Range	Point
8	7.908407481357268e+108	8.800611180477259e+111	1.435883796381114e+111
9	1.1231289846519644e-296	6.9432611851043545e-289	1.5480753463744248e-296
10	-9.047595409010687e+136	-1.802772324569355e+125	-2.8122428251785394e+127

Iters

Range

Point

7.908407481357268e+108

8.800611180477259e+111

1.435883796381114e+111

1.1231289846519644e-296

6.9432611851043545e-289

1.5480753463744248e-296

-9.047595409010687e+136

-1.802772324569355e+125

-2.8122428251785394e+127

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	102	82
1	102	82

end0.0ms (0%)

sample1.3s (21.6%)

Algorithm

1×

intervals

Results

277.0ms	5265×	body	128	valid
275.0ms	1084×	body	2048	valid
141.0ms	725×	body	1024	valid
110.0ms	363×	body	4096	valid
56.0ms	361×	body	512	valid
36.0ms	740×	body	128	nan
21.0ms	401×	body	128	invalid
20.0ms	202×	body	256	valid

Compiler

Compiled 207 to 157 computations (24.2% saved)

Details

analyze455.0ms (7.3%)

sample38.0ms (0.6%)

simplify72.0ms (1.2%)

prune6.0ms (0.1%)

localize11.0ms (0.2%)

rewrite41.0ms (0.7%)

series535.0ms (8.6%)

simplify69.0ms (1.1%)

prune324.0ms (5.2%)

localize14.0ms (0.2%)

rewrite52.0ms (0.8%)

series946.0ms (15.2%)

simplify73.0ms (1.2%)

prune254.0ms (4.1%)

localize12.0ms (0.2%)

rewrite32.0ms (0.5%)

series639.0ms (10.3%)

simplify67.0ms (1.1%)

prune106.0ms (1.7%)

localize12.0ms (0.2%)

rewrite41.0ms (0.7%)

series682.0ms (11%)

simplify72.0ms (1.2%)

prune114.0ms (1.8%)

regimes86.0ms (1.4%)

bsearch104.0ms (1.7%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.3s (21.6%)

Profiling