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	47×	body	640	valid
6.0ms	118×	body	80	valid
3.0ms	23×	body	320	valid
1.0ms	14×	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: 32.4b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

3.5b	(-.f64 (log.f64 (+.f64 N 1.0)) (log.f64 N))
4.2b	(log.f64 (+.f64 N 1.0))

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:

7.0ms	(-.f64 (log.f64 (+.f64 N 1.0)) (log.f64 N))
3.0ms	(log.f64 (+.f64 N 1.0))

series10.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify55.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4923	440
1	4923	440

prune61.0ms

Filtered

34 candidates to 46 candidates (-35.3%)

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

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 1.0 N) (/.f64 0.3333333333333333 (pow.f64 N 3)))
0.1b	(/.f64 0.3333333333333333 (pow.f64 N 3))
0.4b	(/.f64 0.5 (*.f64 N N))
10.8b	(-.f64 (+.f64 (/.f64 1.0 N) (/.f64 0.3333333333333333 (pow.f64 N 3))) (/.f64 0.5 (*.f64 N N)))

rewrite69.0ms

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:

26.0ms	(+.f64 (/.f64 1.0 N) (/.f64 0.3333333333333333 (pow.f64 N 3)))
5.0ms	(/.f64 0.3333333333333333 (pow.f64 N 3))
5.0ms	(/.f64 0.5 (*.f64 N N))
30.0ms	(-.f64 (+.f64 (/.f64 1.0 N) (/.f64 0.3333333333333333 (pow.f64 N 3))) (/.f64 0.5 (*.f64 N N)))

series24.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(+.f64 (/.f64 1.0 N) (/.f64 0.3333333333333333 (pow.f64 N 3)))
5.0ms	(/.f64 0.3333333333333333 (pow.f64 N 3))
4.0ms	(/.f64 0.5 (*.f64 N N))
5.0ms	(-.f64 (+.f64 (/.f64 1.0 N) (/.f64 0.3333333333333333 (pow.f64 N 3))) (/.f64 0.5 (*.f64 N N)))

simplify45.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5000	1465

prune106.0ms

Filtered

80 candidates to 132 candidates (-65.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	131	1	132
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	131	3	134

Merged error: 0.0b

Counts

134 → 3

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (+.f64 N 1.0) N)
3.7b	(log.f64 (/.f64 (+.f64 N 1.0) N))

rewrite156.0ms

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))

series12.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify43.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4954	625
1	4954	625

prune55.0ms

Filtered

45 candidates to 66 candidates (-46.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	65	4	69

Merged error: 0.0b

Counts

69 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (log.f64 (/.f64 (+.f64 N 1.0) N)))
3.7b	(log.f64 (/.f64 (+.f64 N 1.0) N))
3.7b	(log.f64 (/.f64 (+.f64 N 1.0) N))
3.7b	(log.f64 (/.f64 (+.f64 N 1.0) N))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

48×	`log-prod_binary64`
47×	`*-un-lft-identity_binary64`
36×	`times-frac_binary64`
29×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
13×	`add-exp-log_binary64`
9×	`distribute-lft-out_binary64`
8×	`pow1_binary64`
6×	`rem-log-exp_binary64`
4×	`add-log-exp_binary64` `log-pow_binary64` `add-cbrt-cube_binary64` `cbrt-prod_binary64`
3×	`div-inv_binary64` `div-exp_binary64` `log-div_binary64`
1×	`pow1/3_binary64`

Counts

4 → 93

Calls

4 calls:

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

series32.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(cbrt.f64 (log.f64 (/.f64 (+.f64 N 1.0) N)))
6.0ms	(log.f64 (/.f64 (+.f64 N 1.0) N))
5.0ms	(log.f64 (/.f64 (+.f64 N 1.0) N))
6.0ms	(log.f64 (/.f64 (+.f64 N 1.0) N))

simplify68.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4950	1201
1	4950	1201

prune121.0ms

Filtered

76 candidates to 105 candidates (-38.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	104	1	105
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	105	4	109

Merged error: 0b

Counts

109 → 4

regimes36.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 31.6b

bsearch11.0ms

Steps

Iters	Range		Point
8	46.411787995442566	414138.19612384395	7834.05326038219

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

531.0ms	1739×	body	1280	valid
256.0ms	1272×	body	640	valid
218.0ms	4081×	body	80	valid
79.0ms	602×	body	320	valid
27.0ms	306×	body	160	valid

Details

analyze2.0ms

sample40.0ms

simplify7.0ms

prune2.0ms

localize6.0ms

rewrite12.0ms

series10.0ms

simplify55.0ms

prune61.0ms

localize9.0ms

rewrite69.0ms

series24.0ms

simplify45.0ms

prune106.0ms

localize4.0ms

rewrite156.0ms

series12.0ms

simplify43.0ms

prune55.0ms

localize8.0ms

rewrite19.0ms

series32.0ms

simplify68.0ms

prune121.0ms

regimes36.0ms

bsearch11.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling