Details

sample1.2s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 30.853271%

Guaranteed chance to sample good point: 79.08465%

Results

37.0ms	61×	body	1280	valid
13.0ms	38×	body	640	valid
11.0ms	135×	body	80	valid
5.0ms	61×	body	80	overflowed
4.0ms	14×	body	320	valid
3.0ms	39×	body	80	invalid
1.0ms	8×	body	160	valid
1.0ms	1×	body	1280	invalid
0.0ms	1×	body	640	invalid

simplify37.0ms

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

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: 28.7b

Counts

2 → 1

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))))
1.9b	(- (* (+ 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 → 173

Calls

4 calls:

8.0ms	(* (- 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)))))

series80.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(* (- 1.0 eps) x)
15.0ms	(* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x))))
10.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
50.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

simplify149.0ms

Algorithm

egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 2 (114.0ms)

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

prune361.0ms

Filtered

95 candidates to 185 candidates (-94.7%)

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: 0.4b

Counts

186 → 2

localize10.0ms

Local error

Found 2 expressions with local error:

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

series10.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(* 0.6666666666666667 (pow x 3))
6.0ms	(- (+ (* 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

prune79.0ms

Filtered

31 candidates to 51 candidates (-64.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	50	1	51
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	51	2	53

Merged error: 0.4b

Counts

53 → 2

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* 0.6666666666666667 x) x)
0.6b	(cbrt x)
0.7b	(pow (cbrt x) 3)
5.4b	(- (+ (* (* (* 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)))

series65.0ms

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 (62.0ms)

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

prune108.0ms

Filtered

47 candidates to 85 candidates (-80.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	85	2	87

Merged error: 0.4b

Counts

87 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.7b	(pow (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (cbrt x))) 3)
5.4b	(- (+ (* (* (* 0.6666666666666667 x) x) (pow (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (cbrt x))) 3)) 2.0) (* 1.0 (pow x 2)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-log-exp`
7×	`pow1` `add-exp-log` `cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`add-cbrt-cube`
4×	`pow-pow` `pow1/3`
3×	`pow-unpow`
2×	`diff-log` `pow-prod-down` `pow-exp` `rem-cube-cbrt`
1×	`cube-mult` `pow-to-exp` `sub-neg` `unpow-prod-down` `flip3--` `unpow3` `cube-prod` `pow3` `prod-exp` `associate--l+` `sum-log` `flip--` `cbrt-unprod` `sqr-pow`

Counts

4 → 60

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
7.0ms	(pow (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (cbrt x))) 3)
10.0ms	(- (+ (* (* (* 0.6666666666666667 x) x) (pow (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (cbrt x))) 3)) 2.0) (* 1.0 (pow x 2)))

series80.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(cbrt x)
22.0ms	(cbrt x)
30.0ms	(pow (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (cbrt x))) 3)
7.0ms	(- (+ (* (* (* 0.6666666666666667 x) x) (pow (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (cbrt x))) 3)) 2.0) (* 1.0 (pow x 2)))

simplify42.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	266	632
1	1067	528
2	5002	369

prune119.0ms

Filtered

53 candidates to 72 candidates (-35.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	72	2	74

Merged error: 0.4b

Counts

74 → 2

regimes81.0ms

Accuracy

97% (0.5b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 16.7b

bsearch111.0ms

Steps

Iters	Range		Point
10	1.2205598459966065e-18	5.187232899519626	2.236493068216784

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	37
1	63	37
2	63	37

end0.0ms

sample3.6s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 30.853271%

Guaranteed chance to sample good point: 79.08465%

Results

931.0ms	1658×	body	1280	valid
451.0ms	1265×	body	640	valid
343.0ms	4151×	body	80	valid
155.0ms	629×	body	320	valid
148.0ms	1839×	body	80	overflowed
82.0ms	1008×	body	80	invalid
47.0ms	297×	body	160	valid
10.0ms	17×	body	1280	invalid
7.0ms	16×	body	640	invalid
1.0ms	5×	body	320	invalid
1.0ms	4×	body	160	invalid

Details

sample1.2s

simplify37.0ms

prune7.0ms

localize18.0ms

rewrite60.0ms

series80.0ms

simplify149.0ms

prune361.0ms

localize10.0ms

rewrite14.0ms

series10.0ms

simplify33.0ms

prune79.0ms

localize14.0ms

rewrite21.0ms

series65.0ms

simplify68.0ms

prune108.0ms

localize19.0ms

rewrite21.0ms

series80.0ms

simplify42.0ms

prune119.0ms

regimes81.0ms

bsearch111.0ms

simplify2.0ms

end0.0ms

sample3.6s

Profiling