Details

analyze456.0ms (6.2%)

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	176×	body	128	valid
7.0ms	32×	body	2048	valid
4.0ms	23×	body	1024	valid
3.0ms	12×	body	4096	valid
1.0ms	9×	body	512	valid
1.0ms	22×	body	128	nan
1.0ms	11×	body	128	invalid
0.0ms	4×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify232.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	927	24
1	927	24

prune6.0ms (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: 34.1b

Counts

2 → 1

Compiler

Compiled 65 to 53 computations (18.5% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
1.0b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite38.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_445`
14×	`*-un-lft-identity_binary64_423`
9×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
8×	`add-cube-cbrt_binary64_458` `add-log-exp_binary64_462`
6×	`times-frac_binary64_429` `sqrt-prod_binary64_439` `difference-of-squares_binary64_392` `associate-/l*_binary64_368`
5×	`pow1_binary64_484`
4×	`cancel-sign-sub-inv_binary64_389` `flip3--_binary64_427` `flip--_binary64_398`
3×	`distribute-lft-out--_binary64_375`
2×	`sqrt-div_binary64_440` `sub-neg_binary64_416` `diff-log_binary64_515` `associate-/l/_binary64_370` `cbrt-undiv_binary64_457` `div-exp_binary64_474`
1×	`prod-exp_binary64_472` `rem-sqrt-square_binary64_436` `div-sub_binary64_428` `clear-num_binary64_422` `frac-2neg_binary64_434` `pow1/2_binary64_503` `sqrt-pow1_binary64_441` `div-inv_binary64_420` `associate-/r*_binary64_367` `cbrt-unprod_binary64_456`

Counts

4 → 74

Calls

4 calls:

13.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series519.0ms (7.1%)

Counts

4 → 12

Calls

4 calls:

209.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
124.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
122.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
63.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify69.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5031	1979

prune404.0ms (5.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	79	7	86
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	79	8	87

Merged error: 6.8b

Counts

87 → 8

Compiler

Compiled 7791 to 5569 computations (28.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) 2)))
1.0b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite119.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

693×	`times-frac_binary64_429`
439×	`add-sqr-sqrt_binary64_445`
364×	`*-un-lft-identity_binary64_423`
290×	`add-cube-cbrt_binary64_458`
74×	`difference-of-squares_binary64_392`
71×	`associate-/r*_binary64_367`
40×	`sqrt-prod_binary64_439`
37×	`distribute-lft-out--_binary64_375`
25×	`add-exp-log_binary64_461`
17×	`div-inv_binary64_420`
15×	`div-exp_binary64_474`
13×	`add-cbrt-cube_binary64_459`
8×	`add-log-exp_binary64_462`
6×	`pow1_binary64_484` `cbrt-undiv_binary64_457`
5×	`associate-/r/_binary64_369`
4×	`cancel-sign-sub-inv_binary64_389`
3×	`rec-exp_binary64_473` `1-exp_binary64_467` `flip3--_binary64_427` `flip--_binary64_398` `associate-/l*_binary64_368`
2×	`sqrt-div_binary64_440` `sub-neg_binary64_416` `diff-log_binary64_515`
1×	`rem-sqrt-square_binary64_436` `clear-num_binary64_422` `frac-2neg_binary64_434` `pow-flip_binary64_497` `pow1/2_binary64_503` `sqrt-pow1_binary64_441` `inv-pow_binary64_508`

Counts

4 → 356

Calls

4 calls:

26.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) 2)))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
7.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series552.0ms (7.6%)

Counts

4 → 12

Calls

4 calls:

242.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) 2)))
127.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
122.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
61.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify203.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

368 → 368

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4947	16295
1	4947	16295

prune773.0ms (10.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	367	1	368
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	367	9	376

