Details

analyze606.0ms (9.5%)

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)

sample42.0ms (0.7%)

Algorithm

1×

intervals

Results

9.0ms	28×	body	2048	valid
8.0ms	164×	body	128	valid
6.0ms	29×	body	1024	valid
4.0ms	15×	body	4096	valid
1.0ms	11×	body	512	valid
1.0ms	21×	body	128	nan
1.0ms	9×	body	256	valid
0.0ms	6×	body	128	invalid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify198.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	309	20
1	309	20

prune11.0ms (0.2%)

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: 35.2b

Counts

2 → 1

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize12.0ms (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)
0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
2.1b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
24.4b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite45.0ms (0.7%)

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:

14.0ms	(/.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)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series457.0ms (7.1%)

Counts

4 → 12

Calls

4 calls:

150.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
129.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
127.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
51.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify85.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4935	2578
1	4935	2578

prune431.0ms (6.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	97	11	108
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	97	12	109

Merged error: 6.1b

Counts

109 → 12

Compiler

Compiled 9438 to 4148 computations (56.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
3.5b	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
10.4b	(/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
24.4b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite57.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64`
58×	`add-sqr-sqrt_binary64`
43×	`*-un-lft-identity_binary64`
29×	`add-cube-cbrt_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`difference-of-squares_binary64`
13×	`associate-/l*_binary64`
10×	`associate-/r/_binary64` `sqrt-prod_binary64`
9×	`associate-/r*_binary64`
7×	`flip3--_binary64` `cbrt-undiv_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `flip--_binary64`
6×	`add-log-exp_binary64` `div-inv_binary64`
5×	`pow1_binary64`
3×	`cancel-sign-sub-inv_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `sqrt-div_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 129

Calls

4 calls:

17.0ms	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
12.0ms	(/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series891.0ms (13.9%)

Counts

4 → 12

Calls

4 calls:

370.0ms	(/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
298.0ms	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
117.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
105.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify60.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	4953	4034
1	4953	4034

prune309.0ms (4.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	135	6	141
Fresh	6	4	10
Picked	1	0	1
Done	0	1	1
Total	142	11	153

Merged error: 6.0b

Counts

153 → 11

Compiler

Compiled 7327 to 2875 computations (60.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
24.4b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite37.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
18×	`times-frac_binary64`
17×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`
8×	`add-log-exp_binary64` `sqrt-prod_binary64`
6×	`associate-/r*_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-lft-out--_binary64`
4×	`flip3--_binary64` `cancel-sign-sub-inv_binary64` `flip--_binary64`
3×	`associate-/l*_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `associate-/r/_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 85

Calls

4 calls:

11.0ms	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
5.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
5.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series630.0ms (9.9%)

Counts

4 → 12

Calls

4 calls:

354.0ms	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
117.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
107.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
52.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify70.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4911	2126
1	4911	2126

prune89.0ms (1.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	97	11	108

Merged error: 6.0b

Counts

108 → 11

Compiler

Compiled 2441 to 810 computations (66.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) c))
0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
24.4b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite50.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64`
122×	`add-sqr-sqrt_binary64`
95×	`*-un-lft-identity_binary64`
69×	`add-cube-cbrt_binary64`
26×	`difference-of-squares_binary64`
22×	`associate-/r*_binary64`
16×	`sqrt-prod_binary64`
15×	`add-exp-log_binary64`
13×	`distribute-lft-out--_binary64`
9×	`add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`div-exp_binary64`
6×	`pow1_binary64`
5×	`div-inv_binary64`
4×	`cancel-sign-sub-inv_binary64`
3×	`flip3--_binary64` `cbrt-undiv_binary64` `associate-/l*_binary64` `flip--_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `1-exp_binary64` `rec-exp_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `pow-flip_binary64`

Counts

4 → 156

Calls

4 calls:

13.0ms	(/.f64 1 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) c))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
5.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series506.0ms (7.9%)

Counts

4 → 12

Calls

4 calls:

218.0ms	(/.f64 1 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) c))
120.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
105.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
63.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify98.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5196	4864

prune157.0ms (2.5%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	167	1	168
Fresh	1	7	8
Picked	0	1	1
Done	0	2	2
Total	168	11	179

Merged error: 6.0b

Counts

179 → 11

Compiler

Compiled 4405 to 1023 computations (76.8% saved)

regimes161.0ms (2.5%)

Compiler: Compiled 676 to 498 computations (26.3% saved)

bsearch101.0ms (1.6%)

Steps

Iters	Range	Point
7	1.3458593302197346e+101	1.7253578096583875e+103	1.7008502192479382e+103
9	1.1899857569594048e-253	4.952441610662435e-245	1.0948972513238597e-251
9	-1.8084373769306673e+109	-7.821142621831562e+100	-3.79715392863884e+108

Iters

Range

Point

1.3458593302197346e+101

1.7253578096583875e+103

1.7008502192479382e+103

1.1899857569594048e-253

4.952441610662435e-245

1.0948972513238597e-251

-1.8084373769306673e+109

-7.821142621831562e+100

-3.79715392863884e+108

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	92	70
1	92	70

end0.0ms (0%)

sample1.3s (19.6%)

Algorithm

1×

intervals

Results

243.0ms	5226×	body	128	valid
234.0ms	1104×	body	2048	valid
123.0ms	731×	body	1024	valid
114.0ms	413×	body	4096	valid
45.0ms	343×	body	512	valid
36.0ms	797×	body	128	nan
18.0ms	183×	body	256	valid
12.0ms	263×	body	128	invalid

Compiler

Compiled 222 to 156 computations (29.7% saved)

Details

analyze606.0ms (9.5%)

sample42.0ms (0.7%)

simplify198.0ms (3.1%)

prune11.0ms (0.2%)

localize12.0ms (0.2%)

rewrite45.0ms (0.7%)

series457.0ms (7.1%)

simplify85.0ms (1.3%)

prune431.0ms (6.7%)

localize10.0ms (0.2%)

rewrite57.0ms (0.9%)

series891.0ms (13.9%)

simplify60.0ms (0.9%)

prune309.0ms (4.8%)

localize10.0ms (0.2%)

rewrite37.0ms (0.6%)

series630.0ms (9.9%)

simplify70.0ms (1.1%)

prune89.0ms (1.4%)

localize12.0ms (0.2%)

rewrite50.0ms (0.8%)

series506.0ms (7.9%)

simplify98.0ms (1.5%)

prune157.0ms (2.5%)

regimes161.0ms (2.5%)

bsearch101.0ms (1.6%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.3s (19.6%)

Profiling