Details

analyze269.0ms (8.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	50%	25%	4
25%	37.5%	37.5%	5
25%	31.2%	43.8%	6
25%	28.1%	46.9%	7
25%	26.5%	48.5%	8
25%	25.8%	49.2%	9
25%	25.4%	49.6%	10
25%	25.2%	49.8%	11
25%	25.1%	49.9%	12
25%	25%	50%	13
25%	25%	50%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample54.0ms (1.7%)

Algorithm

1×

intervals

Results

19.0ms	125×	body	2048	nan
11.0ms	256×	body	128	valid
8.0ms	67×	body	1024	nan
3.0ms	35×	body	512	nan
1.0ms	20×	body	256	nan
1.0ms	20×	body	128	nan

Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify243.0ms (7.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (146.0ms)

Iter	Nodes	Cost
0	4922	14
1	4922	14

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

28.9b

Counts

2 → 1

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
0.0b	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
26.8b	(sqrt.f64 (-.f64 (*.f64 x x) 1))

rewrite21.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64_4170`
7×	`add-sqr-sqrt_binary64_4192`
6×	`sqrt-prod_binary64_4186`
5×	`pow1_binary64_4231` `add-log-exp_binary64_4209` `add-cube-cbrt_binary64_4205`
4×	`add-exp-log_binary64_4208` `log-prod_binary64_4256`
3×	`add-cbrt-cube_binary64_4206`
2×	`sqrt-div_binary64_4187` `flip-+_binary64_4144` `difference-of-squares_binary64_4139` `flip3-+_binary64_4173` `log-div_binary64_4257` `distribute-lft-out_binary64_4121`
1×	`rem-log-exp_binary64_4211` `flip3--_binary64_4174` `log-pow_binary64_4259` `pow1/2_binary64_4250` `+-commutative_binary64_4100` `sqrt-pow1_binary64_4188` `rem-sqrt-square_binary64_4183` `sum-log_binary64_4261` `flip--_binary64_4145` `difference-of-sqr-1_binary64_4140`

Counts

3 → 45

Calls

3 calls:

7.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
7.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
5.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))

series92.0ms (2.9%)

Counts

3 → 9

Calls

3 calls:

43.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
28.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
21.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))

simplify63.0ms (2%)

Algorithm

1×	egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4931	923
1	4931	923

prune48.0ms (1.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	52	2	54
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	52	3	55

Error

Counts

55 → 3

Compiler

Compiled 831 to 552 computations (33.6% saved)

localize11.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))))
0.0b	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))
0.5b	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))

rewrite23.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_4192`
15×	`sqrt-prod_binary64_4186`
13×	`*-un-lft-identity_binary64_4170`
12×	`sqrt-div_binary64_4187`
10×	`associate-r_binary64_4110`
8×	`pow1_binary64_4231` `add-cube-cbrt_binary64_4205`
7×	`associate-l_binary64_4111`
6×	`add-exp-log_binary64_4208`
5×	`flip-+_binary64_4144` `add-cbrt-cube_binary64_4206` `flip3-+_binary64_4173` `add-log-exp_binary64_4209`
4×	`frac-times_binary64_4180` `unswap-sqr_binary64_4138`
3×	`flip3--_binary64_4174` `log-prod_binary64_4256` `pow-prod-down_binary64_4241` `flip--_binary64_4145`
2×	`associate-r/_binary64_4112` `associate-l/_binary64_4113` `difference-of-squares_binary64_4139` `pow1/2_binary64_4250` `sqrt-pow1_binary64_4188` `log-div_binary64_4257`
1×	`rem-log-exp_binary64_4211` `prod-exp_binary64_4219` `cbrt-unprod_binary64_4203` `log-pow_binary64_4259` `sqrt-unprod_binary64_4190` `distribute-lft-out--_binary64_4122` `+-commutative_binary64_4100` `*-commutative_binary64_4101` `sum-log_binary64_4261` `distribute-lft-out_binary64_4121` `difference-of-sqr-1_binary64_4140`

Counts

3 → 68

Calls

3 calls:

13.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))
3.0ms	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))
2.0ms	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))))

series105.0ms (3.3%)

Counts

3 → 9

Calls

3 calls:

