Details

analyze452.0ms (6.6%)

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 (0.6%)

Algorithm

1×

intervals

Results

9.0ms	166×	body	128	valid
8.0ms	30×	body	2048	valid
5.0ms	24×	body	1024	valid
4.0ms	12×	body	4096	valid
2.0ms	16×	body	512	valid
1.0ms	8×	body	256	valid
1.0ms	10×	body	128	nan
1.0ms	10×	body	128	invalid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify231.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	927	24
1	927	24

prune5.0ms (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

Merged error: 36.3b

Counts

2 → 1

Compiler

Compiled 65 to 53 computations (18.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
2.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite36.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_423`
15×	`add-sqr-sqrt_binary64_445`
14×	`add-cube-cbrt_binary64_458`
12×	`times-frac_binary64_429`
8×	`add-log-exp_binary64_462`
6×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
5×	`distribute-lft-out_binary64_374` `pow1_binary64_484`
4×	`associate-/l*_binary64_368`
3×	`sqrt-prod_binary64_439` `associate-/r*_binary64_367`
2×	`sqrt-div_binary64_440` `flip-+_binary64_397` `flip3--_binary64_427` `associate-/l/_binary64_370` `flip3-+_binary64_426` `flip--_binary64_398`
1×	`sub-neg_binary64_416` `diff-log_binary64_515` `cancel-sign-sub-inv_binary64_389` `+-commutative_binary64_353` `rem-sqrt-square_binary64_436` `clear-num_binary64_422` `frac-2neg_binary64_434` `pow1/2_binary64_503` `sqrt-pow1_binary64_441` `div-inv_binary64_420` `cbrt-undiv_binary64_457` `div-exp_binary64_474` `sum-log_binary64_514`

Counts

4 → 72

Calls

4 calls:

11.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
8.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series456.0ms (6.7%)

Counts

4 → 12

Calls

4 calls:

139.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
127.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
125.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
64.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify73.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5101	2019

prune556.0ms (8.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	75	9	84
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	9	85

Merged error: 6.5b

Counts

85 → 9

Compiler

Compiled 11225 to 7478 computations (33.4% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
2.9b	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
10.4b	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite62.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64_429`
53×	`add-sqr-sqrt_binary64_445`
40×	`*-un-lft-identity_binary64_423`
28×	`add-cube-cbrt_binary64_458`
27×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
13×	`associate-/l*_binary64_368`
12×	`difference-of-squares_binary64_392`
10×	`associate-/r/_binary64_369` `cbrt-undiv_binary64_457` `div-exp_binary64_474`
9×	`sqrt-prod_binary64_439` `associate-/r*_binary64_367`
7×	`flip3--_binary64_427` `flip--_binary64_398`
6×	`prod-exp_binary64_472` `distribute-lft-out--_binary64_375` `add-log-exp_binary64_462` `div-inv_binary64_420` `cbrt-unprod_binary64_456`
5×	`pow1_binary64_484`
2×	`sqrt-div_binary64_440` `clear-num_binary64_422` `frac-2neg_binary64_434`
1×	`sub-neg_binary64_416` `diff-log_binary64_515` `cancel-sign-sub-inv_binary64_389` `rem-sqrt-square_binary64_436` `associate-/l/_binary64_370` `pow1/2_binary64_503` `sqrt-pow1_binary64_441`

Counts

4 → 128

Calls

4 calls:

18.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
15.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series942.0ms (13.8%)

Counts

4 → 12

Calls

4 calls:

420.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
333.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
124.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
64.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify72.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5507	4685

prune308.0ms (4.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	137	3	140
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	141	8	149

Merged error: 6.5b

Counts

149 → 8

Compiler

Compiled 6596 to 3947 computations (40.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
1.0b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite42.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64_445`
28×	`*-un-lft-identity_binary64_423`
18×	`times-frac_binary64_429` `add-cube-cbrt_binary64_458`
11×	`sqrt-prod_binary64_439`
10×	`difference-of-squares_binary64_392`
8×	`add-log-exp_binary64_462`
7×	`cancel-sign-sub-inv_binary64_389`
6×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459` `associate-/r*_binary64_367`
5×	`pow1_binary64_484` `distribute-lft-out--_binary64_375`
4×	`flip3--_binary64_427` `flip--_binary64_398`
3×	`associate-/l*_binary64_368`
2×	`sqrt-div_binary64_440` `sub-neg_binary64_416` `diff-log_binary64_515` `associate-/r/_binary64_369`
1×	`rem-sqrt-square_binary64_436` `clear-num_binary64_422` `frac-2neg_binary64_434` `pow1/2_binary64_503` `sqrt-pow1_binary64_441` `div-inv_binary64_420` `cbrt-undiv_binary64_457` `div-exp_binary64_474`

