Details

analyze448.0ms (6.4%)

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)

sample40.0ms (0.6%)

Algorithm

1×

intervals

Results

8.0ms	167×	body	128	valid
7.0ms	32×	body	2048	valid
6.0ms	23×	body	1024	valid
4.0ms	15×	body	4096	valid
2.0ms	11×	body	512	valid
1.0ms	18×	body	128	invalid
1.0ms	17×	body	128	nan
1.0ms	8×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify229.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (66.0ms)

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: 33.5b

Counts

2 → 1

Compiler

Compiled 65 to 53 computations (18.5% saved)

localize13.0ms (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))
0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
21.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite38.0ms (0.5%)

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)))

series499.0ms (7.1%)

Counts

4 → 12

Calls

4 calls:

202.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
119.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
117.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
61.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify70.0ms (1%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4895	1979
1	4895	1979

prune509.0ms (7.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	76	10	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	77	10	87

Merged error: 5.7b

Counts

87 → 10

Compiler

Compiled 10390 to 6945 computations (33.2% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4)))) b) (.f64 a 2))
0.8b	(+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))
1.0b	(-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))) b)
21.9b	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

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`
3×	`cancel-sign-sub-inv_binary64_733` `distribute-lft-out--_binary64_719`
2×	`associate-/l/_binary64_714` `cbrt-undiv_binary64_801` `flip-+_binary64_741` `flip3-+_binary64_770` `flip--_binary64_742` `div-exp_binary64_818` `flip3--_binary64_771` `sqrt-div_binary64_784`
1×	`frac-2neg_binary64_778` `rem-sqrt-square_binary64_780` `associate-/r*_binary64_711` `cbrt-unprod_binary64_800` `sub-neg_binary64_760` `prod-exp_binary64_816` `diff-log_binary64_859` `+-commutative_binary64_697` `sum-log_binary64_858` `pow1/2_binary64_847` `sqrt-pow1_binary64_785` `div-sub_binary64_772` `clear-num_binary64_766` `div-inv_binary64_764`

Counts

4 → 73

Calls

4 calls:

14.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4)))) b) (.f64 a 2))
9.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))) b)
5.0ms	(+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))
5.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

series517.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

210.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4)))) b) (.f64 a 2))
123.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))
118.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))) b)
65.0ms	(+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))

simplify90.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4872	1965
1	4872	1965

prune113.0ms (1.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	84	11	95

Merged error: 5.7b

Counts

95 → 11

Compiler

Compiled 2469 to 1505 computations (39% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
21.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite118.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

693×	`times-frac_binary64_773`
439×	`add-sqr-sqrt_binary64_789`
364×	`*-un-lft-identity_binary64_767`
290×	`add-cube-cbrt_binary64_802`
74×	`difference-of-squares_binary64_736`
71×	`associate-/r*_binary64_711`
40×	`sqrt-prod_binary64_783`
37×	`distribute-lft-out--_binary64_719`
25×	`add-exp-log_binary64_805`
17×	`div-inv_binary64_764`
15×	`div-exp_binary64_818`
13×	`add-cbrt-cube_binary64_803`
8×	`add-log-exp_binary64_806`
6×	`cbrt-undiv_binary64_801` `pow1_binary64_828`
5×	`associate-/r/_binary64_713`
4×	`cancel-sign-sub-inv_binary64_733`
3×	`1-exp_binary64_811` `associate-/l*_binary64_712` `rec-exp_binary64_817` `flip--_binary64_742` `flip3--_binary64_771`
2×	`sub-neg_binary64_760` `diff-log_binary64_859` `sqrt-div_binary64_784`
1×	`frac-2neg_binary64_778` `rem-sqrt-square_binary64_780` `pow-flip_binary64_841` `pow1/2_binary64_847` `sqrt-pow1_binary64_785` `clear-num_binary64_766` `inv-pow_binary64_852`

Counts

4 → 356

Calls

4 calls:

26.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 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)))

series558.0ms (7.9%)

Counts

4 → 12

Calls

4 calls:

251.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
122.0ms	(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)
64.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify180.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

368 → 368

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5062	16295

prune874.0ms (12.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	366	2	368
Fresh	2	7	9
Picked	0	1	1
Done	0	1	1
Total	368	11	379

Merged error: 5.6b

Counts

379 → 11

Compiler

Compiled 16442 to 9814 computations (40.3% saved)

localize11.0ms (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))
0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
21.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite44.0ms (0.6%)

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:

17.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
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)))

series529.0ms (7.5%)

Counts

4 → 12

Calls

4 calls:

207.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
132.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
125.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
65.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify61.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5045	2239

prune126.0ms (1.8%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	1	7	8
Picked	0	1	1
Done	0	2	2
Total	95	11	106

Merged error: 5.6b

Counts

106 → 11

Compiler

Compiled 2668 to 1530 computations (42.7% saved)

regimes379.0ms (5.4%)

Compiler: Compiled 576 to 465 computations (19.3% saved)

bsearch102.0ms (1.5%)

Steps

Iters	Range		Point
9	250566454504151.5	3.764613681933625e+19	1602861300811727.2
9	3.1902810220304265e-164	3.004645438473775e-156	2.824022959997043e-156
9	-1.1728433930348086e+159	-6.078197847532872e+152	-4.30899153131526e+153

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	108	91
1	108	91

end0.0ms (0%)

sample1.4s (20%)

Algorithm

1×

intervals

Results

270.0ms	5217×	body	128	valid
267.0ms	1114×	body	2048	valid
148.0ms	719×	body	1024	valid
122.0ms	406×	body	4096	valid
52.0ms	371×	body	512	valid
36.0ms	695×	body	128	nan
20.0ms	397×	body	128	invalid
16.0ms	173×	body	256	valid

Compiler

Compiled 311 to 233 computations (25.1% saved)

Details

analyze448.0ms (6.4%)

sample40.0ms (0.6%)

simplify229.0ms (3.3%)

prune5.0ms (0.1%)

localize13.0ms (0.2%)

rewrite38.0ms (0.5%)

series499.0ms (7.1%)

simplify70.0ms (1%)

prune509.0ms (7.2%)

localize11.0ms (0.2%)

rewrite40.0ms (0.6%)

series517.0ms (7.4%)

simplify90.0ms (1.3%)

prune113.0ms (1.6%)

localize12.0ms (0.2%)

rewrite118.0ms (1.7%)

series558.0ms (7.9%)

simplify180.0ms (2.6%)

prune874.0ms (12.4%)

localize11.0ms (0.2%)

rewrite44.0ms (0.6%)

series529.0ms (7.5%)

simplify61.0ms (0.9%)

prune126.0ms (1.8%)

regimes379.0ms (5.4%)

bsearch102.0ms (1.5%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.4s (20%)

Profiling