Details

analyze475.0ms (5.7%)

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 (0.5%)

Algorithm

1×

intervals

Results

9.0ms	172×	body	128	valid
6.0ms	26×	body	2048	valid
5.0ms	27×	body	1024	valid
3.0ms	11×	body	4096	valid
2.0ms	14×	body	512	valid
1.0ms	24×	body	128	nan
1.0ms	18×	body	128	invalid
1.0ms	6×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify231.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (68.0ms)

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	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 35.0b

Counts

2 → 1

Compiler

Compiled 66 to 54 computations (18.2% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
0.6b	(-.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))))
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite39.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64_2143`
10×	`add-log-exp_binary64_2182`
9×	`add-exp-log_binary64_2181` `add-cbrt-cube_binary64_2179`
8×	`add-sqr-sqrt_binary64_2165`
7×	`add-cube-cbrt_binary64_2178`
6×	`distribute-lft-out_binary64_2094`
5×	`pow1_binary64_2204` `associate-/l*_binary64_2088` `times-frac_binary64_2149`
3×	`distribute-rgt-neg-in_binary64_2101` `sqrt-prod_binary64_2159`
2×	`sqrt-div_binary64_2160` `cbrt-undiv_binary64_2177` `flip--_binary64_2118` `associate-+l-_binary64_2078` `neg-sub0_binary64_2138` `sum-log_binary64_2234` `flip3--_binary64_2147` `flip3-+_binary64_2146` `flip-+_binary64_2117` `div-exp_binary64_2194` `associate-/l/_binary64_2090`
1×	`rem-sqrt-square_binary64_2156` `pow1/2_binary64_2223` `+-commutative_binary64_2073` `diff-log_binary64_2235` `clear-num_binary64_2142` `associate-/r*_binary64_2087` `sub-neg_binary64_2136` `div-inv_binary64_2140` `cbrt-unprod_binary64_2176` `prod-exp_binary64_2192` `cancel-sign-sub-inv_binary64_2109` `neg-log_binary64_2236` `sqrt-pow1_binary64_2161` `frac-2neg_binary64_2154` `div-sub_binary64_2148`

Counts

4 → 70

Calls

4 calls:

14.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
10.0ms	(+.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)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series530.0ms (6.4%)

Counts

4 → 12

Calls

4 calls:

213.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
125.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
125.0ms	(+.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))

simplify57.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5290	1826

prune438.0ms (5.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	75	7	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	7	83

Merged error: 7.0b

Counts

83 → 7

Compiler

Compiled 8648 to 6115 computations (29.3% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
3.5b	(/.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))
9.6b	(/.f64 (.f64 (.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite70.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64_2181` `add-cbrt-cube_binary64_2179`
34×	`add-sqr-sqrt_binary64_2165` `times-frac_binary64_2149`
33×	`*-un-lft-identity_binary64_2143`
17×	`cbrt-undiv_binary64_2177` `div-exp_binary64_2194`
14×	`associate-/l*_binary64_2088`
13×	`cbrt-unprod_binary64_2176` `prod-exp_binary64_2192` `add-cube-cbrt_binary64_2178`
11×	`sqrt-prod_binary64_2159`
10×	`distribute-lft-out--_binary64_2095` `difference-of-squares_binary64_2112`
8×	`add-log-exp_binary64_2182` `associate-/r*_binary64_2087`
6×	`associate-/r/_binary64_2089` `cancel-sign-sub-inv_binary64_2109`
5×	`pow1_binary64_2204` `flip--_binary64_2118` `distribute-rgt-neg-in_binary64_2101` `flip3--_binary64_2147`
4×	`div-inv_binary64_2140`
2×	`sqrt-div_binary64_2160` `diff-log_binary64_2235` `clear-num_binary64_2142` `frac-2neg_binary64_2154`
1×	`rem-sqrt-square_binary64_2156` `pow1/2_binary64_2223` `sub-neg_binary64_2136` `associate--l-_binary64_2081` `neg-sub0_binary64_2138` `neg-log_binary64_2236` `sqrt-pow1_binary64_2161` `associate-/l/_binary64_2090`