Counts

4 → 88

Calls

4 calls:

11.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
8.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
7.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series663.0ms (9.7%)

Counts

4 → 12

Calls

4 calls:

376.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
117.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
107.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
62.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify78.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4898	2580
1	4898	2580

prune152.0ms (2.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	100	8	108

Merged error: 6.5b

Counts

108 → 8

Compiler

Compiled 3328 to 2039 computations (38.7% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 4 (/.f64 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) c))
1.0b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite58.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64_429`
123×	`add-sqr-sqrt_binary64_445`
96×	`*-un-lft-identity_binary64_423`
70×	`add-cube-cbrt_binary64_458`
26×	`difference-of-squares_binary64_392`
22×	`associate-/r*_binary64_367`
19×	`sqrt-prod_binary64_439`
13×	`distribute-lft-out--_binary64_375`
9×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
8×	`add-log-exp_binary64_462`
7×	`cancel-sign-sub-inv_binary64_389`
5×	`pow1_binary64_484` `div-inv_binary64_420`
3×	`flip3--_binary64_427` `flip--_binary64_398` `associate-/l*_binary64_368` `cbrt-undiv_binary64_457` `div-exp_binary64_474`
2×	`sqrt-div_binary64_440` `sub-neg_binary64_416` `diff-log_binary64_515`
1×	`rem-sqrt-square_binary64_436` `associate-/r/_binary64_369` `clear-num_binary64_422` `frac-2neg_binary64_434` `pow1/2_binary64_503` `sqrt-pow1_binary64_441`

Counts

4 → 153

Calls

4 calls:

15.0ms	(/.f64 4 (/.f64 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) c))
8.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series574.0ms (8.4%)

Counts

4 → 12

Calls

4 calls:

266.0ms	(/.f64 4 (/.f64 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) c))
122.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
120.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
65.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify124.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4905	5781
1	4905	5781

prune249.0ms (3.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	165	0	165
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	165	8	173

Merged error: 6.5b

Counts

173 → 8

Compiler

Compiled 5340 to 3102 computations (41.9% saved)

regimes103.0ms (1.5%)

Compiler: Compiled 474 to 378 computations (20.3% saved)

bsearch86.0ms (1.3%)

Steps

Iters	Range		Point
6	3.453198629799523e+50	2.437223188812816e+51	2.404688834790521e+51
5	1.4879601855401445e-294	4.1080958905033815e-294	2.48045852321778e-294
9	-1.8084373769306673e+109	-7.821142621831562e+100	-5.193186085288575e+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	99	92
1	99	92

end0.0ms (0%)

sample1.4s (20.7%)

Algorithm

1×

intervals

Results

280.0ms	1092×	body	2048	valid
279.0ms	5243×	body	128	valid
151.0ms	719×	body	1024	valid
131.0ms	415×	body	4096	valid
55.0ms	369×	body	512	valid
34.0ms	684×	body	128	nan
20.0ms	392×	body	128	invalid
16.0ms	162×	body	256	valid

Compiler

Compiled 278 to 209 computations (24.8% saved)

Details

analyze452.0ms (6.6%)

sample38.0ms (0.6%)

simplify231.0ms (3.4%)

prune5.0ms (0.1%)

localize11.0ms (0.2%)

rewrite36.0ms (0.5%)

series456.0ms (6.7%)

simplify73.0ms (1.1%)

prune556.0ms (8.1%)

localize13.0ms (0.2%)

rewrite62.0ms (0.9%)

series942.0ms (13.8%)

simplify72.0ms (1.1%)

prune308.0ms (4.5%)

localize13.0ms (0.2%)

rewrite42.0ms (0.6%)

series663.0ms (9.7%)

simplify78.0ms (1.1%)

prune152.0ms (2.2%)

localize14.0ms (0.2%)

rewrite58.0ms (0.8%)

series574.0ms (8.4%)

simplify124.0ms (1.8%)

prune249.0ms (3.6%)

regimes103.0ms (1.5%)

bsearch86.0ms (1.3%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.4s (20.7%)

Profiling