Details

analyze467.0ms

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

sample57.0ms

Algorithm

intervals

Results

21.0ms	92×	body	2560	nan
10.0ms	256×	body	80	valid
9.0ms	59×	body	1280	nan
5.0ms	41×	body	640	nan
2.0ms	23×	body	320	nan
1.0ms	9×	body	160	nan
0.0ms	8×	body	80	nan

simplify79.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	5257	9

prune2.0ms

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: 31.6b

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)))
0.2b	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1.0))))
29.4b	(sqrt.f64 (-.f64 (*.f64 x x) 1.0))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 43

Calls

3 calls:

7.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1.0)))
7.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1.0))))
5.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1.0))

series23.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1.0)))
11.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1.0))))
5.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1.0))

simplify51.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5188	615

prune55.0ms

Filtered

43 candidates to 52 candidates (-20.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	50	2	52
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	51	2	53

Merged error: 0b

Counts

53 → 2

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 0.25 (*.f64 x x)) (log.f64 x))
0.1b	(-.f64 (log.f64 2) (+.f64 (/.f64 0.09375 (pow.f64 x 4)) (-.f64 (/.f64 0.25 (*.f64 x x)) (log.f64 x))))
0.2b	(/.f64 0.25 (*.f64 x x))
0.4b	(/.f64 0.09375 (pow.f64 x 4))

rewrite45.0ms

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 0.25 (*.f64 x x)) (log.f64 x))
23.0ms	(-.f64 (log.f64 2) (+.f64 (/.f64 0.09375 (pow.f64 x 4)) (-.f64 (/.f64 0.25 (*.f64 x x)) (log.f64 x))))
5.0ms	(/.f64 0.25 (*.f64 x x))
5.0ms	(/.f64 0.09375 (pow.f64 x 4))

series66.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(-.f64 (/.f64 0.25 (*.f64 x x)) (log.f64 x))
14.0ms	(-.f64 (log.f64 2) (+.f64 (/.f64 0.09375 (pow.f64 x 4)) (-.f64 (/.f64 0.25 (*.f64 x x)) (log.f64 x))))
4.0ms	(/.f64 0.25 (*.f64 x x))
6.0ms	(/.f64 0.09375 (pow.f64 x 4))

simplify63.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4932	1445
1	4932	1445

prune109.0ms

Filtered

80 candidates to 123 candidates (-53.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

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

Merged error: 0b

Counts

125 → 2

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b

(+.f64 x (*.f64 (sqrt.f64 (+.f64 x (sqrt.f64 1.0))) (sqrt.f64 (-.f64 x (sqrt.f64 1.0)))))

0.2b

(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x (sqrt.f64 1.0))) (sqrt.f64 (-.f64 x (sqrt.f64 1.0))))))

0.5b

(*.f64 (sqrt.f64 (+.f64 x (sqrt.f64 1.0))) (sqrt.f64 (-.f64 x (sqrt.f64 1.0))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
15×	`sqrt-prod_binary64`
12×	`*-un-lft-identity_binary64` `sqrt-div_binary64`
9×	`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` `sqrt-unprod_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

3 → 67

Calls

3 calls:

3.0ms

(+.f64 x (*.f64 (sqrt.f64 (+.f64 x (sqrt.f64 1.0))) (sqrt.f64 (-.f64 x (sqrt.f64 1.0)))))

3.0ms

(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x (sqrt.f64 1.0))) (sqrt.f64 (-.f64 x (sqrt.f64 1.0))))))

13.0ms

(*.f64 (sqrt.f64 (+.f64 x (sqrt.f64 1.0))) (sqrt.f64 (-.f64 x (sqrt.f64 1.0))))

series44.0ms

Counts

3 → 9

Calls

3 calls:

13.0ms

(+.f64 x (*.f64 (sqrt.f64 (+.f64 x (sqrt.f64 1.0))) (sqrt.f64 (-.f64 x (sqrt.f64 1.0)))))

16.0ms

(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x (sqrt.f64 1.0))) (sqrt.f64 (-.f64 x (sqrt.f64 1.0))))))

15.0ms

(*.f64 (sqrt.f64 (+.f64 x (sqrt.f64 1.0))) (sqrt.f64 (-.f64 x (sqrt.f64 1.0))))

simplify46.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4963	1255
1	4963	1255

prune80.0ms

Filtered

58 candidates to 76 candidates (-31.0%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	76	2	78

Merged error: 0b

Counts

78 → 2

regimes24.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	181	17
1	181	17

end0.0ms

sample1.8s

Algorithm

intervals

Results

596.0ms	3053×	body	2560	nan
391.0ms	2514×	body	1280	nan
315.0ms	8000×	body	80	valid
154.0ms	1250×	body	640	nan
60.0ms	615×	body	320	nan
21.0ms	324×	body	160	nan
10.0ms	317×	body	80	nan

Details

analyze467.0ms

sample57.0ms

simplify79.0ms

prune2.0ms

localize7.0ms

rewrite19.0ms

series23.0ms

simplify51.0ms

prune55.0ms

localize13.0ms

rewrite45.0ms

series66.0ms

simplify63.0ms

prune109.0ms

localize10.0ms

rewrite22.0ms

series44.0ms

simplify46.0ms

prune80.0ms

regimes24.0ms

bsearch0.0ms

simplify4.0ms

end0.0ms

sample1.8s

Profiling