Details

analyze454.0ms (6.6%)

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	37×	body	2048	valid
9.0ms	173×	body	128	valid
4.0ms	22×	body	1024	valid
3.0ms	11×	body	4096	valid
1.0ms	23×	body	128	nan
1.0ms	7×	body	512	valid
1.0ms	12×	body	128	invalid
1.0ms	6×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify225.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (61.0ms)

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: 35.1b

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 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
0.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.6b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
25.3b	(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_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-/l*_binary64_712`
3×	`associate-/r*_binary64_711` `sqrt-prod_binary64_783`
2×	`associate-/l/_binary64_714` `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:

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

series451.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

143.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
129.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
119.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
61.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify76.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5101	2019

prune532.0ms (7.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	75	9	84
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	9	85

Merged error: 5.9b

Counts

85 → 9

Compiler

Compiled 10287 to 6992 computations (32% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.8b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
2.3b	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
11.0b	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
25.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite62.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64_773`
59×	`add-sqr-sqrt_binary64_789`
44×	`*-un-lft-identity_binary64_767`
30×	`add-cube-cbrt_binary64_802`
27×	`add-exp-log_binary64_805` `add-cbrt-cube_binary64_803`
14×	`difference-of-squares_binary64_736`
13×	`associate-/l*_binary64_712` `sqrt-prod_binary64_783`
10×	`cbrt-undiv_binary64_801` `associate-/r/_binary64_713` `div-exp_binary64_818`
9×	`associate-/r*_binary64_711`
7×	`distribute-lft-out--_binary64_719` `flip--_binary64_742` `flip3--_binary64_771`
6×	`cbrt-unprod_binary64_800` `prod-exp_binary64_816` `add-log-exp_binary64_806` `cancel-sign-sub-inv_binary64_733` `div-inv_binary64_764`
5×	`pow1_binary64_828`
2×	`frac-2neg_binary64_778` `clear-num_binary64_766` `sqrt-div_binary64_784`
1×	`rem-sqrt-square_binary64_780` `associate-/l/_binary64_714` `sub-neg_binary64_760` `diff-log_binary64_859` `pow1/2_binary64_847` `sqrt-pow1_binary64_785`

Counts

4 → 136

Calls

4 calls:

16.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
14.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
8.0ms	(-.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))))

series985.0ms (14.4%)

Counts

4 → 12

Calls

4 calls:

414.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
325.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
125.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
121.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))

simplify89.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5217	5032

prune358.0ms (5.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	144	4	148
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	149	8	157

Merged error: 5.8b

Counts

157 → 8

Compiler

Compiled 7254 to 4493 computations (38.1% 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))))))
0.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.8b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
25.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite38.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64_789`
28×	`*-un-lft-identity_binary64_767`
18×	`times-frac_binary64_773` `add-cube-cbrt_binary64_802`
11×	`sqrt-prod_binary64_783`
10×	`difference-of-squares_binary64_736`
8×	`add-log-exp_binary64_806`
7×	`cancel-sign-sub-inv_binary64_733`
6×	`associate-/r*_binary64_711` `add-exp-log_binary64_805` `add-cbrt-cube_binary64_803`
5×	`pow1_binary64_828` `distribute-lft-out--_binary64_719`
4×	`flip--_binary64_742` `flip3--_binary64_771`
3×	`associate-/l*_binary64_712`
2×	`associate-/r/_binary64_713` `sub-neg_binary64_760` `diff-log_binary64_859` `sqrt-div_binary64_784`
1×	`frac-2neg_binary64_778` `rem-sqrt-square_binary64_780` `cbrt-undiv_binary64_801` `pow1/2_binary64_847` `div-exp_binary64_818` `sqrt-pow1_binary64_785` `clear-num_binary64_766` `div-inv_binary64_764`

Counts

4 → 88

Calls

4 calls:

9.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
8.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
7.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series647.0ms (9.4%)

Counts

4 → 12

Calls

4 calls:

