Details

analyze470.0ms (6.7%)

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
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)

sample37.0ms (0.5%)

Algorithm

1×

intervals

Results

9.0ms	175×	body	128	valid
7.0ms	28×	body	2048	valid
5.0ms	27×	body	1024	valid
3.0ms	10×	body	4096	valid
1.0ms	9×	body	512	valid
1.0ms	19×	body	128	nan
1.0ms	7×	body	256	valid
1.0ms	12×	body	128	invalid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify228.0ms (3.2%)

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: 33.0b

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)
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.6b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
23.9b	(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:

12.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
7.0ms	(+.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)))

series467.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

151.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
129.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
124.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
63.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify72.0ms (1%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5101	2019

prune536.0ms (7.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	75	9	84
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	75	10	85

Merged error: 6.7b

Counts

85 → 10

Compiler

Compiled 10606 to 7169 computations (32.4% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (/.f64 1 a))
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.6b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
23.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite39.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_445`
18×	`*-un-lft-identity_binary64_423`
13×	`add-cube-cbrt_binary64_458` `associate-r_binary64_363` `add-exp-log_binary64_461`
11×	`times-frac_binary64_429`
9×	`add-cbrt-cube_binary64_459`
8×	`add-log-exp_binary64_462`
7×	`pow1_binary64_484`
4×	`associate-l_binary64_364` `prod-exp_binary64_472`
3×	`flip-+_binary64_397` `sqrt-prod_binary64_439` `flip3-+_binary64_426` `unswap-sqr_binary64_391`
2×	`sqrt-div_binary64_440` `frac-times_binary64_433` `distribute-lft-out_binary64_374` `flip3--_binary64_427` `associate-*l/_binary64_366` `flip--_binary64_398` `div-exp_binary64_474` `cbrt-unprod_binary64_456`
1×	`rec-exp_binary64_473` `1-exp_binary64_467` `pow-prod-down_binary64_494` `sub-neg_binary64_416` `diff-log_binary64_515` `un-div-inv_binary64_421` `cancel-sign-sub-inv_binary64_389` `+-commutative_binary64_353` `rem-sqrt-square_binary64_436` `associate-r/_binary64_365` `-commutative_binary64_354` `pow1/2_binary64_503` `sqrt-pow1_binary64_441` `div-inv_binary64_420` `cbrt-undiv_binary64_457` `sum-log_binary64_514`

Counts

4 → 80

Calls

4 calls:

15.0ms	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (/.f64 1 a))
7.0ms	(+.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))))

series454.0ms (6.4%)

Counts

4 → 12

Calls

4 calls:

151.0ms	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (/.f64 1 a))
126.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
113.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
64.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify91.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4920	2059
1	4920	2059

prune120.0ms (1.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	92	10	102

Merged error: 6.7b

Counts

102 → 10

Compiler

Compiled 2680 to 1578 computations (41.1% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.1b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
3.2b	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
12.3b	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
23.9b	(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`
59×	`add-sqr-sqrt_binary64_445`
44×	`*-un-lft-identity_binary64_423`
30×	`add-cube-cbrt_binary64_458`
27×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
14×	`difference-of-squares_binary64_392`
13×	`sqrt-prod_binary64_439` `associate-/l*_binary64_368`
10×	`associate-/r/_binary64_369` `cbrt-undiv_binary64_457` `div-exp_binary64_474`
9×	`associate-/r*_binary64_367`
7×	`flip3--_binary64_427` `distribute-lft-out--_binary64_375` `flip--_binary64_398`
6×	`cancel-sign-sub-inv_binary64_389` `prod-exp_binary64_472` `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` `rem-sqrt-square_binary64_436` `associate-/l/_binary64_370` `pow1/2_binary64_503` `sqrt-pow1_binary64_441`

Counts

4 → 136

Calls

4 calls:

16.0ms	(/.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))))))
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))))

series1.2s (16.6%)

Counts

4 → 12

Calls

4 calls:

595.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
324.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
129.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
124.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify92.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5217	5032

prune320.0ms (4.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	145	3	148
Fresh	2	5	7
Picked	1	0	1
Done	0	2	2
Total	148	10	158

Merged error: 6.6b

Counts

158 → 10

Compiler

Compiled 6967 to 4145 computations (40.5% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.1b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
23.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite37.0ms (0.5%)

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:

9.0ms	(/.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)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series692.0ms (9.8%)

Counts

4 → 12

Calls

4 calls:

376.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
140.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
112.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
64.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify79.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4898	2580
1	4898	2580

prune168.0ms (2.4%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	99	11	110

Merged error: 6.6b

Counts

110 → 11

Compiler

Compiled 3606 to 2250 computations (37.6% saved)

regimes192.0ms (2.7%)

Compiler: Compiled 732 to 573 computations (21.7% saved)

bsearch109.0ms (1.5%)

Steps

Iters	Range	Point
8	1.8214039147413959e+114	3.0936283487967313e+118	2.1578323955249213e+116
11	2.2854952522798188e-282	3.904822145804709e-260	1.4031237401242977e-270
7	-1.2753667153502532e+154	-8.990067059825001e+151	-1.3091834909018501e+152

Iters

Range

Point

1.8214039147413959e+114

3.0936283487967313e+118

2.1578323955249213e+116

2.2854952522798188e-282

3.904822145804709e-260

1.4031237401242977e-270

-1.2753667153502532e+154

-8.990067059825001e+151

-1.3091834909018501e+152

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	100	92
1	100	92

end0.0ms (0%)

sample1.5s (21.4%)

Algorithm

1×

intervals

Results

311.0ms	1188×	body	2048	valid
280.0ms	5184×	body	128	valid
149.0ms	716×	body	1024	valid
120.0ms	363×	body	4096	valid
55.0ms	367×	body	512	valid
35.0ms	692×	body	128	nan
21.0ms	410×	body	128	invalid
18.0ms	182×	body	256	valid

Compiler

Compiled 364 to 274 computations (24.7% saved)

Details

analyze470.0ms (6.7%)

sample37.0ms (0.5%)

simplify228.0ms (3.2%)

prune5.0ms (0.1%)

localize11.0ms (0.2%)

rewrite36.0ms (0.5%)

series467.0ms (6.6%)

simplify72.0ms (1%)

prune536.0ms (7.6%)

localize15.0ms (0.2%)

rewrite39.0ms (0.6%)

series454.0ms (6.4%)

simplify91.0ms (1.3%)

prune120.0ms (1.7%)

localize12.0ms (0.2%)

rewrite62.0ms (0.9%)

series1.2s (16.6%)

simplify92.0ms (1.3%)

prune320.0ms (4.5%)

localize16.0ms (0.2%)

rewrite37.0ms (0.5%)

series692.0ms (9.8%)

simplify79.0ms (1.1%)

prune168.0ms (2.4%)

regimes192.0ms (2.7%)

bsearch109.0ms (1.5%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.5s (21.4%)

Profiling