Details

analyze457.0ms (6.9%)

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)

sample39.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms	174×	body	128	valid
7.0ms	30×	body	2048	valid
6.0ms	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)

simplify74.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	927	24
1	927	24

prune9.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 33.5b

Counts

2 → 2

Compiler

Compiled 82 to 67 computations (18.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 4 a) c)
0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.7b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
23.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite33.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`add-cube-cbrt_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `prod-exp_binary64` `sqrt-prod_binary64`
2×	`flip3--_binary64` `distribute-lft-out_binary64` `flip--_binary64` `sqrt-div_binary64` `sum-log_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `neg-sub0_binary64` `associate-l_binary64` `associate-+l-_binary64` `cancel-sign-sub-inv_binary64` `sqrt-pow1_binary64` `distribute-rgt-neg-in_binary64` `rem-sqrt-square_binary64` `neg-log_binary64` `+-commutative_binary64` `flip-+_binary64` `*-commutative_binary64`

Counts

4 → 60

Calls

4 calls:

10.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
6.0ms	(.f64 (.f64 4 a) c)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series341.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

125.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
120.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
67.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
29.0ms	(.f64 (.f64 4 a) c)

simplify66.0ms (1%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5409	1184

prune257.0ms (3.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	66	6	72
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	67	7	74

Merged error: 10.7b

Counts

74 → 7

Compiler

Compiled 4529 to 3237 computations (28.5% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.9b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
2.7b	(/.f64 (/.f64 (.f64 (.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 2 a))
8.1b	(/.f64 (.f64 (.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
23.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite74.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
34×	`add-sqr-sqrt_binary64` `times-frac_binary64`
33×	`*-un-lft-identity_binary64`
17×	`cbrt-undiv_binary64` `div-exp_binary64`
14×	`associate-/l*_binary64`
13×	`cbrt-unprod_binary64` `add-cube-cbrt_binary64` `prod-exp_binary64`
11×	`sqrt-prod_binary64`
10×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
8×	`associate-/r*_binary64` `add-log-exp_binary64`
6×	`associate-/r/_binary64` `cancel-sign-sub-inv_binary64`
5×	`pow1_binary64` `flip3--_binary64` `distribute-rgt-neg-in_binary64` `flip--_binary64`
4×	`div-inv_binary64`
2×	`diff-log_binary64` `clear-num_binary64` `frac-2neg_binary64` `sqrt-div_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `pow1/2_binary64` `associate--l-_binary64` `neg-sub0_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `neg-log_binary64`

Counts

4 → 125

Calls

4 calls:

21.0ms	(/.f64 (/.f64 (.f64 (.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 2 a))
16.0ms	(/.f64 (.f64 (.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
12.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series994.0ms (15%)

Counts

4 → 12

Calls

4 calls:

408.0ms	(/.f64 (.f64 (.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
327.0ms	(/.f64 (/.f64 (.f64 (.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 2 a))
133.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
126.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify103.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4944	4228
1	4944	4228

prune452.0ms (6.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	130	7	137
Fresh	3	2	5
Picked	1	0	1
Done	0	1	1
Total	134	10	144

Merged error: 8.8b

Counts

144 → 10

Compiler

Compiled 9104 to 6088 computations (33.1% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.9b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
2.0b	(.f64 (.f64 a 2) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
2.7b	(/.f64 (.f64 (.f64 a 2) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))) a)
23.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite79.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64`
36×	`*-un-lft-identity_binary64`
34×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
27×	`associate-r_binary64`
24×	`times-frac_binary64`
20×	`add-cube-cbrt_binary64`
12×	`cbrt-unprod_binary64` `prod-exp_binary64`
10×	`pow1_binary64` `sqrt-prod_binary64`
9×	`cbrt-undiv_binary64` `div-exp_binary64`
8×	`add-log-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
6×	`cancel-sign-sub-inv_binary64`
4×	`distribute-rgt-neg-in_binary64`
3×	`pow-prod-down_binary64` `associate-/r*_binary64` `flip3--_binary64` `flip--_binary64`
2×	`diff-log_binary64` `associate-*r/_binary64` `associate-/r/_binary64` `div-inv_binary64` `sqrt-div_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `pow1/2_binary64` `associate--l-_binary64` `neg-sub0_binary64` `associate-l_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `neg-log_binary64` `frac-2neg_binary64` `associate-/l_binary64` `-commutative_binary64`

