Details

analyze2.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	0%	50%	4

sample40.0ms

Algorithm

intervals

Results

16.0ms	54×	body	1280	valid
9.0ms	50×	body	640	valid
6.0ms	125×	body	80	valid
2.0ms	15×	body	320	valid
1.0ms	12×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	71	7
1	71	7

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: 30.5b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

2.6b	(log.f64 (+.f64 N 1.0))
2.8b	(-.f64 (log.f64 (+.f64 N 1.0)) (log.f64 N))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
11×	`log-prod_binary64`
7×	`pow1_binary64` `add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64` `log-pow_binary64`
4×	`distribute-lft-out--_binary64` `log-div_binary64` `associate--l+_binary64`
3×	`associate--r+_binary64` `add-exp-log_binary64`
2×	`flip3-+_binary64` `add-log-exp_binary64` `associate--l-_binary64` `distribute-lft-out_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `rem-log-exp_binary64` `difference-of-squares_binary64` `flip--_binary64`

Counts

2 → 40

Calls

2 calls:

4.0ms	(log.f64 (+.f64 N 1.0))
7.0ms	(-.f64 (log.f64 (+.f64 N 1.0)) (log.f64 N))

series10.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(log.f64 (+.f64 N 1.0))
6.0ms	(-.f64 (log.f64 (+.f64 N 1.0)) (log.f64 N))

simplify54.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4922	434
1	4922	434

prune57.0ms

Filtered

35 candidates to 46 candidates (-31.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	44	2	46
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	2	47

Merged error: 0.0b

Counts

47 → 2

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (+.f64 N 1.0) N)
2.7b	(log.f64 (/.f64 (+.f64 N 1.0) N))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

33×	`*-un-lft-identity_binary64`
24×	`times-frac_binary64`
19×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
16×	`log-prod_binary64`
7×	`distribute-lft-out_binary64` `add-exp-log_binary64`
4×	`add-cbrt-cube_binary64` `associate-/l*_binary64`
3×	`associate-/r*_binary64` `pow1_binary64`
2×	`associate-/l/_binary64` `add-log-exp_binary64` `rem-log-exp_binary64` `div-inv_binary64` `div-exp_binary64`
1×	`flip3-+_binary64` `cbrt-undiv_binary64` `log-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `log-div_binary64` `flip-+_binary64`

Counts

2 → 60

Calls

2 calls:

6.0ms	(/.f64 (+.f64 N 1.0) N)
5.0ms	(log.f64 (/.f64 (+.f64 N 1.0) N))

series18.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(/.f64 (+.f64 N 1.0) N)
6.0ms	(log.f64 (/.f64 (+.f64 N 1.0) N))

simplify44.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4954	625
1	4954	625

prune48.0ms

Filtered

45 candidates to 66 candidates (-46.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	66	2	68

Merged error: 0.0b

Counts

68 → 2

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 0.3333333333333333 (pow.f64 N 3)) (/.f64 1.0 N))
0.5b	(/.f64 0.5 (*.f64 N N))
0.6b	(/.f64 0.3333333333333333 (pow.f64 N 3))
13.2b	(-.f64 (+.f64 (/.f64 0.3333333333333333 (pow.f64 N 3)) (/.f64 1.0 N)) (/.f64 0.5 (*.f64 N N)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity_binary64` `times-frac_binary64`
35×	`add-sqr-sqrt_binary64`
31×	`add-cube-cbrt_binary64`
14×	`add-exp-log_binary64`
13×	`associate-/r*_binary64`
12×	`unpow-prod-down_binary64` `cube-prod_binary64`
11×	`add-log-exp_binary64` `add-cbrt-cube_binary64`
6×	`associate-/l*_binary64`
5×	`div-exp_binary64`
4×	`pow1_binary64` `sqr-pow_binary64` `unpow3_binary64` `cube-mult_binary64`
3×	`distribute-lft-out_binary64` `cbrt-undiv_binary64` `frac-sub_binary64`
2×	`flip3-+_binary64` `diff-log_binary64` `frac-add_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `flip-+_binary64` `sum-log_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `+-commutative_binary64` `flip--_binary64` `pow-exp_binary64` `associate--l+_binary64`

Counts

4 → 120

Calls

4 calls:

