Details

sample1.1s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 43.353271%

Guaranteed chance to sample good point: 74.469346%

Results

34.0ms	62×	body	1280	valid
14.0ms	42×	body	640	valid
10.0ms	123×	body	80	valid
5.0ms	62×	body	80	overflowed
4.0ms	17×	body	320	valid
2.0ms	12×	body	160	valid
1.0ms	1×	body	1280	invalid
0.0ms	1×	body	320	invalid
0.0ms	1×	body	80	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

prune10.0ms

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: 31.1b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* (- 1.0 eps) x))
0.0b	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
0.0b	(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
2.1b	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

118×	`*-un-lft-identity`
106×	`times-frac`
90×	`add-sqr-sqrt`
34×	`add-cube-cbrt`
26×	`distribute-lft-out--`
17×	`difference-of-squares`
10×	`distribute-lft-out` `associate-/l*` `add-log-exp`
8×	`add-cbrt-cube`
6×	`add-exp-log` `associate-/r*`
4×	`pow1` `div-inv` `associate-/l/`
3×	`div-sub`
2×	`cbrt-undiv` `flip3--` `exp-to-pow` `frac-2neg` `diff-log` `div-exp` `clear-num` `flip--`
1×	`sub-neg` `exp-prod` `distribute-rgt-out--` `flip3-+` `frac-sub` `flip-+` `rem-exp-log` `sub-div` `associate--r-`

Counts

4 → 127

Calls

4 calls:

3.0ms	(exp (* (- 1.0 eps) x))
11.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
11.0ms	(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
144.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

series82.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(exp (* (- 1.0 eps) x))
11.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
11.0ms	(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
54.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

simplify57.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	617	1951
1	1860	1845
2	5001	1835

prune341.0ms

Filtered

101 candidates to 139 candidates (-37.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	136	3	139
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	137	3	140

Merged error: 0.2b

Counts

140 → 3

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 0.5 (pow x 2))
0.1b	(* 0.33333333333333337 (pow x 3))
7.0b	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

rewrite20.0ms

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)))

series11.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify44.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (38.0ms)

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

prune106.0ms

Filtered

48 candidates to 81 candidates (-68.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	80	1	81
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	81	3	84

Merged error: 0.2b

Counts

84 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 0.5 (pow x 2))
0.1b	(* 0.33333333333333337 (pow x 3))
2.0b	(log (exp (* 0.5 (pow x 2))))
12.8b	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (log (exp (* 0.5 (pow x 2)))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
20×	`associate-r`
16×	`*-un-lft-identity`
14×	`add-exp-log`
13×	`add-cube-cbrt`
8×	`unpow-prod-down` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
6×	`pow1` `log-prod` `associate-l` `prod-exp`
4×	`cube-prod` `log-pow` `sqr-pow`
3×	`associate--r+`
2×	`pow-to-exp` `diff-log` `pow-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out--` `unpow2`
1×	`cube-mult` `sub-neg` `exp-prod` `flip3--` `exp-to-pow` `unpow3` `rem-log-exp` `associate--l+` `sum-log` `flip--` `difference-of-squares`

Counts

4 → 92

Calls

4 calls:

7.0ms	(* 0.5 (pow x 2))
6.0ms	(* 0.33333333333333337 (pow x 3))
2.0ms	(log (exp (* 0.5 (pow x 2))))
9.0ms	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (log (exp (* 0.5 (pow x 2)))))

series14.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify46.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	318	516
1	1271	447
2	5002	433

prune166.0ms

Filtered

64 candidates to 104 candidates (-62.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	104	3	107

Merged error: 0.2b

Counts

107 → 3

localize17.0ms

Local error

Found 4 expressions with local error:

2.0b	(log (exp (* 0.5 (pow x 2))))
12.8b	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (log (exp (* 0.5 (pow x 2)))))
12.8b	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (log (exp (* 0.5 (pow x 2)))))
12.8b	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (log (exp (* 0.5 (pow x 2)))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
14×	`add-sqr-sqrt` `add-log-exp`
12×	`log-prod`
9×	`associate--r+`
8×	`pow1` `add-cube-cbrt`
6×	`diff-log` `log-pow` `distribute-lft-out--`
4×	`add-exp-log` `add-cbrt-cube`
3×	`sub-neg` `flip3--` `associate--l+` `sum-log` `flip--` `difference-of-squares`
1×	`exp-prod` `exp-to-pow` `rem-log-exp`

Counts

4 → 74

Calls

4 calls:

2.0ms	(log (exp (* 0.5 (pow x 2))))
9.0ms	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (log (exp (* 0.5 (pow x 2)))))
9.0ms	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (log (exp (* 0.5 (pow x 2)))))
9.0ms	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (log (exp (* 0.5 (pow x 2)))))

series16.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify84.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 3 (73.0ms)

Iter	Nodes	Cost
0	135	792
1	440	700
2	2188	670
3	5002	661

prune366.0ms

Filtered

60 candidates to 86 candidates (-43.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	86	3	89

Merged error: 0.2b

Counts

89 → 3

regimes133.0ms

Accuracy

98.1% (0.4b remaining)

Error of 0.8b against oracle of 0.4b and baseline of 19.2b

bsearch94.0ms

Steps

Iters	Range		Point
8	0.00028346090052719397	4.273587695826267	1.302816513994034

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	62
1	55	62

end0.0ms

sample3.6s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 43.353271%

Guaranteed chance to sample good point: 74.469346%

Results

1.1s	2028×	body	1280	valid
481.0ms	1431×	body	640	valid
272.0ms	3530×	body	80	valid
168.0ms	2148×	body	80	overflowed
150.0ms	646×	body	320	valid
56.0ms	365×	body	160	valid
8.0ms	15×	body	1280	invalid
5.0ms	55×	body	80	invalid
3.0ms	9×	body	640	invalid
2.0ms	6×	body	320	invalid
1.0ms	3×	body	160	invalid

Details

sample1.1s

simplify37.0ms

prune10.0ms

localize17.0ms

rewrite175.0ms

series82.0ms

simplify57.0ms

prune341.0ms

localize9.0ms

rewrite20.0ms

series11.0ms

simplify44.0ms

prune106.0ms

localize11.0ms

rewrite26.0ms

series14.0ms

simplify46.0ms

prune166.0ms

localize17.0ms

rewrite32.0ms

series16.0ms

simplify84.0ms

prune366.0ms

regimes133.0ms

bsearch94.0ms

simplify2.0ms

end0.0ms

sample3.6s

Profiling