Details

analyze603.0ms (12.3%)

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
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample40.0ms (0.8%)

Algorithm

1×

intervals

Results

9.0ms	178×	body	128	valid
7.0ms	34×	body	2048	valid
6.0ms	12×	body	4096	valid
3.0ms	19×	body	1024	valid
1.0ms	27×	body	128	nan
1.0ms	9×	body	512	valid
0.0ms	4×	body	256	valid
0.0ms	7×	body	128	invalid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify170.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	714	20
1	714	20

prune4.0ms (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: 29.3b

Counts

2 → 1

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
0.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.5b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
17.2b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite52.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64`
39×	`*-un-lft-identity_binary64`
21×	`times-frac_binary64`
19×	`add-cube-cbrt_binary64`
11×	`sqrt-prod_binary64`
10×	`add-log-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
7×	`cancel-sign-sub-inv_binary64` `associate-/l*_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-rgt-neg-in_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`associate-/r*_binary64` `diff-log_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate--l-_binary64` `neg-sub0_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `neg-log_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 96

Calls

4 calls:

20.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
11.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
6.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
5.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series223.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

75.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
63.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
57.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
28.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify69.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4941	2578
1	4941	2578

prune112.0ms (2.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	98	10	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	99	10	109

Merged error: 5.0b

Counts

109 → 10

Compiler

Compiled 2392 to 474 computations (80.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
0.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.5b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
17.2b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite60.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

165×	`times-frac_binary64`
132×	`add-sqr-sqrt_binary64`
131×	`*-un-lft-identity_binary64`
79×	`add-cube-cbrt_binary64`
27×	`associate-/r*_binary64`
26×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
19×	`sqrt-prod_binary64`
15×	`add-exp-log_binary64`
13×	`distribute-rgt-neg-in_binary64`
10×	`add-log-exp_binary64`
9×	`add-cbrt-cube_binary64` `associate-/r/_binary64`
7×	`flip3--_binary64` `cancel-sign-sub-inv_binary64` `div-exp_binary64` `flip--_binary64`
6×	`pow1_binary64`
5×	`div-inv_binary64`
3×	`diff-log_binary64` `cbrt-undiv_binary64` `associate-/l*_binary64`
2×	`sub-neg_binary64` `1-exp_binary64` `rec-exp_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate--l-_binary64` `neg-sub0_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `neg-log_binary64` `frac-2neg_binary64` `pow-flip_binary64`

Counts

4 → 182

Calls

4 calls:

17.0ms	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
10.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series238.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

100.0ms	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
57.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
55.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
26.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify97.0ms (2%)

Algorithm

1×	egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5030	5933

prune167.0ms (3.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	191	3	194
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	194	10	204

Merged error: 5.0b

Counts

204 → 10

Compiler

Compiled 5002 to 995 computations (80.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.2b	(.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
0.5b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
17.2b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite45.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64`
24×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`
13×	`associate-r_binary64` `add-exp-log_binary64`
11×	`times-frac_binary64`
10×	`add-log-exp_binary64`
9×	`add-cbrt-cube_binary64`
8×	`sqrt-prod_binary64`
7×	`pow1_binary64` `associate-l_binary64` `cancel-sign-sub-inv_binary64`
5×	`flip3--_binary64` `flip--_binary64`
4×	`prod-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
3×	`diff-log_binary64` `unswap-sqr_binary64`
2×	`sub-neg_binary64` `cbrt-unprod_binary64` `distribute-rgt-neg-in_binary64` `div-exp_binary64` `frac-times_binary64` `sqrt-div_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `associate--l-_binary64` `1-exp_binary64` `neg-sub0_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `neg-log_binary64` `rec-exp_binary64` `un-div-inv_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

4 → 94

Calls

4 calls:

19.0ms	(.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
10.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series218.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

73.0ms	(.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
58.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
57.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
30.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify62.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4941	2204
1	4941	2204

prune85.0ms (1.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	106	10	116

Merged error: 5.0b

Counts

116 → 10

Compiler

Compiled 2293 to 625 computations (72.7% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.0b	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
14.6b	(/.f64 (*.f64 a c) a)
17.2b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite26.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
10×	`add-log-exp_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
5×	`pow1_binary64`
3×	`associate-/r*_binary64` `times-frac_binary64` `sqrt-prod_binary64`
2×	`flip3--_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `flip--_binary64` `sqrt-div_binary64` `sum-log_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `neg-sub0_binary64` `associate-+l-_binary64` `cancel-sign-sub-inv_binary64` `sqrt-pow1_binary64` `distribute-rgt-neg-in_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `neg-log_binary64` `prod-exp_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64` `+-commutative_binary64` `flip-+_binary64`

Counts

4 → 63

Calls

4 calls:

9.0ms	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
4.0ms	(/.f64 (*.f64 a c) a)
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series151.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

60.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
55.0ms	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
27.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
9.0ms	(/.f64 (*.f64 a c) a)

simplify73.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4840	973
1	4840	973

prune55.0ms (1.1%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	1	6	7
Picked	0	1	1
Done	0	2	2
Total	75	10	85

Merged error: 5.0b

Counts

85 → 10

Compiler

Compiled 1541 to 295 computations (80.9% saved)

regimes512.0ms (10.5%)

Compiler: Compiled 3543 to 2198 computations (38% saved)

bsearch99.0ms (2%)

Steps

Iters	Range		Point
9	6.839208250010194e+45	2.024719952789733e+54	1.982631369672776e+54
9	3.88928738868131e-218	2.224942237452931e-212	5.565296970572364e-216
9	-6.241733792850973e+165	-2.0661026109791683e+158	-2.0927171321286513e+158

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	89	70
1	89	70

end0.0ms (0%)

sample1.7s (34.4%)

Algorithm

1×

intervals

Results

234.0ms	5210×	body	128	valid
231.0ms	1106×	body	2048	valid
119.0ms	728×	body	1024	valid
106.0ms	400×	body	4096	valid
47.0ms	358×	body	512	valid
33.0ms	804×	body	128	nan
18.0ms	198×	body	256	valid
12.0ms	268×	body	128	invalid

Compiler

Compiled 903 to 561 computations (37.9% saved)

Details

analyze603.0ms (12.3%)

sample40.0ms (0.8%)

simplify170.0ms (3.5%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite52.0ms (1.1%)

series223.0ms (4.6%)

simplify69.0ms (1.4%)

prune112.0ms (2.3%)

localize10.0ms (0.2%)

rewrite60.0ms (1.2%)

series238.0ms (4.9%)

simplify97.0ms (2%)

prune167.0ms (3.4%)

localize10.0ms (0.2%)

rewrite45.0ms (0.9%)

series218.0ms (4.5%)

simplify62.0ms (1.3%)

prune85.0ms (1.7%)

localize11.0ms (0.2%)

rewrite26.0ms (0.5%)

series151.0ms (3.1%)

simplify73.0ms (1.5%)

prune55.0ms (1.1%)

regimes512.0ms (10.5%)

bsearch99.0ms (2%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.7s (34.4%)

Profiling