28.0ms	(+.f64 (/.f64 0.3333333333333333 (pow.f64 N 3)) (/.f64 1.0 N))
5.0ms	(/.f64 0.5 (*.f64 N N))
6.0ms	(/.f64 0.3333333333333333 (pow.f64 N 3))
34.0ms	(-.f64 (+.f64 (/.f64 0.3333333333333333 (pow.f64 N 3)) (/.f64 1.0 N)) (/.f64 0.5 (*.f64 N N)))

series32.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+.f64 (/.f64 0.3333333333333333 (pow.f64 N 3)) (/.f64 1.0 N))
4.0ms	(/.f64 0.5 (*.f64 N N))
9.0ms	(/.f64 0.3333333333333333 (pow.f64 N 3))
5.0ms	(-.f64 (+.f64 (/.f64 0.3333333333333333 (pow.f64 N 3)) (/.f64 1.0 N)) (/.f64 0.5 (*.f64 N N)))

simplify62.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4986	1451
1	4986	1451

prune109.0ms

Filtered

81 candidates to 132 candidates (-63.0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	130	2	132
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	130	4	134

Merged error: 0.0b

Counts

134 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(/.f64 0.5 (*.f64 N N))
0.6b	(/.f64 0.3333333333333333 (pow.f64 N 3))
13.2b	(-.f64 (cbrt.f64 (pow.f64 (+.f64 (/.f64 0.3333333333333333 (pow.f64 N 3)) (/.f64 1.0 N)) 3)) (/.f64 0.5 (*.f64 N N)))
27.2b	(cbrt.f64 (pow.f64 (+.f64 (/.f64 0.3333333333333333 (pow.f64 N 3)) (/.f64 1.0 N)) 3))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt_binary64`
48×	`*-un-lft-identity_binary64` `times-frac_binary64`
34×	`add-cube-cbrt_binary64`
24×	`cbrt-prod_binary64`
19×	`unpow-prod-down_binary64` `cube-prod_binary64`
14×	`add-exp-log_binary64`
13×	`associate-/r*_binary64`
11×	`add-cbrt-cube_binary64`
10×	`difference-of-squares_binary64`
7×	`sqr-pow_binary64`
6×	`cbrt-div_binary64` `add-log-exp_binary64` `cube-div_binary64` `associate-/l*_binary64`
5×	`div-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
4×	`pow1_binary64` `distribute-lft-out_binary64`
3×	`cbrt-undiv_binary64` `frac-sub_binary64`
2×	`flip3-+_binary64` `frac-add_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `flip-+_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `rem-cbrt-cube_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `pow1/3_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `pow-exp_binary64`

Counts

4 → 139

Calls

4 calls:

5.0ms	(/.f64 0.5 (*.f64 N N))
6.0ms	(/.f64 0.3333333333333333 (pow.f64 N 3))
39.0ms	(-.f64 (cbrt.f64 (pow.f64 (+.f64 (/.f64 0.3333333333333333 (pow.f64 N 3)) (/.f64 1.0 N)) 3)) (/.f64 0.5 (*.f64 N N)))
30.0ms	(cbrt.f64 (pow.f64 (+.f64 (/.f64 0.3333333333333333 (pow.f64 N 3)) (/.f64 1.0 N)) 3))

series38.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(/.f64 0.5 (*.f64 N N))
6.0ms	(/.f64 0.3333333333333333 (pow.f64 N 3))
8.0ms	(-.f64 (cbrt.f64 (pow.f64 (+.f64 (/.f64 0.3333333333333333 (pow.f64 N 3)) (/.f64 1.0 N)) 3)) (/.f64 0.5 (*.f64 N N)))
20.0ms	(cbrt.f64 (pow.f64 (+.f64 (/.f64 0.3333333333333333 (pow.f64 N 3)) (/.f64 1.0 N)) 3))

simplify53.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5017	1958

prune121.0ms

Filtered

88 candidates to 151 candidates (-71.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	150	1	151
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	151	4	155

Merged error: 0.0b

Counts

155 → 4

regimes33.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 30.0b

bsearch15.0ms

Steps

Iters	Range		Point
9	0.0006503813431540223	60978.321201749655	8131.4453676694275

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	25
1	37	25

end0.0ms

sample1.2s

Algorithm

intervals

Results

512.0ms	1736×	body	1280	valid
247.0ms	1309×	body	640	valid
202.0ms	3981×	body	80	valid
84.0ms	637×	body	320	valid
27.0ms	337×	body	160	valid

Details

analyze2.0ms

sample40.0ms

simplify7.0ms

prune2.0ms

localize6.0ms

rewrite12.0ms

series10.0ms

simplify54.0ms

prune57.0ms

localize4.0ms

rewrite12.0ms

series18.0ms

simplify44.0ms

prune48.0ms

localize9.0ms

rewrite76.0ms

series32.0ms

simplify62.0ms

prune109.0ms

localize12.0ms

rewrite87.0ms

series38.0ms

simplify53.0ms

prune121.0ms

regimes33.0ms

bsearch15.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling