Details

sample105.0ms

Algorithm

intervals

Results

29.0ms	56×	body	1280	valid
22.0ms	329×	body	80	valid
15.0ms	48×	body	640	valid
5.0ms	22×	body	320	valid
4.0ms	59×	body	80	overflowed
1.0ms	8×	body	160	valid

simplify36.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (35.0ms)

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

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: 31.1b

Counts

2 → 2

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
0.0b	(* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x))))
0.0b	(* (+ 1.0 eps) x)
1.5b	(- (* (+ 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/`
31×	`flip3--` `flip3-+` `flip--` `flip-+`
21×	`add-sqr-sqrt`
20×	`un-div-inv`
16×	`*-un-lft-identity`
14×	`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` `unswap-sqr`
2×	`distribute-lft-out` `difference-of-squares`
1×	`sub-neg` `times-frac` `diff-log` `distribute-lft-out--`

Counts

4 → 172

Calls

4 calls:

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

series79.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
12.0ms	(* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x))))
5.0ms	(* (+ 1.0 eps) x)
52.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

simplify154.0ms

Algorithm

egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1253	4061
1	4767	3783
2	5002	3783

prune1.3s

Filtered

184 candidates to 94 candidates (48.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	181	3	184
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	183	3	186

Merged error: 0.9b

Counts

186 → 3

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 0.6666666666666667 (pow x 3))
5.8b	(- (+ (* 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)))

simplify33.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (28.0ms)

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

prune160.0ms

Filtered

51 candidates to 31 candidates (39.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	48	3	51
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	49	5	54

Merged error: 0.9b

Counts

54 → 5

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 0.6666666666666667 (pow x 3))
5.8b	(+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (pow x 2))))

rewrite13.0ms

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` `associate-+r+` `sum-log` `sqr-pow`
1×	`+-commutative` `cube-mult` `pow-to-exp` `associate-+r-` `sub-neg` `flip3-+` `diff-log` `unpow3` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`

Counts

2 → 46

Calls

2 calls:

6.0ms	(* 0.6666666666666667 (pow x 3))
6.0ms	(+ (* 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))))

simplify34.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	203	267
1	840	244
2	5002	243

prune130.0ms

Filtered

52 candidates to 32 candidates (38.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	52	5	57

Merged error: 0.9b

Counts

57 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* 0.6666666666666667 x) x)
0.7b	(cbrt x)
0.7b	(pow (cbrt x) 3)
5.8b	(- (+ (* (* (* 0.6666666666666667 x) x) (pow (cbrt x) 3)) 2.0) (* 1.0 (pow x 2)))

rewrite23.0ms

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)
5.0ms	(pow (cbrt x) 3)
11.0ms	(- (+ (* (* (* 0.6666666666666667 x) x) (pow (cbrt x) 3)) 2.0) (* 1.0 (pow x 2)))

series64.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (* 0.6666666666666667 x) x)
22.0ms	(cbrt x)
32.0ms	(pow (cbrt x) 3)
7.0ms	(- (+ (* (* (* 0.6666666666666667 x) x) (pow (cbrt x) 3)) 2.0) (* 1.0 (pow x 2)))

simplify68.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (61.0ms)

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

prune333.0ms

Filtered

85 candidates to 47 candidates (44.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	83	2	85
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	85	5	90

Merged error: 0.9b

Counts

90 → 5

regimes115.0ms

Accuracy

97.1% (0.5b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 16.3b

bsearch160.0ms

Steps

Iters	Range		Point
9	5.042106407826366e-05	28.700163284045342	0.4483322262182013

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	33
1	57	33
2	57	33

end0.0ms

sample2.7s

Algorithm

intervals

Results

853.0ms	1696×	body	1280	valid
693.0ms	10267×	body	80	valid
416.0ms	1345×	body	640	valid
132.0ms	2000×	body	80	overflowed
128.0ms	620×	body	320	valid
47.0ms	341×	body	160	valid

Details

sample105.0ms

simplify36.0ms

prune15.0ms

localize20.0ms

rewrite57.0ms

series79.0ms

simplify154.0ms

prune1.3s

localize10.0ms

rewrite14.0ms

series9.0ms

simplify33.0ms

prune160.0ms

localize10.0ms

rewrite13.0ms

series9.0ms

simplify34.0ms

prune130.0ms

localize13.0ms

rewrite23.0ms

series64.0ms

simplify68.0ms

prune333.0ms

regimes115.0ms

bsearch160.0ms

simplify2.0ms

end0.0ms

sample2.7s

Profiling