Merged error: 6.7b

Counts

376 → 9

Compiler

Compiled 13666 to 8406 computations (38.5% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.0b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
3.2b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
11.4b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite55.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
22×	`times-frac_binary64_429`
21×	`*-un-lft-identity_binary64_423`
17×	`cbrt-undiv_binary64_457` `div-exp_binary64_474`
13×	`prod-exp_binary64_472` `cbrt-unprod_binary64_456`
12×	`add-sqr-sqrt_binary64_445`
11×	`add-cube-cbrt_binary64_458` `associate-/l*_binary64_368`
6×	`associate-/r/_binary64_369` `add-log-exp_binary64_462`
5×	`distribute-lft-out_binary64_374` `pow1_binary64_484` `associate-/r*_binary64_367`
4×	`flip-+_binary64_397` `flip3-+_binary64_426` `div-inv_binary64_420`
3×	`sqrt-prod_binary64_439`
2×	`sqrt-div_binary64_440` `clear-num_binary64_422` `frac-2neg_binary64_434`
1×	`+-commutative_binary64_353` `rem-sqrt-square_binary64_436` `flip3--_binary64_427` `associate-/l/_binary64_370` `pow1/2_binary64_503` `sqrt-pow1_binary64_441` `flip--_binary64_398` `sum-log_binary64_514`

Counts

4 → 102

Calls

4 calls:

18.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
12.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series947.0ms (13%)

Counts

4 → 12

Calls

4 calls:

378.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
322.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
129.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
118.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify77.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5005	3121

prune272.0ms (3.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	110	4	114
Fresh	3	3	6
Picked	1	0	1
Done	1	1	2
Total	115	8	123

Merged error: 6.7b

Counts

123 → 8

Compiler

Compiled 5576 to 3767 computations (32.4% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
1.0b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
2.0b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite32.0ms (0.4%)

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-/r*_binary64_367`
3×	`sqrt-prod_binary64_439` `associate-/l*_binary64_368`
2×	`sqrt-div_binary64_440` `flip-+_binary64_397` `flip3--_binary64_427` `associate-/r/_binary64_369` `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:

9.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series637.0ms (8.7%)

Counts

4 → 12

Calls

4 calls:

315.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
142.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
118.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
62.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify71.0ms (1%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5099	1969

prune144.0ms (2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	84	8	92

Merged error: 6.7b

Counts

92 → 8

Compiler

Compiled 2989 to 1982 computations (33.7% saved)

regimes150.0ms (2.1%)

Compiler: Compiled 444 to 366 computations (17.6% saved)

bsearch109.0ms (1.5%)

Steps

Iters	Range	Point
10	1.6829726428472436e+90	9.502704283103217e+100	8.333589530494835e+96
10	-1.2588982842552305e-284	-1.8487720490174733e-296	-5.904324843765853e-289
7	-6.919883347824696e+71	-4.350875564320368e+69	-5.785370549652638e+71

Iters

Range

Point

1.6829726428472436e+90

9.502704283103217e+100

8.333589530494835e+96

-1.2588982842552305e-284

-1.8487720490174733e-296

-5.904324843765853e-289

-6.919883347824696e+71

-4.350875564320368e+69

-5.785370549652638e+71

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	105	82
1	105	82

end0.0ms (0%)

sample1.3s (18.4%)

Algorithm

1×

intervals

Results

266.0ms	5224×	body	128	valid
261.0ms	1093×	body	2048	valid
141.0ms	712×	body	1024	valid
130.0ms	427×	body	4096	valid
53.0ms	362×	body	512	valid
34.0ms	654×	body	128	nan
20.0ms	389×	body	128	invalid
17.0ms	182×	body	256	valid

Compiler

Compiled 219 to 169 computations (22.8% saved)

Details

analyze456.0ms (6.2%)

sample37.0ms (0.5%)

simplify232.0ms (3.2%)

prune6.0ms (0.1%)

localize11.0ms (0.1%)

rewrite38.0ms (0.5%)

series519.0ms (7.1%)

simplify69.0ms (0.9%)

prune404.0ms (5.5%)

localize12.0ms (0.2%)

rewrite119.0ms (1.6%)

series552.0ms (7.6%)

simplify203.0ms (2.8%)

prune773.0ms (10.6%)

localize14.0ms (0.2%)

rewrite55.0ms (0.7%)

series947.0ms (13%)

simplify77.0ms (1.1%)

prune272.0ms (3.7%)

localize14.0ms (0.2%)

rewrite32.0ms (0.4%)

series637.0ms (8.7%)

simplify71.0ms (1%)

prune144.0ms (2%)

regimes150.0ms (2.1%)

bsearch109.0ms (1.5%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.3s (18.4%)

Profiling