Counts

4 → 125

Calls

4 calls:

19.0ms	(/.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)))))
11.0ms	(-.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)))

series970.0ms (11.7%)

Counts

4 → 12

Calls

4 calls:

411.0ms	(/.f64 (.f64 (.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
306.0ms	(/.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))
134.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
118.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify102.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4940	4228
1	4940	4228

prune260.0ms (3.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	135	2	137
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	137	7	144

Merged error: 6.9b

Counts

144 → 7

Compiler

Compiled 5834 to 3617 computations (38% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
1.6b	(.f64 (.f64 4 a) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
3.5b	(/.f64 (.f64 (.f64 4 a) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (.f64 2 a))
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite71.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`add-exp-log_binary64_2181` `add-cbrt-cube_binary64_2179`
35×	`add-sqr-sqrt_binary64_2165`
34×	`*-un-lft-identity_binary64_2143`
27×	`associate-r_binary64_2083`
23×	`cbrt-unprod_binary64_2176` `prod-exp_binary64_2192`
22×	`times-frac_binary64_2149`
18×	`add-cube-cbrt_binary64_2178`
16×	`cbrt-undiv_binary64_2177` `div-exp_binary64_2194`
10×	`pow1_binary64_2204` `sqrt-prod_binary64_2159`
8×	`add-log-exp_binary64_2182` `distribute-lft-out--_binary64_2095` `difference-of-squares_binary64_2112`
6×	`cancel-sign-sub-inv_binary64_2109`
4×	`distribute-rgt-neg-in_binary64_2101`
3×	`flip--_binary64_2118` `flip3--_binary64_2147` `pow-prod-down_binary64_2214`
2×	`sqrt-div_binary64_2160` `diff-log_binary64_2235` `associate-/r/_binary64_2089` `div-inv_binary64_2140` `associate-*r/_binary64_2085`
1×	`rem-sqrt-square_binary64_2156` `pow1/2_binary64_2223` `clear-num_binary64_2142` `associate-/r_binary64_2087` `sub-neg_binary64_2136` `associate-/l_binary64_2088` `associate--l-_binary64_2081` `neg-sub0_binary64_2138` `associate-l_binary64_2084` `neg-log_binary64_2236` `sqrt-pow1_binary64_2161` `*-commutative_binary64_2074` `frac-2neg_binary64_2154` `associate-/l/_binary64_2090`

Counts

4 → 119

Calls

4 calls:

20.0ms	(/.f64 (.f64 (.f64 4 a) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (.f64 2 a))
19.0ms	(.f64 (.f64 4 a) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
11.0ms	(-.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)))

series969.0ms (11.7%)

Counts

4 → 12

Calls

4 calls:

409.0ms	(.f64 (.f64 4 a) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
309.0ms	(/.f64 (.f64 (.f64 4 a) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (.f64 2 a))
130.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
120.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify102.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4901	3363
1	4901	3363

prune184.0ms (2.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	131	7	138

Merged error: 6.9b

Counts

138 → 7

Compiler

Compiled 4190 to 2487 computations (40.6% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 1 (/.f64 1/2 (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))))
0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.8b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite141.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

