Details

analyze449.0ms (6%)

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)

sample38.0ms (0.5%)

Algorithm

1×

intervals

Results

8.0ms	161×	body	128	valid
8.0ms	33×	body	2048	valid
5.0ms	26×	body	1024	valid
4.0ms	14×	body	4096	valid
2.0ms	12×	body	512	valid
1.0ms	25×	body	128	nan
1.0ms	10×	body	256	valid
1.0ms	10×	body	128	invalid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify393.0ms (5.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (301.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune4.0ms (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

Error

34.7b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (0.1%)

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))
0.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
20.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite34.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_441`
14×	`*-un-lft-identity_binary64_419`
9×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
8×	`add-log-exp_binary64_458` `add-cube-cbrt_binary64_454`
6×	`times-frac_binary64_425` `difference-of-squares_binary64_388` `sqrt-prod_binary64_435` `associate-/l*_binary64_364`
5×	`pow1_binary64_480`
4×	`flip3--_binary64_423` `flip--_binary64_394` `cancel-sign-sub-inv_binary64_385`
3×	`distribute-lft-out--_binary64_371`
2×	`sqrt-div_binary64_436` `sub-neg_binary64_412` `diff-log_binary64_511` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `associate-/l/_binary64_366`
1×	`clear-num_binary64_418` `pow1/2_binary64_499` `div-inv_binary64_416` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `frac-2neg_binary64_430` `sqrt-pow1_binary64_437` `associate-/r*_binary64_363` `rem-sqrt-square_binary64_432` `div-sub_binary64_424`

Counts

4 → 74

Calls

4 calls:

11.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series672.0ms (9%)

Counts

4 → 72

Calls

4 calls:

219.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
157.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
154.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
142.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 2110 to 1780 computations (15.6% saved)

simplify86.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4943	2996
1	4943	2996

prune168.0ms (2.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	138	8	146
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	139	8	147

Error

4.3b

Counts

147 → 8

Compiler

Compiled 3040 to 1618 computations (46.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2))
0.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
20.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite49.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64_425`
122×	`add-sqr-sqrt_binary64_441`
95×	`*-un-lft-identity_binary64_419`
69×	`add-cube-cbrt_binary64_454`
26×	`difference-of-squares_binary64_388`
22×	`associate-/r*_binary64_363`
16×	`sqrt-prod_binary64_435`
13×	`distribute-lft-out--_binary64_371`
9×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
8×	`add-log-exp_binary64_458`
5×	`div-inv_binary64_416` `pow1_binary64_480`
4×	`cancel-sign-sub-inv_binary64_385`
3×	`flip3--_binary64_423` `flip--_binary64_394` `div-exp_binary64_470` `associate-/l*_binary64_364` `cbrt-undiv_binary64_453`
2×	`sqrt-div_binary64_436` `sub-neg_binary64_412` `diff-log_binary64_511`
1×	`clear-num_binary64_418` `pow1/2_binary64_499` `associate-/r/_binary64_365` `frac-2neg_binary64_430` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432`

Counts

4 → 150

Calls

4 calls:

12.0ms	(/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2))
8.0ms	(-.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))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series785.0ms (10.6%)

Counts

4 → 74

Calls

4 calls:

301.0ms	(/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2))
164.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
161.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
159.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)

Compiler

Compiled 2418 to 2033 computations (15.9% saved)

simplify91.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

224 → 224

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5078	6788

prune312.0ms (4.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	221	3	224
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	223	9	232

Error

4.1b

Counts

232 → 9

Compiler

Compiled 6186 to 3481 computations (43.7% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
1.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
20.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
20.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite32.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_441`
12×	`*-un-lft-identity_binary64_419`
8×	`add-log-exp_binary64_458` `add-cube-cbrt_binary64_454` `sqrt-prod_binary64_435`
6×	`cancel-sign-sub-inv_binary64_385` `pow1_binary64_480`
4×	`sqrt-div_binary64_436` `difference-of-squares_binary64_388` `flip3--_binary64_423` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `flip--_binary64_394`
2×	`sub-neg_binary64_412` `pow1/2_binary64_499` `distribute-lft-out--_binary64_371` `diff-log_binary64_511` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432`

Counts

4 → 64

Calls

4 calls:

8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
8.0ms	(-.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))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series656.0ms (8.8%)

Counts

4 → 74

Calls

4 calls:

