Details

analyze232.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	87.4%	12.6%	6
20.3%	59.3%	20.4%	7
21.1%	51.5%	27.4%	8
35.5%	30.4%	34%	9
35.7%	26.1%	38.1%	10
42.8%	15.4%	41.8%	11
42.9%	13.2%	44%	12
46.4%	7.8%	45.8%	13
46.4%	6.6%	47%	14

sample72.0ms

Algorithm

intervals

Results

31.0ms	58×	body	1280	valid
13.0ms	39×	body	640	valid
10.0ms	131×	body	80	valid
5.0ms	20×	body	320	valid
1.0ms	8×	body	160	valid
1.0ms	8×	body	80	overflowed
1.0ms	6×	body	80	invalid

simplify45.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5720	27

prune15.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 29.2b

Counts

2 → 2

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- 1.0 eps) x)
0.0b	(* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x))))
0.0b	(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
1.7b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
80×	`exp-neg` `frac-times`
60×	`neg-sub0` `exp-diff`
42×	`associate-*l/`
40×	`associate-*r/`
32×	`flip3--` `flip--`
30×	`flip3-+` `flip-+`
23×	`add-sqr-sqrt`
20×	`un-div-inv`
16×	`*-un-lft-identity`
15×	`associate-l`
10×	`pow1` `add-cube-cbrt` `add-cbrt-cube`
9×	`associate-r`
8×	`add-exp-log`
6×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `difference-of-squares` `unswap-sqr`
2×	`distribute-lft-out--`
1×	`sub-neg` `times-frac` `diff-log` `distribute-lft-out`

Counts

4 → 172

Calls

4 calls:

6.0ms	(* (- 1.0 eps) x)
13.0ms	(* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x))))
12.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
17.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

series71.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (- 1.0 eps) x)
12.0ms	(* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x))))
10.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
45.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

simplify85.0ms

Algorithm

egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4974	6934
1	4974	6934

prune366.0ms

Filtered

99 candidates to 184 candidates (-85.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	182	2	184
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	184	2	186

Merged error: 1.0b

Counts

186 → 2

localize9.0ms

Local error

Found 2 expressions with local error:

0.1b	(* (pow x 3) 0.6666666666666667)
5.4b	(+ (* (pow x 3) 0.6666666666666667) (- 2.0 (* 1.0 (* x x))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`associate-l`
7×	`add-exp-log` `add-log-exp`
6×	`add-cube-cbrt` `*-un-lft-identity`
4×	`unpow-prod-down` `cube-prod` `add-cbrt-cube` `unswap-sqr`
3×	`associate-r` `prod-exp`
2×	`pow1` `sum-log` `sqr-pow`
1×	`+-commutative` `cube-mult` `pow-to-exp` `associate-+r-` `sub-neg` `associate-+r+` `flip3-+` `diff-log` `unpow3` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`

Counts

2 → 45

Calls

2 calls:

5.0ms	(* (pow x 3) 0.6666666666666667)
7.0ms	(+ (* (pow x 3) 0.6666666666666667) (- 2.0 (* 1.0 (* x x))))

series8.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(* (pow x 3) 0.6666666666666667)
4.0ms	(+ (* (pow x 3) 0.6666666666666667) (- 2.0 (* 1.0 (* x x))))

simplify56.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4959	458
1	4959	458

prune87.0ms

Filtered

33 candidates to 51 candidates (-54.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	46	5	51
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	47	6	53

Merged error: 1.0b

Counts

53 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

5.4b	(+ (* (* (cbrt (* (pow x 3) 0.6666666666666667)) (cbrt (* (pow x 3) 0.6666666666666667))) (cbrt (* (pow x 3) 0.6666666666666667))) (- 2.0 (* 1.0 (* x x))))
37.9b	(cbrt (* (pow x 3) 0.6666666666666667))
37.9b	(cbrt (* (pow x 3) 0.6666666666666667))
37.9b	(cbrt (* (pow x 3) 0.6666666666666667))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`cbrt-prod` `pow1/3`
2×	`sum-log`
1×	`+-commutative` `associate-+r-` `sub-neg` `associate-+r+` `flip3-+` `diff-log` `flip-+`