834×	`times-frac_binary64_2149`
487×	`add-sqr-sqrt_binary64_2165`
486×	`*-un-lft-identity_binary64_2143`
338×	`add-cube-cbrt_binary64_2178`
86×	`associate-/r*_binary64_2087`
74×	`distribute-lft-out--_binary64_2095` `difference-of-squares_binary64_2112`
43×	`sqrt-prod_binary64_2159`
37×	`distribute-rgt-neg-in_binary64_2101`
29×	`associate-/r/_binary64_2089`
25×	`add-exp-log_binary64_2181`
17×	`div-inv_binary64_2140`
15×	`flip--_binary64_2118` `flip3--_binary64_2147` `div-exp_binary64_2194`
13×	`add-cbrt-cube_binary64_2179`
10×	`add-log-exp_binary64_2182`
7×	`cancel-sign-sub-inv_binary64_2109`
6×	`pow1_binary64_2204` `cbrt-undiv_binary64_2177`
3×	`diff-log_binary64_2235` `associate-/l*_binary64_2088` `1-exp_binary64_2187` `rec-exp_binary64_2193`
2×	`sqrt-div_binary64_2160` `sub-neg_binary64_2136`
1×	`rem-sqrt-square_binary64_2156` `pow1/2_binary64_2223` `clear-num_binary64_2142` `associate--l-_binary64_2081` `neg-sub0_binary64_2138` `pow-flip_binary64_2217` `neg-log_binary64_2236` `sqrt-pow1_binary64_2161` `inv-pow_binary64_2228` `frac-2neg_binary64_2154`

Counts

4 → 422

Calls

4 calls:

33.0ms	(/.f64 1 (/.f64 1/2 (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))))
13.0ms	(-.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)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series657.0ms (8%)

Counts

4 → 12

Calls

4 calls:

359.0ms	(/.f64 1 (/.f64 1/2 (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))))
127.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
109.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
62.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify218.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

434 → 434

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4942	19878
1	4942	19878

prune952.0ms (11.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	432	2	434
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	433	8	441

Merged error: 6.9b

Counts

441 → 8

Compiler

Compiled 16193 to 9638 computations (40.5% saved)

regimes151.0ms (1.8%)

Compiler: Compiled 486 to 381 computations (21.6% saved)

bsearch116.0ms (1.4%)

Steps

Iters	Range	Point
8	5.047843856159705e+79	3.275486995190224e+82	2.2382631606544506e+82
11	-1.860825766371501e-278	-9.262240264721869e-302	-3.316085297718727e-287
9	-3.141987374119816e+97	-1.5578411367101382e+89	-2.3585860632819396e+97

Iters

Range

Point

5.047843856159705e+79

3.275486995190224e+82

2.2382631606544506e+82

-1.860825766371501e-278

-9.262240264721869e-302

-3.316085297718727e-287

-3.141987374119816e+97

-1.5578411367101382e+89

-2.3585860632819396e+97

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	118	84
1	118	84

end0.0ms (0%)

sample1.4s (17.3%)

Algorithm

1×

intervals

Results

291.0ms	1134×	body	2048	valid
274.0ms	5060×	body	128	valid
154.0ms	792×	body	1024	valid
130.0ms	417×	body	4096	valid
61.0ms	403×	body	512	valid
35.0ms	666×	body	128	nan
20.0ms	380×	body	128	invalid
19.0ms	194×	body	256	valid

Compiler

Compiled 276 to 203 computations (26.4% saved)

Details

analyze475.0ms (5.7%)

sample38.0ms (0.5%)

simplify231.0ms (2.8%)

prune6.0ms (0.1%)

localize12.0ms (0.1%)

rewrite39.0ms (0.5%)

series530.0ms (6.4%)

simplify57.0ms (0.7%)

prune438.0ms (5.3%)

localize14.0ms (0.2%)

rewrite70.0ms (0.8%)

series970.0ms (11.7%)

simplify102.0ms (1.2%)

prune260.0ms (3.1%)

localize16.0ms (0.2%)

rewrite71.0ms (0.9%)

series969.0ms (11.7%)

simplify102.0ms (1.2%)

prune184.0ms (2.2%)

localize14.0ms (0.2%)

rewrite141.0ms (1.7%)

series657.0ms (8%)

simplify218.0ms (2.6%)

prune952.0ms (11.5%)

regimes151.0ms (1.8%)

bsearch116.0ms (1.4%)

simplify4.0ms (0%)

end0.0ms (0%)

sample1.4s (17.3%)

Profiling