173.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
166.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
160.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
157.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 4044 to 3024 computations (25.2% saved)

simplify90.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4965	2744
1	4965	2744

prune198.0ms (2.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	138	0	138
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	138	9	147

Error

4.1b

Counts

147 → 9

Compiler

Compiled 4957 to 2612 computations (47.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (/.f64 a b) (/.f64 b c))
0.9b	(/.f64 1 (-.f64 (/.f64 a b) (/.f64 b c)))

rewrite39.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

83×	`add-sqr-sqrt_binary64_441`
66×	`times-frac_binary64_425`
53×	`*-un-lft-identity_binary64_419`
23×	`add-cube-cbrt_binary64_454`
20×	`difference-of-squares_binary64_388`
13×	`cancel-sign-sub-inv_binary64_385`
10×	`distribute-lft-out--_binary64_371`
9×	`associate-/r*_binary64_363`
6×	`add-exp-log_binary64_457`
4×	`add-log-exp_binary64_458` `add-cbrt-cube_binary64_455`
3×	`associate-/r/_binary64_365` `pow1_binary64_480` `associate-/l*_binary64_364`
2×	`div-inv_binary64_416` `flip3--_binary64_423` `flip--_binary64_394` `div-exp_binary64_470` `frac-sub_binary64_428`
1×	`clear-num_binary64_418` `1-exp_binary64_463` `sub-neg_binary64_412` `inv-pow_binary64_504` `rec-exp_binary64_469` `frac-2neg_binary64_430` `pow-flip_binary64_493` `diff-log_binary64_511` `cbrt-undiv_binary64_453`

Counts

2 → 89

Calls

2 calls:

17.0ms	(/.f64 1 (-.f64 (/.f64 a b) (/.f64 b c)))
13.0ms	(-.f64 (/.f64 a b) (/.f64 b c))

series264.0ms (3.6%)

Counts

2 → 36

Calls

2 calls:

141.0ms	(-.f64 (/.f64 a b) (/.f64 b c))
123.0ms	(/.f64 1 (-.f64 (/.f64 a b) (/.f64 b c)))

Compiler

Compiled 600 to 537 computations (10.5% saved)

simplify76.0ms (1%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4966	2100
1	4966	2100

prune75.0ms (1%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	122	3	125
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	122	12	134

Error

4.1b

Counts

134 → 12

Compiler

Compiled 1789 to 495 computations (72.3% saved)

regimes767.0ms (10.3%)

Accuracy

Total 4.6b remaining (44.9%)

Threshold costs 0b (0%)

Compiler

Compiled 3820 to 2950 computations (22.8% saved)

bsearch58.0ms (0.8%)

Steps

Iters	Range		Point
7	1.4122995127471838e-68	1.8033503858249277e-66	1.691066958601468e-68
9	-3.203657050301464e+105	-6.409993448757428e+99	-3.161255245507665e+105

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	93	52
1	93	52

end0.0ms (0%)

sample2.0s (27.6%)

Algorithm

1×

intervals

Results

279.0ms	5228×	body	128	valid
278.0ms	1110×	body	2048	valid
144.0ms	748×	body	1024	valid
122.0ms	390×	body	4096	valid
50.0ms	332×	body	512	valid
31.0ms	639×	body	128	nan
19.0ms	192×	body	256	valid
18.0ms	359×	body	128	invalid

Compiler

Compiled 1040 to 794 computations (23.7% saved)

Details

analyze449.0ms (6%)

sample38.0ms (0.5%)

simplify393.0ms (5.3%)

prune4.0ms (0.1%)

localize11.0ms (0.1%)

rewrite34.0ms (0.5%)

series672.0ms (9%)

simplify86.0ms (1.2%)

prune168.0ms (2.3%)

localize12.0ms (0.2%)

rewrite49.0ms (0.7%)

series785.0ms (10.6%)

simplify91.0ms (1.2%)

prune312.0ms (4.2%)

localize15.0ms (0.2%)

rewrite32.0ms (0.4%)

series656.0ms (8.8%)

simplify90.0ms (1.2%)

prune198.0ms (2.7%)

localize6.0ms (0.1%)

rewrite39.0ms (0.5%)

series264.0ms (3.6%)

simplify76.0ms (1%)

prune75.0ms (1%)

regimes767.0ms (10.3%)

bsearch58.0ms (0.8%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.0s (27.6%)

Profiling