350.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
120.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
116.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
61.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify76.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4898	2580
1	4898	2580

prune158.0ms (2.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	100	8	108

Merged error: 5.8b

Counts

108 → 8

Compiler

Compiled 3375 to 2122 computations (37.1% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 c (/.f64 1 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))
0.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.8b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
25.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite49.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary64_789`
27×	`*-un-lft-identity_binary64_767`
24×	`associate-r_binary64_707`
20×	`times-frac_binary64_773`
18×	`add-cube-cbrt_binary64_802`
13×	`add-exp-log_binary64_805`
10×	`sqrt-prod_binary64_783`
9×	`add-cbrt-cube_binary64_803`
8×	`add-log-exp_binary64_806` `difference-of-squares_binary64_736`
7×	`pow1_binary64_828` `cancel-sign-sub-inv_binary64_733`
4×	`prod-exp_binary64_816` `distribute-lft-out--_binary64_719` `flip--_binary64_742` `flip3--_binary64_771`
3×	`associate-l_binary64_708` `unswap-sqr_binary64_735`
2×	`cbrt-unprod_binary64_800` `associate-/r/_binary64_713` `sub-neg_binary64_760` `diff-log_binary64_859` `div-exp_binary64_818` `sqrt-div_binary64_784`
1×	`rem-sqrt-square_binary64_780` `cbrt-undiv_binary64_801` `-commutative_binary64_698` `1-exp_binary64_811` `pow1/2_binary64_847` `associate-r/_binary64_709` `rec-exp_binary64_817` `sqrt-pow1_binary64_785` `pow-prod-down_binary64_838` `un-div-inv_binary64_765` `div-inv_binary64_764`

Counts

4 → 94

Calls

4 calls:

20.0ms	(.f64 c (/.f64 1 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))
8.0ms	(-.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)))

series675.0ms (9.8%)

Counts

4 → 12

Calls

4 calls:

366.0ms	(.f64 c (/.f64 1 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))
129.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
118.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
62.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify80.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4943	2315
1	4943	2315

prune141.0ms (2.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	106	8	114

Merged error: 5.8b

Counts

114 → 8

Compiler

Compiled 3135 to 1949 computations (37.8% saved)

regimes138.0ms (2%)

Compiler: Compiled 375 to 336 computations (10.4% saved)

bsearch93.0ms (1.4%)

Steps

Iters	Range	Point
8	9.917751388656248e+82	5.7369441038556414e+85	5.681019323697606e+85
4	1.70529524702673e-275	2.6033404163436034e-275	2.1823817432263188e-275
10	-7.645072331894797e+112	-2.6867025150556605e+98	-3.6561570350872246e+101

Iters

Range

Point

9.917751388656248e+82

5.7369441038556414e+85

5.681019323697606e+85

1.70529524702673e-275

2.6033404163436034e-275

2.1823817432263188e-275

-7.645072331894797e+112

-2.6867025150556605e+98

-3.6561570350872246e+101

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	116	95
1	116	95

end0.0ms (0%)

sample1.4s (20.4%)

Algorithm

1×

intervals

Results

284.0ms	1134×	body	2048	valid
273.0ms	5187×	body	128	valid
152.0ms	774×	body	1024	valid
118.0ms	373×	body	4096	valid
56.0ms	357×	body	512	valid
30.0ms	624×	body	128	nan
22.0ms	392×	body	128	invalid
18.0ms	175×	body	256	valid

Compiler

Compiled 247 to 195 computations (21.1% saved)

Details

analyze454.0ms (6.6%)

sample39.0ms (0.6%)

simplify225.0ms (3.3%)

prune6.0ms (0.1%)

localize11.0ms (0.2%)

rewrite32.0ms (0.5%)

series451.0ms (6.6%)

simplify76.0ms (1.1%)

prune532.0ms (7.8%)

localize13.0ms (0.2%)

rewrite62.0ms (0.9%)

series985.0ms (14.4%)

simplify89.0ms (1.3%)

prune358.0ms (5.2%)

localize13.0ms (0.2%)

rewrite38.0ms (0.6%)

series647.0ms (9.4%)

simplify76.0ms (1.1%)

prune158.0ms (2.3%)

localize14.0ms (0.2%)

rewrite49.0ms (0.7%)

series675.0ms (9.8%)

simplify80.0ms (1.2%)

prune141.0ms (2.1%)

regimes138.0ms (2%)

bsearch93.0ms (1.4%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.4s (20.4%)

Profiling