43.0ms	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))))
35.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))
27.0ms	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))

simplify80.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4977	1681
1	4977	1681

prune84.0ms (2.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	77	3	80

Error

Counts

80 → 3

Compiler

Compiled 1518 to 1152 computations (24.1% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(log.f64 (+.f64 x (exp.f64 (log.f64 (sqrt.f64 (-.f64 (*.f64 x x) 1))))))
0.0b	(+.f64 x (exp.f64 (log.f64 (sqrt.f64 (-.f64 (*.f64 x x) 1)))))
5.7b	(exp.f64 (log.f64 (sqrt.f64 (-.f64 (*.f64 x x) 1))))
26.8b	(sqrt.f64 (-.f64 (*.f64 x x) 1))

rewrite38.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64_4170`
13×	`log-prod_binary64_4256`
12×	`add-sqr-sqrt_binary64_4192` `sqrt-prod_binary64_4186`
9×	`add-cube-cbrt_binary64_4205` `exp-sum_binary64_4216`
8×	`pow1_binary64_4231`
6×	`exp-prod_binary64_4222` `add-log-exp_binary64_4209`
5×	`add-exp-log_binary64_4208`
4×	`sqrt-div_binary64_4187` `add-cbrt-cube_binary64_4206` `log-pow_binary64_4259` `difference-of-squares_binary64_4139` `log-div_binary64_4257`
2×	`flip3--_binary64_4174` `flip-+_binary64_4144` `pow1/2_binary64_4250` `sqrt-pow1_binary64_4188` `flip3-+_binary64_4173` `flip--_binary64_4145` `distribute-lft-out_binary64_4121` `exp-diff_binary64_4218` `difference-of-sqr-1_binary64_4140`
1×	`rem-log-exp_binary64_4211` `+-commutative_binary64_4100` `rem-sqrt-square_binary64_4183` `sum-log_binary64_4261` `rem-exp-log_binary64_4210`

Counts

4 → 70

Calls

4 calls:

13.0ms	(log.f64 (+.f64 x (exp.f64 (log.f64 (sqrt.f64 (-.f64 (*.f64 x x) 1))))))
9.0ms	(+.f64 x (exp.f64 (log.f64 (sqrt.f64 (-.f64 (*.f64 x x) 1)))))
7.0ms	(exp.f64 (log.f64 (sqrt.f64 (-.f64 (*.f64 x x) 1))))
5.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))

series149.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

54.0ms	(exp.f64 (log.f64 (sqrt.f64 (-.f64 (*.f64 x x) 1))))
44.0ms	(log.f64 (+.f64 x (exp.f64 (log.f64 (sqrt.f64 (-.f64 (*.f64 x x) 1))))))
32.0ms	(+.f64 x (exp.f64 (log.f64 (sqrt.f64 (-.f64 (*.f64 x x) 1)))))
19.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))

simplify69.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4771	1228
1	4771	1228

prune72.0ms (2.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	82	3	85

Error

Counts

85 → 3

Compiler

Compiled 1233 to 829 computations (32.8% saved)

regimes36.0ms (1.1%)

Accuracy

Total 0.0b remaining (2.7%)

Threshold costs 0.0b (2.7%)

Compiler

Compiled 156 to 124 computations (20.5% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	19
1	23	19

end0.0ms (0%)

sample1.7s (53.7%)

Algorithm

1×

intervals

Results

630.0ms	4071×	body	2048	nan
342.0ms	8000×	body	128	valid
249.0ms	2004×	body	1024	nan
85.0ms	944×	body	512	nan
34.0ms	524×	body	256	nan
18.0ms	533×	body	128	nan
2.0ms	9×	body	4096	nan

Compiler

Compiled 62 to 51 computations (17.7% saved)

Details

analyze269.0ms (8.4%)

sample54.0ms (1.7%)

simplify243.0ms (7.6%)

prune2.0ms (0.1%)

localize7.0ms (0.2%)

rewrite21.0ms (0.7%)

series92.0ms (2.9%)

simplify63.0ms (2%)

prune48.0ms (1.5%)

localize11.0ms (0.3%)

rewrite23.0ms (0.7%)

series105.0ms (3.3%)

simplify80.0ms (2.5%)

prune84.0ms (2.6%)

localize10.0ms (0.3%)

rewrite38.0ms (1.2%)

series149.0ms (4.7%)

simplify69.0ms (2.2%)

prune72.0ms (2.2%)

regimes36.0ms (1.1%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.7s (53.7%)

Profiling