Details

analyze464.0ms (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)

sample39.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms	171×	body	128	valid
9.0ms	34×	body	2048	valid
6.0ms	28×	body	1024	valid
3.0ms	11×	body	4096	valid
1.0ms	24×	body	128	nan
1.0ms	7×	body	512	valid
0.0ms	5×	body	256	valid
0.0ms	7×	body	128	invalid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify228.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	927	24
1	927	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

Merged error: 34.4b

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))
1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.1b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
23.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite40.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_789`
14×	`*-un-lft-identity_binary64_767`
9×	`add-exp-log_binary64_805` `add-cbrt-cube_binary64_803`
8×	`add-log-exp_binary64_806` `add-cube-cbrt_binary64_802`
6×	`times-frac_binary64_773` `associate-/l*_binary64_712` `sqrt-prod_binary64_783` `difference-of-squares_binary64_736`
5×	`pow1_binary64_828`
4×	`cancel-sign-sub-inv_binary64_733` `flip--_binary64_742` `flip3--_binary64_771`
3×	`distribute-lft-out--_binary64_719`
2×	`associate-/l/_binary64_714` `cbrt-undiv_binary64_801` `sub-neg_binary64_760` `diff-log_binary64_859` `div-exp_binary64_818` `sqrt-div_binary64_784`
1×	`frac-2neg_binary64_778` `rem-sqrt-square_binary64_780` `associate-/r*_binary64_711` `cbrt-unprod_binary64_800` `prod-exp_binary64_816` `pow1/2_binary64_847` `sqrt-pow1_binary64_785` `div-sub_binary64_772` `clear-num_binary64_766` `div-inv_binary64_764`

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

series527.0ms (8.3%)

Counts

4 → 12

Calls

4 calls:

217.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
123.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
121.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
67.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify74.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4895	1979
1	4895	1979

prune434.0ms (6.8%)

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: 5.3b

Counts

87 → 8

Compiler

Compiled 8438 to 5693 computations (32.5% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.7b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.4b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 a 2))
8.0b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
23.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite53.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64_805` `add-cbrt-cube_binary64_803`
22×	`times-frac_binary64_773`
21×	`*-un-lft-identity_binary64_767`
17×	`cbrt-undiv_binary64_801` `div-exp_binary64_818`
13×	`cbrt-unprod_binary64_800` `prod-exp_binary64_816`
12×	`add-sqr-sqrt_binary64_789`
11×	`associate-/l*_binary64_712` `add-cube-cbrt_binary64_802`
6×	`associate-/r/_binary64_713` `add-log-exp_binary64_806`
5×	`distribute-lft-out_binary64_718` `associate-/r*_binary64_711` `pow1_binary64_828`
4×	`flip-+_binary64_741` `flip3-+_binary64_770` `div-inv_binary64_764`
3×	`sqrt-prod_binary64_783`
2×	`frac-2neg_binary64_778` `clear-num_binary64_766` `sqrt-div_binary64_784`
1×	`rem-sqrt-square_binary64_780` `associate-/l/_binary64_714` `+-commutative_binary64_697` `sum-log_binary64_858` `pow1/2_binary64_847` `flip--_binary64_742` `sqrt-pow1_binary64_785` `flip3--_binary64_771`

Counts

4 → 102

Calls

4 calls:

16.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 a 2))
13.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.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	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series952.0ms (14.9%)

Counts

4 → 12

Calls

4 calls:

382.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
309.0ms	(/.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	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
127.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))

simplify76.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4977	3121
1	4977	3121

prune219.0ms (3.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	115	7	122

Merged error: 5.2b

Counts

122 → 7

Compiler

Compiled 4522 to 2845 computations (37.1% 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 4 (*.f64 a c))))))
1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.7b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
23.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite31.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_767`
15×	`add-sqr-sqrt_binary64_789`
14×	`add-cube-cbrt_binary64_802`
12×	`times-frac_binary64_773`
8×	`add-log-exp_binary64_806`
6×	`add-exp-log_binary64_805` `add-cbrt-cube_binary64_803`
5×	`distribute-lft-out_binary64_718` `pow1_binary64_828`
4×	`associate-/r*_binary64_711`
3×	`associate-/l*_binary64_712` `sqrt-prod_binary64_783`
2×	`associate-/r/_binary64_713` `flip-+_binary64_741` `flip3-+_binary64_770` `flip--_binary64_742` `flip3--_binary64_771` `sqrt-div_binary64_784`
1×	`frac-2neg_binary64_778` `rem-sqrt-square_binary64_780` `cbrt-undiv_binary64_801` `sub-neg_binary64_760` `cancel-sign-sub-inv_binary64_733` `diff-log_binary64_859` `+-commutative_binary64_697` `sum-log_binary64_858` `pow1/2_binary64_847` `div-exp_binary64_818` `sqrt-pow1_binary64_785` `clear-num_binary64_766` `div-inv_binary64_764`

