Details

sample34.0ms

Algorithm

intervals

Results

14.0ms	90×	body	1280	valid
5.0ms	198×	body	80	valid
4.0ms	36×	body	640	valid
1.0ms	20×	body	320	valid
1.0ms	15×	body	160	valid

simplify61.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	3
1	18	3
2	27	3
3	50	3
4	115	3
5	329	3
6	1642	3
7	5001	3

prune2.0ms

Filtered

1 candidates to 0 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: 26.2b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
4.1b	(- (exp (* a x)) 1.0)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
6×	`add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `exp-prod` `flip3--` `exp-to-pow` `diff-log` `flip--` `rem-exp-log` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 40

Calls

2 calls:

2.0ms	(exp (* a x))
4.0ms	(- (exp (* a x)) 1.0)

series51.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(exp (* a x))
38.0ms	(- (exp (* a x)) 1.0)

simplify82.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (78.0ms)

Iter	Nodes	Cost
0	173	292
1	562	211
2	2710	200
3	5002	164

prune80.0ms

Filtered

46 candidates to 28 candidates (60.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	39	7	46
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	40	7	47

Merged error: 7.9b

Counts

47 → 7

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (exp (* a x)) 1.0))
0.0b	(exp (* a x))
4.1b	(log (exp (- (exp (* a x)) 1.0)))
4.1b	(- (exp (* a x)) 1.0)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt` `*-un-lft-identity`
27×	`prod-diff`
26×	`add-cube-cbrt`
22×	`exp-sum`
14×	`log-prod`
11×	`exp-prod` `add-log-exp`
6×	`log-pow`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`sub-neg` `fma-neg` `rem-exp-log` `distribute-lft-out--` `difference-of-squares`
2×	`exp-diff` `diff-log`
1×	`log-div` `flip3--` `exp-to-pow` `rem-log-exp` `flip--`

Counts

4 → 99

Calls

4 calls:

5.0ms	(exp (- (exp (* a x)) 1.0))
2.0ms	(exp (* a x))
5.0ms	(log (exp (- (exp (* a x)) 1.0)))
5.0ms	(- (exp (* a x)) 1.0)

series124.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(exp (- (exp (* a x)) 1.0))
12.0ms	(exp (* a x))
34.0ms	(log (exp (- (exp (* a x)) 1.0)))
38.0ms	(- (exp (* a x)) 1.0)

simplify101.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 3 (92.0ms)

Iter	Nodes	Cost
0	249	828
1	718	594
2	3198	484
3	5002	483

prune157.0ms

Filtered

111 candidates to 63 candidates (56.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	111	0	111
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	111	7	118

Merged error: 7.9b

Counts

118 → 7

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* a x))
0.1b	(pow (- (exp (* a x)) 1.0) 3)
0.1b	(cbrt (pow (- (exp (* a x)) 1.0) 3))
4.1b	(- (exp (* a x)) 1.0)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt` `*-un-lft-identity`
17×	`add-cube-cbrt`
16×	`cbrt-prod`
10×	`unpow-prod-down` `cube-prod`
9×	`prod-diff`
8×	`add-log-exp`
5×	`pow1` `add-exp-log` `add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
4×	`cube-div` `expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `flip3--` `fma-neg` `flip--`
2×	`cube-mult` `cbrt-div` `unpow3` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `exp-prod` `exp-to-pow` `pow-pow` `pow1/3` `diff-log` `pow-exp` `rem-cbrt-cube` `rem-exp-log` `rem-cube-cbrt`

Counts

4 → 100

Calls

4 calls:

2.0ms	(exp (* a x))
5.0ms	(pow (- (exp (* a x)) 1.0) 3)
5.0ms	(cbrt (pow (- (exp (* a x)) 1.0) 3))
4.0ms	(- (exp (* a x)) 1.0)

series134.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(exp (* a x))
53.0ms	(pow (- (exp (* a x)) 1.0) 3)
34.0ms	(cbrt (pow (- (exp (* a x)) 1.0) 3))
34.0ms	(- (exp (* a x)) 1.0)

simplify47.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	333	721
1	1342	623
2	5001	613

prune182.0ms

Filtered

112 candidates to 60 candidates (53.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	107	5	112
Fresh	2	3	5
Picked	1	0	1
Done	1	0	1
Total	111	8	119

Merged error: 7.9b

Counts

119 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp (* a x)) 3)
0.1b	(pow (- (pow (exp (* a x)) 3) (pow 1.0 3)) 3)
0.1b	(cbrt (/ (pow (- (pow (exp (* a x)) 3) (pow 1.0 3)) 3) (pow (fma 1.0 (+ (exp (* a x)) 1.0) (exp (+ (* a x) (* a x)))) 3)))
4.0b	(- (pow (exp (* a x)) 3) (pow 1.0 3))

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

938×	`add-sqr-sqrt`
895×	`unpow-prod-down` `cube-prod`
676×	`cbrt-prod`
672×	`times-frac`
560×	`*-un-lft-identity`
432×	`difference-of-squares`
311×	`sqr-pow`
290×	`add-cube-cbrt`
144×	`prod-diff`
135×	`distribute-lft-out--`
95×	`cube-mult` `unpow3`
27×	`difference-cubes`
12×	`fma-neg`
7×	`add-log-exp`
6×	`pow1` `pow-unpow` `add-cbrt-cube`
5×	`add-exp-log`
4×	`expm1-log1p-u` `pow-pow` `log1p-expm1-u`
2×	`cube-div` `pow-to-exp` `flip3--` `pow-exp` `flip--` `rem-cube-cbrt`
1×	`sub-neg` `cbrt-div` `exp-prod` `exp-to-pow` `pow1/3` `diff-log` `div-inv`

Counts

4 → 977

Calls

4 calls:

3.0ms	(pow (exp (* a x)) 3)
18.0ms	(pow (- (pow (exp (* a x)) 3) (pow 1.0 3)) 3)
52.0ms	(cbrt (/ (pow (- (pow (exp (* a x)) 3) (pow 1.0 3)) 3) (pow (fma 1.0 (+ (exp (* a x)) 1.0) (exp (+ (* a x) (* a x)))) 3)))
15.0ms	(- (pow (exp (* a x)) 3) (pow 1.0 3))

series269.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(pow (exp (* a x)) 3)
74.0ms	(pow (- (pow (exp (* a x)) 3) (pow 1.0 3)) 3)
110.0ms	(cbrt (/ (pow (- (pow (exp (* a x)) 3) (pow 1.0 3)) 3) (pow (fma 1.0 (+ (exp (* a x)) 1.0) (exp (+ (* a x) (* a x)))) 3)))
60.0ms	(- (pow (exp (* a x)) 3) (pow 1.0 3))

simplify295.0ms

Algorithm

egg-herbie

Counts

989 → 989

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	1601	27944
1	5001	26767

prune964.0ms

Filtered

989 candidates to 191 candidates (19.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	983	6	989
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	987	10	997

Merged error: 7.9b

Counts

997 → 10

regimes367.0ms

Accuracy

94.1% (1.3b remaining)

Error of 9.3b against oracle of 8.0b and baseline of 29.8b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	27
1	37	27

end0.0ms

sample1.1s

Algorithm

intervals

Results

504.0ms	2723×	body	1280	valid
160.0ms	1305×	body	640	valid
141.0ms	5601×	body	80	valid
65.0ms	751×	body	320	valid
24.0ms	397×	body	160	valid