Counts

4 → 41

Calls

4 calls:

11.0ms	(+ (* (* (cbrt (* (pow x 3) 0.6666666666666667)) (cbrt (* (pow x 3) 0.6666666666666667))) (cbrt (* (pow x 3) 0.6666666666666667))) (- 2.0 (* 1.0 (* x x))))
5.0ms	(cbrt (* (pow x 3) 0.6666666666666667))
3.0ms	(cbrt (* (pow x 3) 0.6666666666666667))
3.0ms	(cbrt (* (pow x 3) 0.6666666666666667))

series23.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+ (* (* (cbrt (* (pow x 3) 0.6666666666666667)) (cbrt (* (pow x 3) 0.6666666666666667))) (cbrt (* (pow x 3) 0.6666666666666667))) (- 2.0 (* 1.0 (* x x))))
4.0ms	(cbrt (* (pow x 3) 0.6666666666666667))
4.0ms	(cbrt (* (pow x 3) 0.6666666666666667))
5.0ms	(cbrt (* (pow x 3) 0.6666666666666667))

simplify25.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5128	460

prune123.0ms

Filtered

37 candidates to 53 candidates (-43.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	52	1	53
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	53	6	59

Merged error: 1.0b

Counts

59 → 6

localize20.0ms

Local error

Found 4 expressions with local error:

37.9b	(cbrt (* (pow x 3) 0.6666666666666667))
37.9b	(cbrt (* (pow x 3) 0.6666666666666667))
37.9b	(cbrt (* (pow x 3) 0.6666666666666667))
37.9b	(cbrt (* (pow x 3) 0.6666666666666667))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `pow1/3` `add-cbrt-cube` `add-log-exp`

Counts

4 → 36

Calls

4 calls:

3.0ms	(cbrt (* (pow x 3) 0.6666666666666667))
4.0ms	(cbrt (* (pow x 3) 0.6666666666666667))
4.0ms	(cbrt (* (pow x 3) 0.6666666666666667))
4.0ms	(cbrt (* (pow x 3) 0.6666666666666667))

series18.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(cbrt (* (pow x 3) 0.6666666666666667))
4.0ms	(cbrt (* (pow x 3) 0.6666666666666667))
4.0ms	(cbrt (* (pow x 3) 0.6666666666666667))
5.0ms	(cbrt (* (pow x 3) 0.6666666666666667))

simplify130.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (126.0ms)

Iter	Nodes	Cost
0	4798	284
1	4798	284

prune178.0ms

Filtered

36 candidates to 48 candidates (-33.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	46	2	48
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	47	7	54

Merged error: 1.0b

Counts

54 → 7

regimes148.0ms

Accuracy

96.4% (0.6b remaining)

Error of 0.9b against oracle of 0.3b and baseline of 16.4b

bsearch71.0ms

Steps

Iters	Range		Point
9	83.90666007278759	61492517.93015762	130.10061969126141

simplify10.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	485	77
1	485	77

end0.0ms

sample2.1s

Algorithm

intervals

Results

929.0ms	1701×	body	1280	valid
425.0ms	1252×	body	640	valid
324.0ms	4093×	body	80	valid
156.0ms	644×	body	320	valid
47.0ms	310×	body	160	valid
17.0ms	208×	body	80	invalid
14.0ms	178×	body	80	overflowed
7.0ms	13×	body	1280	invalid
7.0ms	17×	body	640	invalid
1.0ms	3×	body	320	invalid
0.0ms	2×	body	160	invalid

Details

analyze232.0ms

sample72.0ms

simplify45.0ms

prune15.0ms

localize18.0ms

rewrite60.0ms

series71.0ms

simplify85.0ms

prune366.0ms

localize9.0ms

rewrite13.0ms

series8.0ms

simplify56.0ms

prune87.0ms

localize14.0ms

rewrite24.0ms

series23.0ms

simplify25.0ms

prune123.0ms

localize20.0ms

rewrite15.0ms

series18.0ms

simplify130.0ms

prune178.0ms

regimes148.0ms

bsearch71.0ms

simplify10.0ms

end0.0ms

sample2.1s

Profiling