Details

sample110.0ms

Algorithm

intervals

Results

33.0ms	422×	body	80	valid
22.0ms	40×	body	1280	valid
15.0ms	44×	body	640	valid
11.0ms	141×	body	80	overflowed
4.0ms	19×	body	320	valid
1.0ms	5×	body	160	valid

simplify41.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (39.0ms)

Iter	Nodes	Cost
0	46	16
1	122	16
2	347	16
3	1295	16
4	5001	15

prune7.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 25.5b

Counts

2 → 1

localize17.0ms

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))))
2.4b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

rewrite57.0ms

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 → 173

Calls

4 calls:

6.0ms	(* (- 1.0 eps) x)
12.0ms	(* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x))))
11.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
16.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

series76.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(* (- 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))))
48.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

simplify153.0ms

Algorithm

egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 2 (113.0ms)

Iter	Nodes	Cost
0	1249	4065
1	4707	3787
2	5002	3778

prune351.0ms

Filtered

185 candidates to 95 candidates (48.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	183	2	185
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	184	2	186

Merged error: 0.5b

Counts

186 → 2

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 0.6666666666666667 (pow x 3))
5.6b	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`associate-r`
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-l` `prod-exp`
2×	`pow1` `diff-log` `sqr-pow`
1×	`cube-mult` `pow-to-exp` `sub-neg` `flip3--` `unpow3` `pow-exp` `associate--l+` `sum-log` `*-commutative` `flip--` `cbrt-unprod`

Counts

2 → 45

Calls

2 calls:

6.0ms	(* 0.6666666666666667 (pow x 3))
7.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

series9.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(* 0.6666666666666667 (pow x 3))
5.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

simplify37.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	207	270
1	894	242
2	5002	238

prune85.0ms

Filtered

51 candidates to 31 candidates (39.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	48	3	51
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	49	4	53

Merged error: 0.5b

Counts

53 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* 0.6666666666666667 x) x)
0.6b	(cbrt x)
0.7b	(pow (cbrt x) 3)
5.6b	(- (+ (* (* (* 0.6666666666666667 x) x) (pow (cbrt x) 3)) 2.0) (* 1.0 (pow x 2)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
10×	`pow1` `add-exp-log`
9×	`cbrt-prod` `add-cbrt-cube` `add-log-exp`
6×	`unpow-prod-down` `cube-prod`
3×	`pow-unpow` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`pow-pow` `pow1/3` `diff-log`
1×	`cube-mult` `pow-to-exp` `sub-neg` `flip3--` `unpow3` `associate-l` `pow-exp` `associate--l+` `sum-log` `*-commutative` `flip--` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 73

Calls

4 calls:

5.0ms	(* (* 0.6666666666666667 x) x)
1.0ms	(cbrt x)
3.0ms	(pow (cbrt x) 3)
10.0ms	(- (+ (* (* (* 0.6666666666666667 x) x) (pow (cbrt x) 3)) 2.0) (* 1.0 (pow x 2)))

series66.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (* 0.6666666666666667 x) x)
22.0ms	(cbrt x)
31.0ms	(pow (cbrt x) 3)
10.0ms	(- (+ (* (* (* 0.6666666666666667 x) x) (pow (cbrt x) 3)) 2.0) (* 1.0 (pow x 2)))

simplify69.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	351	412
1	1878	356
2	5001	322

prune118.0ms

Filtered

85 candidates to 47 candidates (44.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	83	2	85
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	84	5	89

Merged error: 0.5b

Counts

89 → 5

localize19.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (cbrt x) 3)
2.6b	(exp (log (* (* 0.6666666666666667 x) x)))
5.6b	(- (+ (* (exp (log (* (* 0.6666666666666667 x) x))) (pow (cbrt x) 3)) 2.0) (* 1.0 (pow x 2)))
34.3b	(log (* (* 0.6666666666666667 x) x))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

17×	`pow1`
11×	`add-exp-log`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`add-log-exp`
6×	`cbrt-prod` `unpow-prod-down` `exp-prod` `cube-prod` `pow-prod-down` `log-pow`
4×	`add-cbrt-cube`
3×	`pow-unpow` `rem-log-exp` `prod-exp`
2×	`log-prod` `pow-pow` `diff-log`
1×	`cube-mult` `pow-to-exp` `sub-neg` `flip3--` `pow1/3` `unpow3` `exp-sum` `pow-exp` `associate--l+` `sum-log` `flip--` `rem-exp-log` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 73

Calls

4 calls:

3.0ms	(pow (cbrt x) 3)
5.0ms	(exp (log (* (* 0.6666666666666667 x) x)))
12.0ms	(- (+ (* (exp (log (* (* 0.6666666666666667 x) x))) (pow (cbrt x) 3)) 2.0) (* 1.0 (pow x 2)))
4.0ms	(log (* (* 0.6666666666666667 x) x))

series55.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(pow (cbrt x) 3)
3.0ms	(exp (log (* (* 0.6666666666666667 x) x)))
7.0ms	(- (+ (* (exp (log (* (* 0.6666666666666667 x) x))) (pow (cbrt x) 3)) 2.0) (* 1.0 (pow x 2)))
12.0ms	(log (* (* 0.6666666666666667 x) x))

simplify49.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	316	466
1	1396	399
2	5001	364

prune116.0ms

Filtered

85 candidates to 46 candidates (45.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	85	5	90

Merged error: 0.5b

Counts

90 → 5

regimes132.0ms

Accuracy

95.3% (0.7b remaining)

Error of 1.3b against oracle of 0.5b and baseline of 16.3b

bsearch101.0ms

Steps

Iters	Range		Point
9	0.0067536449693491665	1385.5180662189646	307.62602048009825

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	62	46
1	70	46
2	70	46

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.1s	13501×	body	80	valid
798.0ms	1357×	body	1280	valid
379.0ms	1041×	body	640	valid
300.0ms	3746×	body	80	overflowed
138.0ms	560×	body	320	valid
42.0ms	262×	body	160	valid

Details

sample110.0ms

simplify41.0ms

prune7.0ms

localize17.0ms

rewrite57.0ms

series76.0ms

simplify153.0ms

prune351.0ms

localize10.0ms

rewrite14.0ms

series9.0ms

simplify37.0ms

prune85.0ms

localize13.0ms

rewrite21.0ms

series66.0ms

simplify69.0ms

prune118.0ms

localize19.0ms

rewrite26.0ms

series55.0ms

simplify49.0ms

prune116.0ms

regimes132.0ms

bsearch101.0ms

simplify2.0ms

end0.0ms

sample3.3s

Profiling