Details

analyze281.0ms

Algorithm

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

sample61.0ms

Algorithm

intervals

Results

20.0ms	100×	body	2560	nan
13.0ms	82×	body	1280	nan
10.0ms	256×	body	80	valid
6.0ms	47×	body	640	nan
2.0ms	22×	body	320	nan
0.0ms	5×	body	160	nan
0.0ms	8×	body	80	nan

simplify225.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (216.0ms)

Iter	Nodes	Cost
0	5002	14

prune1.0ms

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

Merged error: 32.9b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
30.7b	(sqrt.f64 (-.f64 (*.f64 x x) 1))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64` `sqrt-prod_binary64`
4×	`pow1_binary64` `log-prod_binary64` `add-cube-cbrt_binary64`
3×	`add-exp-log_binary64`
2×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `log-div_binary64` `sqrt-div_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `flip3--_binary64` `distribute-lft-out_binary64` `rem-log-exp_binary64` `log-pow_binary64` `difference-of-sqr-1_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip--_binary64` `flip-+_binary64`

Counts

2 → 33

Calls

2 calls:

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

series80.0ms

Counts

2 → 6

Calls

2 calls:

62.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
18.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))

simplify132.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 0 (110.0ms)

Iter	Nodes	Cost
0	4881	666
1	4881	666

prune32.0ms

Filtered

30 candidates to 39 candidates (-30.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	37	2	39
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	38	2	40

Merged error: 0b

Counts

40 → 2

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(log.f64 (+.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)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
15×	`sqrt-prod_binary64`
12×	`*-un-lft-identity_binary64` `sqrt-div_binary64`
10×	`associate-r_binary64`
7×	`pow1_binary64` `add-cube-cbrt_binary64` `associate-l_binary64`
5×	`add-exp-log_binary64`
4×	`flip3-+_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64` `flip-+_binary64` `frac-times_binary64`
3×	`pow-prod-down_binary64` `flip3--_binary64` `log-prod_binary64` `flip--_binary64`
2×	`add-log-exp_binary64` `pow1/2_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `difference-of-squares_binary64` `log-div_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `distribute-lft-out_binary64` `rem-log-exp_binary64` `log-pow_binary64` `difference-of-sqr-1_binary64` `sqrt-unprod_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `*-commutative_binary64`

Counts

2 → 57

Calls

2 calls:

3.0ms	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))))
12.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))

series96.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))))
54.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))

simplify78.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5090	1377

prune52.0ms

Filtered

46 candidates to 63 candidates (-37.0%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	63	0	63
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	63	2	65

Merged error: 0b

Counts

65 → 2

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (cbrt.f64 (-.f64 (*.f64 x x) 1)))
0.3b	(.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 x x) 1))) (sqrt.f64 (cbrt.f64 (-.f64 (*.f64 x x) 1))))
31.6b	(cbrt.f64 (-.f64 (*.f64 x x) 1))
31.6b	(cbrt.f64 (-.f64 (*.f64 x x) 1))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

26×	`cbrt-prod_binary64`
24×	`add-sqr-sqrt_binary64`
20×	`sqrt-prod_binary64`
16×	`*-un-lft-identity_binary64`
12×	`associate-r_binary64` `add-cube-cbrt_binary64`
8×	`cbrt-div_binary64` `difference-of-squares_binary64`
7×	`pow1_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `flip3--_binary64` `difference-of-sqr-1_binary64` `flip--_binary64` `sqrt-div_binary64`
3×	`pow1/3_binary64` `associate-l_binary64` `unswap-sqr_binary64`
2×	`associate-*r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 86

Calls

4 calls:

9.0ms	(sqrt.f64 (cbrt.f64 (-.f64 (*.f64 x x) 1)))
17.0ms	(.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 x x) 1))) (sqrt.f64 (cbrt.f64 (-.f64 (*.f64 x x) 1))))
8.0ms	(cbrt.f64 (-.f64 (*.f64 x x) 1))
8.0ms	(cbrt.f64 (-.f64 (*.f64 x x) 1))

series257.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(sqrt.f64 (cbrt.f64 (-.f64 (*.f64 x x) 1)))
104.0ms	(.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 x x) 1))) (sqrt.f64 (cbrt.f64 (-.f64 (*.f64 x x) 1))))
53.0ms	(cbrt.f64 (-.f64 (*.f64 x x) 1))
54.0ms	(cbrt.f64 (-.f64 (*.f64 x x) 1))

simplify127.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (100.0ms)

Iter	Nodes	Cost
0	4906	2048
1	4906	2048

prune102.0ms

Filtered

79 candidates to 98 candidates (-24.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	98	2	100

Merged error: 0b

Counts

100 → 2

regimes9.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 0.1b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	19
1	24	19

end0.0ms

sample1.8s

Algorithm

intervals

Results

603.0ms	2989×	body	2560	nan
419.0ms	2458×	body	1280	nan
328.0ms	8000×	body	80	valid
167.0ms	1240×	body	640	nan
62.0ms	621×	body	320	nan
21.0ms	305×	body	160	nan
10.0ms	300×	body	80	nan

Details

analyze281.0ms

sample61.0ms

simplify225.0ms

prune1.0ms

localize9.0ms

rewrite12.0ms

series80.0ms

simplify132.0ms

prune32.0ms

localize9.0ms

rewrite17.0ms

series96.0ms

simplify78.0ms

prune52.0ms

localize11.0ms

rewrite46.0ms

series257.0ms

simplify127.0ms

prune102.0ms

regimes9.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample1.8s

Profiling