Details

sample130.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 73.520795%

Results

30.0ms	53×	body	1280	valid
26.0ms	343×	body	80	valid
21.0ms	44×	body	640	valid
4.0ms	17×	body	320	valid
4.0ms	50×	body	80	overflowed
0.0ms	3×	body	160	valid

simplify39.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (37.0ms)

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

prune8.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 26.8b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
0.0b	(* (- 1.0 eps) x)
0.0b	(* (+ 1.0 eps) x)
1.0b	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

rewrite173.0ms

Algorithm

rewrite-expression-head

Rules

109×	`*-un-lft-identity`
94×	`times-frac`
91×	`add-sqr-sqrt`
29×	`add-cube-cbrt`
27×	`distribute-lft-out--`
18×	`difference-of-squares`
10×	`add-cbrt-cube`
9×	`add-exp-log` `associate-l`
8×	`pow1`
7×	`distribute-lft-out`
6×	`associate-r` `associate-/l*` `add-log-exp`
4×	`associate-*l/`
3×	`flip3--` `div-sub` `associate-/r*` `flip--` `div-inv`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `distribute-rgt-out--` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `frac-sub` `flip-+` `sub-div` `associate--r-`

Counts

4 → 126

Calls

4 calls:

11.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
6.0ms	(* (- 1.0 eps) x)
6.0ms	(* (+ 1.0 eps) x)
143.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

series83.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
5.0ms	(* (- 1.0 eps) x)
5.0ms	(* (+ 1.0 eps) x)
61.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

simplify68.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	619	1697
1	2085	1604
2	5003	1604

prune342.0ms

Filtered

99 candidates to 138 candidates (-39.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	136	2	138
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	137	2	139

Merged error: 0.3b

Counts

139 → 2

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 0.5 (pow x 2))
0.1b	(* 0.33333333333333337 (pow x 3))
6.0b	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
20×	`associate-r`
13×	`add-exp-log`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp` `unswap-sqr`
7×	`add-cbrt-cube`
6×	`associate-l` `prod-exp`
4×	`cube-prod` `sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `diff-log` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`cube-mult` `sub-neg` `flip3--` `unpow3` `associate--l+` `sum-log` `flip--`

Counts

3 → 72

Calls

3 calls:

5.0ms	(* 0.5 (pow x 2))
6.0ms	(* 0.33333333333333337 (pow x 3))
7.0ms	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

series12.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(* 0.5 (pow x 2))
4.0ms	(* 0.33333333333333337 (pow x 3))
5.0ms	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

simplify48.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	281	367
1	1210	327
2	5001	314

prune116.0ms

Filtered

48 candidates to 81 candidates (-68.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	79	2	81
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	79	4	83

Merged error: 0.3b

Counts

83 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

6.0b	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
10.6b	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
10.6b	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
10.6b	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

7.0ms	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
7.0ms	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
7.0ms	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
7.0ms	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

series37.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
10.0ms	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
10.0ms	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
12.0ms	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

simplify143.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	253	983
1	904	924
2	4252	836
3	5001	836

prune351.0ms

Filtered

59 candidates to 65 candidates (-10.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	63	2	65
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	65	4	69

Merged error: 0.3b

Counts

69 → 4

localize25.0ms

Local error

Found 4 expressions with local error:

10.6b	(cbrt (+ (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
10.6b	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
10.6b	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
11.2b	(- (* (+ (* 0.33333333333333337 (pow x 3)) 1.0) (+ (* 0.33333333333333337 (pow x 3)) 1.0)) (* (* 0.5 (pow x 2)) (* 0.5 (pow x 2))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`flip3--` `pow1/3` `flip--`
2×	`associate--l+`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `diff-log` `flip-+` `difference-of-squares`

Counts

4 → 54

Calls

4 calls:

6.0ms	(cbrt (+ (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
7.0ms	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
7.0ms	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
14.0ms	(- (* (+ (* 0.33333333333333337 (pow x 3)) 1.0) (+ (* 0.33333333333333337 (pow x 3)) 1.0)) (* (* 0.5 (pow x 2)) (* 0.5 (pow x 2))))

series40.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(cbrt (+ (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
10.0ms	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
10.0ms	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
9.0ms	(- (* (+ (* 0.33333333333333337 (pow x 3)) 1.0) (+ (* 0.33333333333333337 (pow x 3)) 1.0)) (* (* 0.5 (pow x 2)) (* 0.5 (pow x 2))))

simplify56.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	374	1120
1	1487	1025
2	5001	946

prune538.0ms

Filtered

63 candidates to 66 candidates (-4.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	67	3	70

Merged error: 0.3b

Counts

70 → 3

regimes113.0ms

Accuracy

97.5% (0.4b remaining)

Error of 1.1b against oracle of 0.7b and baseline of 17.0b

bsearch101.0ms

Steps

Iters	Range		Point
10	3.328979679342993e-06	131215.07867019402	352.38826299575146

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	23
1	40	23

end0.0ms

sample3.1s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 73.520795%

Results

973.0ms	1705×	body	1280	valid
815.0ms	10026×	body	80	valid
471.0ms	1300×	body	640	valid
148.0ms	616×	body	320	valid
140.0ms	1776×	body	80	overflowed
46.0ms	292×	body	160	valid

Details

sample130.0ms

simplify39.0ms

prune8.0ms

localize18.0ms

rewrite173.0ms

series83.0ms

simplify68.0ms

prune342.0ms

localize9.0ms

rewrite21.0ms

series12.0ms

simplify48.0ms

prune116.0ms

localize17.0ms

rewrite29.0ms

series37.0ms

simplify143.0ms

prune351.0ms

localize25.0ms

rewrite35.0ms

series40.0ms

simplify56.0ms

prune538.0ms

regimes113.0ms

bsearch101.0ms

simplify2.0ms

end0.0ms

sample3.1s

Profiling