Counts

4 → 72

Calls

4 calls:

8.0ms	(/.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))))

series662.0ms (10.4%)

Counts

4 → 12

Calls

4 calls:

350.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
128.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
115.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
68.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify68.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5091	1969

prune94.0ms (1.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	84	7	91

Merged error: 5.2b

Counts

91 → 7

Compiler

Compiled 2175 to 1236 computations (43.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.1b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
23.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite42.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64_789`
18×	`*-un-lft-identity_binary64_767`
14×	`add-cube-cbrt_binary64_802`
13×	`associate-r_binary64_707`
10×	`times-frac_binary64_773`
9×	`add-exp-log_binary64_805` `add-cbrt-cube_binary64_803`
8×	`add-log-exp_binary64_806`
7×	`pow1_binary64_828`
6×	`associate-l_binary64_708`
5×	`sqrt-prod_binary64_783` `flip--_binary64_742` `flip3--_binary64_771`
4×	`cancel-sign-sub-inv_binary64_733` `difference-of-squares_binary64_736`
2×	`frac-times_binary64_777` `unswap-sqr_binary64_735` `cbrt-unprod_binary64_800` `sub-neg_binary64_760` `prod-exp_binary64_816` `diff-log_binary64_859` `distribute-lft-out--_binary64_719` `associate-*l/_binary64_710` `sqrt-div_binary64_784`
1×	`rem-sqrt-square_binary64_780` `cbrt-undiv_binary64_801` `-commutative_binary64_698` `pow1/2_binary64_847` `associate-r/_binary64_709` `div-exp_binary64_818` `sqrt-pow1_binary64_785` `pow-prod-down_binary64_838` `div-inv_binary64_764`

Counts

4 → 83

Calls

4 calls:

16.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series544.0ms (8.5%)

Counts

4 → 12

Calls

4 calls:

226.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
129.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
121.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
68.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify60.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5045	2239

prune97.0ms (1.5%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	95	7	102

Merged error: 5.2b

Counts

102 → 7

Compiler

Compiled 2216 to 1182 computations (46.7% saved)

regimes141.0ms (2.2%)

Compiler: Compiled 294 to 258 computations (12.2% saved)

bsearch103.0ms (1.6%)

Steps

Iters	Range	Point
8	6.787489049073195e+118	7.133955408180205e+122	5.525835260688754e+121
9	2.173626231849138e-227	1.6620553427918547e-219	7.131198222427231e-227
8	-1.6407368404235515e+56	-3.3624292403433257e+53	-1.5894887112160012e+56

Iters

Range

Point

6.787489049073195e+118

7.133955408180205e+122

5.525835260688754e+121

2.173626231849138e-227

1.6620553427918547e-219

7.131198222427231e-227

-1.6407368404235515e+56

-3.3624292403433257e+53

-1.5894887112160012e+56

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	105	82
1	105	82

end0.0ms (0%)

sample1.4s (21.5%)

Algorithm

1×

intervals

Results

284.0ms	5258×	body	128	valid
284.0ms	1104×	body	2048	valid
135.0ms	682×	body	1024	valid
127.0ms	398×	body	4096	valid
57.0ms	372×	body	512	valid
33.0ms	662×	body	128	nan
21.0ms	186×	body	256	valid
19.0ms	360×	body	128	invalid

Compiler

Compiled 211 to 159 computations (24.6% saved)

Details

analyze464.0ms (7.3%)

sample39.0ms (0.6%)

simplify228.0ms (3.6%)

prune5.0ms (0.1%)

localize11.0ms (0.2%)

rewrite40.0ms (0.6%)

series527.0ms (8.3%)

simplify74.0ms (1.2%)

prune434.0ms (6.8%)

localize18.0ms (0.3%)

rewrite53.0ms (0.8%)

series952.0ms (14.9%)

simplify76.0ms (1.2%)

prune219.0ms (3.4%)

localize13.0ms (0.2%)

rewrite31.0ms (0.5%)

series662.0ms (10.4%)

simplify68.0ms (1.1%)

prune94.0ms (1.5%)

localize12.0ms (0.2%)

rewrite42.0ms (0.7%)

series544.0ms (8.5%)

simplify60.0ms (0.9%)

prune97.0ms (1.5%)

regimes141.0ms (2.2%)

bsearch103.0ms (1.6%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.4s (21.5%)

Profiling