Details

analyze463.0ms (6.9%)

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)

sample41.0ms (0.6%)

Algorithm

1×

intervals

Results

11.0ms	167×	body	128	valid
8.0ms	31×	body	2048	valid
5.0ms	25×	body	1024	valid
5.0ms	16×	body	4096	valid
2.0ms	15×	body	512	valid
1.0ms	14×	body	128	nan
0.0ms	9×	body	128	invalid
0.0ms	2×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify66.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	927	24
1	927	24

prune6.0ms (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: 30.8b

Counts

2 → 2

Compiler

Compiled 82 to 67 computations (18.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
0.3b	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
19.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite44.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64`
10×	`add-log-exp_binary64`
9×	`add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-prod_binary64`
7×	`cancel-sign-sub-inv_binary64` `associate-/l*_binary64` `times-frac_binary64`
6×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
5×	`pow1_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`diff-log_binary64` `distribute-rgt-neg-in_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`associate-/r*_binary64` `pow1/2_binary64` `associate--l-_binary64` `cbrt-unprod_binary64` `neg-sub0_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `neg-log_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

4 → 82

Calls

4 calls:

14.0ms	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
13.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series491.0ms (7.3%)

Counts

4 → 12

Calls

4 calls:

161.0ms	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
139.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
125.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
67.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify64.0ms (1%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	6114	2287

prune394.0ms (5.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	90	4	94
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	91	5	96

Merged error: 5.1b

Counts

96 → 5

Compiler

Compiled 7377 to 4942 computations (33% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
5.0b	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b)) (.f64 2 a))
8.3b	(/.f64 (.f64 4 (.f64 a c)) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b))
19.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite60.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
33×	`add-sqr-sqrt_binary64`
30×	`times-frac_binary64`
22×	`*-un-lft-identity_binary64`
17×	`cbrt-undiv_binary64` `div-exp_binary64`
13×	`cbrt-unprod_binary64` `prod-exp_binary64` `associate-/l*_binary64`
12×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`
8×	`sqrt-prod_binary64`
7×	`associate-/r*_binary64`
6×	`add-log-exp_binary64` `associate-/r/_binary64`
5×	`pow1_binary64` `flip3--_binary64` `distribute-lft-out--_binary64` `flip--_binary64`
4×	`div-inv_binary64`
3×	`cancel-sign-sub-inv_binary64`
2×	`clear-num_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 → 115

Calls

4 calls:

17.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b)) (.f64 2 a))
14.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b))
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))))

series1.0s (15.1%)

Counts

4 → 12

Calls

4 calls:

405.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b))
334.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b)) (.f64 2 a))
137.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
136.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify92.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4947	3682
1	4947	3682

prune306.0ms (4.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	124	3	127
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	125	7	132

Merged error: 5.0b

Counts

132 → 7

Compiler

Compiled 6396 to 3937 computations (38.4% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b))
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
19.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite41.0ms (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 b) (.f64 4 (*.f64 a c)))) b))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
7.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series693.0ms (10.3%)

Counts

4 → 12

Calls

4 calls:

379.0ms	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b))
132.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
118.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
63.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify71.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4904	2453
1	4904	2453

prune121.0ms (1.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	97	7	104

Merged error: 5.0b

Counts

104 → 7

Compiler

Compiled 2723 to 1553 computations (43% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 1 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) c))
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
19.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite239.0ms (3.6%)

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`
13×	`distribute-lft-out--_binary64`
12×	`add-exp-log_binary64`
9×	`add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
6×	`pow1_binary64`
5×	`div-inv_binary64`
4×	`cancel-sign-sub-inv_binary64` `div-exp_binary64`
3×	`flip3--_binary64` `cbrt-undiv_binary64` `associate-/l*_binary64` `flip--_binary64`
2×	`sub-neg_binary64` `diff-log_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 → 154

Calls

4 calls:

198.0ms	(/.f64 1 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) c))
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)))

series509.0ms (7.6%)

Counts

4 → 12

Calls

4 calls:

216.0ms	(/.f64 1 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) c))
122.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
107.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
64.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify106.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4982	5472
1	4982	5472

prune241.0ms (3.6%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	166	0	166
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	166	7	173

Merged error: 5.0b

Counts

173 → 7

Compiler

Compiled 5192 to 2946 computations (43.3% saved)

regimes155.0ms (2.3%)

Compiler: Compiled 408 to 358 computations (12.3% saved)

bsearch72.0ms (1.1%)

Steps

Iters	Range		Point
6	3.1566005766712353e+129	3.5462725150946685e+130	6.914177626537424e+129
5	5.6707999874284e-240	1.3699498127563673e-239	8.005947987748499e-240
7	-5.675444860155148e+83	-1.0924929008488078e+82	-5.566759220787537e+83

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	124	80
1	124	80

end0.0ms (0%)

sample1.4s (20.5%)

Algorithm

1×

intervals

Results

298.0ms	1139×	body	2048	valid
279.0ms	5205×	body	128	valid
143.0ms	720×	body	1024	valid
120.0ms	381×	body	4096	valid
55.0ms	379×	body	512	valid
36.0ms	712×	body	128	nan
20.0ms	380×	body	128	invalid
18.0ms	176×	body	256	valid

Compiler

Compiled 205 to 157 computations (23.4% saved)

Details

analyze463.0ms (6.9%)

sample41.0ms (0.6%)

simplify66.0ms (1%)

prune6.0ms (0.1%)

localize12.0ms (0.2%)

rewrite44.0ms (0.7%)

series491.0ms (7.3%)

simplify64.0ms (1%)

prune394.0ms (5.9%)

localize14.0ms (0.2%)

rewrite60.0ms (0.9%)

series1.0s (15.1%)

simplify92.0ms (1.4%)

prune306.0ms (4.6%)

localize12.0ms (0.2%)

rewrite41.0ms (0.6%)

series693.0ms (10.3%)

simplify71.0ms (1.1%)

prune121.0ms (1.8%)

localize13.0ms (0.2%)

rewrite239.0ms (3.6%)

series509.0ms (7.6%)

simplify106.0ms (1.6%)

prune241.0ms (3.6%)

regimes155.0ms (2.3%)

bsearch72.0ms (1.1%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.4s (20.5%)

Profiling