Details

analyze297.0ms

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

sample58.0ms

Algorithm

intervals

Results

18.0ms	102×	body	2560	nan
14.0ms	93×	body	1280	nan
10.0ms	256×	body	80	valid
5.0ms	42×	body	640	nan
2.0ms	17×	body	320	nan
1.0ms	14×	body	160	nan
0.0ms	9×	body	80	nan

simplify237.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (228.0ms)

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: 33.9b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
0.2b	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
31.4b	(sqrt.f64 (-.f64 (*.f64 x x) 1))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`sqrt-prod_binary64`
5×	`add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
4×	`log-prod_binary64` `add-exp-log_binary64`
3×	`add-cbrt-cube_binary64`
2×	`flip3-+_binary64` `distribute-lft-out_binary64` `difference-of-squares_binary64` `log-div_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `flip3--_binary64` `rem-log-exp_binary64` `log-pow_binary64` `difference-of-sqr-1_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

3 → 45

Calls

3 calls:

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

series95.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
50.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
18.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))

simplify73.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4995	923
1	4995	923

prune45.0ms

Filtered

43 candidates to 54 candidates (-25.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	52	2	54
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	2	55

Merged error: 0.0b

Counts

55 → 2

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))
0.2b	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))))
0.4b	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
15×	`sqrt-prod_binary64`
13×	`*-un-lft-identity_binary64`
12×	`sqrt-div_binary64`
10×	`associate-r_binary64`
8×	`pow1_binary64` `add-cube-cbrt_binary64`
7×	`associate-l_binary64`
6×	`add-exp-log_binary64`
5×	`flip3-+_binary64` `add-log-exp_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`
4×	`unswap-sqr_binary64` `frac-times_binary64`
3×	`pow-prod-down_binary64` `flip3--_binary64` `log-prod_binary64` `flip--_binary64`
2×	`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` `sum-log_binary64` `*-commutative_binary64`

Counts

3 → 68

Calls

3 calls:

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

series120.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))
48.0ms	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))))
41.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))

simplify87.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4920	1681
1	4920	1681

prune67.0ms

Filtered

59 candidates to 77 candidates (-30.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	77	2	79

Merged error: 0.0b

Counts

79 → 2

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x))
0.2b	(-.f64 (log.f64 2) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x))))
0.5b	(/.f64 3/32 (pow.f64 x 4))
0.8b	(/.f64 1/4 (*.f64 x x))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

47×	`*-un-lft-identity_binary64`
30×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
24×	`add-cube-cbrt_binary64`
14×	`add-exp-log_binary64` `distribute-lft-out--_binary64`
12×	`unpow-prod-down_binary64`
11×	`pow1_binary64` `add-cbrt-cube_binary64`
10×	`add-log-exp_binary64`
8×	`associate-/r*_binary64`
7×	`log-pow_binary64`
6×	`distribute-lft-out_binary64` `log-prod_binary64` `associate-/l*_binary64`
5×	`diff-log_binary64` `div-exp_binary64`
4×	`associate--r+_binary64` `sqr-pow_binary64`
3×	`cbrt-undiv_binary64` `difference-of-squares_binary64` `associate--l+_binary64`
2×	`sub-neg_binary64` `flip3--_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `flip--_binary64` `sum-log_binary64`
1×	`pow-to-exp_binary64` `associate-+r-_binary64` `cbrt-unprod_binary64` `associate--r-_binary64` `prod-exp_binary64` `pow-exp_binary64`

Counts

4 → 111

Calls

4 calls:

8.0ms	(-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x))
23.0ms	(-.f64 (log.f64 2) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x))))
5.0ms	(/.f64 3/32 (pow.f64 x 4))
5.0ms	(/.f64 1/4 (*.f64 x x))

series196.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x))
49.0ms	(-.f64 (log.f64 2) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x))))
24.0ms	(/.f64 3/32 (pow.f64 x 4))
20.0ms	(/.f64 1/4 (*.f64 x x))

simplify79.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4955	2166
1	4955	2166

prune106.0ms

Filtered

80 candidates to 123 candidates (-53.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	123	2	125

Merged error: 0b

Counts

125 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(/.f64 3/32 (pow.f64 x 4))
0.6b	(cbrt.f64 (pow.f64 (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x)) 3))
0.7b	(pow.f64 (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x)) 3)
0.8b	(/.f64 1/4 (*.f64 x x))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64`
40×	`*-un-lft-identity_binary64`
28×	`add-cube-cbrt_binary64` `times-frac_binary64`
26×	`unpow-prod-down_binary64`
20×	`cbrt-prod_binary64`
15×	`add-exp-log_binary64`
14×	`cube-prod_binary64`
12×	`add-cbrt-cube_binary64`
9×	`pow1_binary64`
8×	`associate-/r*_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
6×	`sqr-pow_binary64` `associate-/l*_binary64`
5×	`div-exp_binary64`
4×	`add-log-exp_binary64` `log-pow_binary64` `cube-div_binary64`
3×	`pow-unpow_binary64` `cbrt-undiv_binary64`
2×	`cbrt-div_binary64` `pow-to-exp_binary64` `flip3--_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `flip--_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`rem-cbrt-cube_binary64` `cbrt-unprod_binary64` `pow1/3_binary64` `pow-pow_binary64` `rem-cube-cbrt_binary64` `prod-exp_binary64`

Counts

4 → 130

Calls

4 calls:

4.0ms	(/.f64 3/32 (pow.f64 x 4))
9.0ms	(cbrt.f64 (pow.f64 (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x)) 3))
11.0ms	(pow.f64 (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x)) 3)
5.0ms	(/.f64 1/4 (*.f64 x x))

series212.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/.f64 3/32 (pow.f64 x 4))
102.0ms	(cbrt.f64 (pow.f64 (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x)) 3))
64.0ms	(pow.f64 (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x)) 3)
21.0ms	(/.f64 1/4 (*.f64 x x))

simplify57.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5032	2436

prune120.0ms

Filtered

82 candidates to 142 candidates (-73.2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	142	2	144

Merged error: 0b

Counts

144 → 2

regimes7.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	19
1	24	19

end0.0ms

sample1.7s

Algorithm

intervals

Results

535.0ms	2883×	body	2560	nan
376.0ms	2471×	body	1280	nan
310.0ms	8000×	body	80	valid
151.0ms	1247×	body	640	nan
53.0ms	573×	body	320	nan
19.0ms	303×	body	160	nan
11.0ms	281×	body	80	nan

Details

analyze297.0ms

sample58.0ms

simplify237.0ms

prune1.0ms

localize7.0ms

rewrite22.0ms

series95.0ms

simplify73.0ms

prune45.0ms

localize9.0ms

rewrite19.0ms

series120.0ms

simplify87.0ms

prune67.0ms

localize15.0ms

rewrite44.0ms

series196.0ms

simplify79.0ms

prune106.0ms

localize17.0ms

rewrite34.0ms

series212.0ms

simplify57.0ms

prune120.0ms

regimes7.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample1.7s

Profiling