Details

analyze607.0ms (9.7%)

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)

sample37.0ms (0.6%)

Algorithm

1×

intervals

Results

8.0ms	174×	body	128	valid
8.0ms	35×	body	2048	valid
3.0ms	12×	body	4096	valid
3.0ms	18×	body	1024	valid
2.0ms	11×	body	512	valid
1.0ms	25×	body	128	nan
1.0ms	6×	body	256	valid
0.0ms	11×	body	128	invalid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify202.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	309	20
1	309	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: 34.2b

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)
0.6b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
24.9b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite55.0ms (0.9%)

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))))
7.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
5.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series458.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

149.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
133.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
123.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
53.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify90.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4935	2578
1	4935	2578

prune469.0ms (7.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	99	9	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	100	9	109

Merged error: 6.3b

Counts

109 → 9

Compiler

Compiled 9630 to 4359 computations (54.7% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.4b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
3.1b	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
11.6b	(/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
24.9b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite60.0ms (1%)

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:

16.0ms	(/.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))
12.0ms	(-.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)))

series915.0ms (14.7%)

Counts

4 → 12

Calls

4 calls:

388.0ms	(/.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)
122.0ms	(-.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)))

simplify61.0ms (1%)

Algorithm

1×	egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	4953	4034
1	4953	4034

prune276.0ms (4.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	138	3	141
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	141	9	150

Merged error: 6.2b

Counts

150 → 9

Compiler

Compiled 6391 to 2318 computations (63.7% saved)

localize11.0ms (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))
1.4b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
24.9b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite38.0ms (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)
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series635.0ms (10.2%)

Counts

4 → 12

Calls

4 calls:

363.0ms	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
109.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
102.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
61.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify70.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4911	2126
1	4911	2126

prune91.0ms (1.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	97	9	106

Merged error: 6.2b

Counts

106 → 9

Compiler

Compiled 2408 to 793 computations (67.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
0.6b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
24.9b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite51.0ms (0.8%)

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))
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))

series449.0ms (7.2%)

Counts

4 → 12

Calls

4 calls:

160.0ms	(.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
124.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
110.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
55.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify62.0ms (1%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5299	2204

prune79.0ms (1.3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	106	9	115

Merged error: 6.2b

Counts

115 → 9

Compiler

Compiled 2197 to 549 computations (75% saved)

regimes154.0ms (2.5%)

Compiler: Compiled 411 to 315 computations (23.4% saved)

bsearch98.0ms (1.6%)

Steps

Iters	Range		Point
7	1.8636084122990392e+97	1.9135304727080364e+99	1.6213649525072984e+98
9	7.342863312857922e-248	7.37490432424297e-239	2.508993614835235e-240
10	-5.152623447754484e+85	-4.850229697172641e+74	-5.0970974227683685e+85

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	136	71
1	136	71

end0.0ms (0%)

sample1.2s (19.6%)

Algorithm

1×

intervals

Results

238.0ms	1126×	body	2048	valid
229.0ms	5163×	body	128	valid
131.0ms	768×	body	1024	valid
109.0ms	395×	body	4096	valid
44.0ms	359×	body	512	valid
34.0ms	826×	body	128	nan
16.0ms	189×	body	256	valid
11.0ms	254×	body	128	invalid

Compiler

Compiled 197 to 141 computations (28.4% saved)

Details

analyze607.0ms (9.7%)

sample37.0ms (0.6%)

simplify202.0ms (3.2%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite55.0ms (0.9%)

series458.0ms (7.4%)

simplify90.0ms (1.5%)

prune469.0ms (7.5%)

localize10.0ms (0.2%)

rewrite60.0ms (1%)

series915.0ms (14.7%)

simplify61.0ms (1%)

prune276.0ms (4.4%)

localize11.0ms (0.2%)

rewrite38.0ms (0.6%)

series635.0ms (10.2%)

simplify70.0ms (1.1%)

prune91.0ms (1.5%)

localize10.0ms (0.2%)

rewrite51.0ms (0.8%)

series449.0ms (7.2%)

simplify62.0ms (1%)

prune79.0ms (1.3%)

regimes154.0ms (2.5%)

bsearch98.0ms (1.6%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample1.2s (19.6%)

Profiling