Counts

4 → 113

Calls

4 calls:

22.0ms	(.f64 (.f64 a 2) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
21.0ms	(/.f64 (.f64 (.f64 a 2) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))) a)
12.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series990.0ms (15%)

Counts

4 → 12

Calls

4 calls:

412.0ms	(.f64 (.f64 a 2) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
328.0ms	(/.f64 (.f64 (.f64 a 2) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))) a)
137.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
112.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify79.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4940	3223
1	4940	3223

prune281.0ms (4.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	120	5	125
Fresh	5	3	8
Picked	1	0	1
Done	0	1	1
Total	126	9	135

Merged error: 8.5b

Counts

135 → 9

Compiler

Compiled 5715 to 3686 computations (35.5% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 4 a) c)
0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.9b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
23.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite36.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64`
10×	`add-log-exp_binary64` `pow1_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-cube-cbrt_binary64`
7×	`cancel-sign-sub-inv_binary64` `sqrt-prod_binary64`
3×	`pow-prod-down_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `prod-exp_binary64` `flip--_binary64`
2×	`sub-neg_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate--l-_binary64` `neg-sub0_binary64` `associate-l_binary64` `sqrt-pow1_binary64` `distribute-rgt-neg-in_binary64` `rem-sqrt-square_binary64` `neg-log_binary64` `*-commutative_binary64`

Counts

4 → 68

Calls

4 calls:

12.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
6.0ms	(.f64 (.f64 4 a) c)
6.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series361.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

142.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
115.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
75.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
28.0ms	(.f64 (.f64 4 a) c)

simplify71.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5654	1423

prune114.0ms (1.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	79	1	80
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	80	9	89

Merged error: 7.2b

Counts

89 → 9

Compiler

Compiled 2322 to 1471 computations (36.6% saved)

regimes126.0ms (1.9%)

Compiler: Compiled 776 to 622 computations (19.8% saved)

bsearch114.0ms (1.7%)

Steps

Iters	Range	Point
8	7.908407481357268e+108	8.800611180477259e+111	1.435883796381114e+111
9	1.1231289846519644e-296	6.9432611851043545e-289	1.1385720630965241e-296
10	-9.047595409010687e+136	-1.802772324569355e+125	-8.959285179359827e+136

Iters

Range

Point

7.908407481357268e+108

8.800611180477259e+111

1.435883796381114e+111

1.1231289846519644e-296

6.9432611851043545e-289

1.1385720630965241e-296

-9.047595409010687e+136

-1.802772324569355e+125

-8.959285179359827e+136

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	112	112
1	112	112

end0.0ms (0%)

sample1.4s (21.3%)

Algorithm

1×

intervals

Results

292.0ms	5265×	body	128	valid
275.0ms	1084×	body	2048	valid
146.0ms	725×	body	1024	valid
115.0ms	363×	body	4096	valid
53.0ms	361×	body	512	valid
38.0ms	740×	body	128	nan
22.0ms	401×	body	128	invalid
20.0ms	202×	body	256	valid

Compiler

Compiled 277 to 211 computations (23.8% saved)

Details

analyze457.0ms (6.9%)

sample39.0ms (0.6%)

simplify74.0ms (1.1%)

prune9.0ms (0.1%)

localize12.0ms (0.2%)

rewrite33.0ms (0.5%)

series341.0ms (5.2%)

simplify66.0ms (1%)

prune257.0ms (3.9%)

localize13.0ms (0.2%)

rewrite74.0ms (1.1%)

series994.0ms (15%)

simplify103.0ms (1.6%)

prune452.0ms (6.8%)

localize14.0ms (0.2%)

rewrite79.0ms (1.2%)

series990.0ms (15%)

simplify79.0ms (1.2%)

prune281.0ms (4.2%)

localize16.0ms (0.2%)

rewrite36.0ms (0.5%)

series361.0ms (5.5%)

simplify71.0ms (1.1%)

prune114.0ms (1.7%)

regimes126.0ms (1.9%)

bsearch114.0ms (1.7%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.4s (21.3%)

Profiling