Details

analyze462.0ms (8%)

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 (0.6%)

Algorithm

1×

intervals

Results

10.0ms	185×	body	128	valid
6.0ms	26×	body	2048	valid
4.0ms	17×	body	1024	valid
3.0ms	9×	body	4096	valid
2.0ms	15×	body	512	valid
1.0ms	27×	body	128	nan
1.0ms	17×	body	128	invalid
0.0ms	4×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify228.0ms (3.9%)

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: 31.5b

Counts

2 → 1

Compiler

Compiled 65 to 53 computations (18.5% saved)

localize10.0ms (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)
0.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
23.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite36.0ms (0.6%)

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:

10.0ms	(/.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)))

series461.0ms (8%)

Counts

4 → 12

Calls

4 calls:

152.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
125.0ms	(+.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))))
59.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify70.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5101	2019

prune493.0ms (8.5%)

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: 6.4b

Counts

85 → 10

Compiler

Compiled 9499 to 6416 computations (32.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (/.f64 1 a))
0.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
23.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite42.0ms (0.7%)

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

series454.0ms (7.8%)

Counts

4 → 12

Calls

4 calls:

144.0ms	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (/.f64 1 a))
127.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
119.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
64.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify91.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4920	2059
1	4920	2059

prune142.0ms (2.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	90	2	92
Fresh	3	5	8
Picked	0	1	1
Done	0	1	1
Total	93	9	102

Merged error: 6.4b

Counts

102 → 9

Compiler

Compiled 2972 to 1817 computations (38.9% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

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)))))
15.0b	(/.f64 (.f64 4 (.f64 a c)) a)
23.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite31.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

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

series341.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

132.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
122.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
66.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
22.0ms	(/.f64 (.f64 4 (.f64 a c)) a)

simplify57.0ms (1%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4982	1372
1	4982	1372

prune162.0ms (2.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	80	2	82
Fresh	1	5	6
Picked	1	0	1
Done	1	1	2
Total	83	8	91

Merged error: 6.3b

Counts

91 → 8

Compiler

Compiled 3271 to 2046 computations (37.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (.f64 4 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))))

rewrite36.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64_445`
15×	`*-un-lft-identity_binary64_423`
9×	`add-cube-cbrt_binary64_458` `sqrt-prod_binary64_439` `add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
8×	`add-log-exp_binary64_462`
7×	`cancel-sign-sub-inv_binary64_389`
6×	`times-frac_binary64_429` `difference-of-squares_binary64_392` `associate-/r*_binary64_367`
5×	`pow1_binary64_484`
4×	`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-/r/_binary64_369` `cbrt-undiv_binary64_457` `div-exp_binary64_474`
1×	`prod-exp_binary64_472` `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` `associate-/l*_binary64_368` `cbrt-unprod_binary64_456`

Counts

4 → 76

Calls

4 calls:

12.0ms	(/.f64 (.f64 4 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)))

series731.0ms (12.6%)

Counts

4 → 12

Calls

4 calls:

409.0ms	(/.f64 (.f64 4 c) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))))
136.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
122.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
63.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify62.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4935	2059
1	4935	2059

prune143.0ms (2.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	88	8	96

Merged error: 6.3b

Counts

96 → 8

Compiler

Compiled 2985 to 1885 computations (36.9% saved)

regimes170.0ms (2.9%)

Compiler: Compiled 420 to 354 computations (15.7% saved)

bsearch83.0ms (1.4%)

Steps

Iters	Range		Point
8	1.926398635008391e+97	1.2558611526501326e+101	7.922796939806533e+99
7	-9.131643782654936e-299	-6.405261263554672e-301	-6.510183985272386e-301
6	-6.201624392123495e+73	-6.987174791110545e+72	-6.063829179971075e+73

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	98	92
1	98	92

end0.0ms (0%)

sample1.4s (24.2%)

Algorithm

1×

intervals

Results

283.0ms	1111×	body	2048	valid
282.0ms	5197×	body	128	valid
145.0ms	725×	body	1024	valid
117.0ms	380×	body	4096	valid
59.0ms	376×	body	512	valid
36.0ms	695×	body	128	nan
21.0ms	211×	body	256	valid
19.0ms	374×	body	128	invalid

Compiler

Compiled 260 to 201 computations (22.7% saved)

Details

analyze462.0ms (8%)

sample37.0ms (0.6%)

simplify228.0ms (3.9%)

prune5.0ms (0.1%)

localize10.0ms (0.2%)

rewrite36.0ms (0.6%)

series461.0ms (8%)

simplify70.0ms (1.2%)

prune493.0ms (8.5%)

localize12.0ms (0.2%)

rewrite42.0ms (0.7%)

series454.0ms (7.8%)

simplify91.0ms (1.6%)

prune142.0ms (2.5%)

localize13.0ms (0.2%)

rewrite31.0ms (0.5%)

series341.0ms (5.9%)

simplify57.0ms (1%)

prune162.0ms (2.8%)

localize12.0ms (0.2%)

rewrite36.0ms (0.6%)

series731.0ms (12.6%)

simplify62.0ms (1.1%)

prune143.0ms (2.5%)

regimes170.0ms (2.9%)

bsearch83.0ms (1.4%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.4s (24.2%)

Profiling