Details

sample34.0ms

Algorithm

intervals

Results

14.0ms	96×	body	1280	valid
6.0ms	174×	body	80	valid
3.0ms	35×	body	640	valid
1.0ms	18×	body	320	valid
1.0ms	15×	body	160	valid

simplify59.0ms

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

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.1b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
3.6b	(- (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:

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

series45.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(exp (* a x))
33.0ms	(- (exp (* a x)) 1.0)

simplify80.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (77.0ms)

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

prune89.0ms

Filtered

46 candidates to 28 candidates (60.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.4b

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (- (exp (* a x)) 1.0))
3.6b	(- (exp (* a x)) 1.0)
3.6b	(- (exp (* a x)) 1.0)
3.6b	(- (exp (* a x)) 1.0)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt` `*-un-lft-identity`
27×	`prod-diff`
26×	`add-cube-cbrt`
10×	`add-log-exp`
9×	`fma-neg`
5×	`cbrt-prod`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `diff-log`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 101

Calls

4 calls:

3.0ms	(cbrt (- (exp (* a x)) 1.0))
5.0ms	(- (exp (* a x)) 1.0)
5.0ms	(- (exp (* a x)) 1.0)
5.0ms	(- (exp (* a x)) 1.0)

series191.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(cbrt (- (exp (* a x)) 1.0))
35.0ms	(- (exp (* a x)) 1.0)
32.0ms	(- (exp (* a x)) 1.0)
33.0ms	(- (exp (* a x)) 1.0)

simplify105.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 3 (97.0ms)

Iter	Nodes	Cost
0	227	927
1	730	660
2	3541	616
3	5001	569

prune271.0ms

Filtered

113 candidates to 73 candidates (64.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.4b

localize12.0ms

Local error

Found 4 expressions with local error:

3.6b	(- (exp (* a x)) 1.0)
3.6b	(- (exp (* a x)) 1.0)
3.6b	(- (exp (* a x)) 1.0)
3.7b	(log (exp (- (exp (* a x)) 1.0)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt` `*-un-lft-identity`
36×	`prod-diff`
33×	`add-cube-cbrt`
14×	`log-prod`
11×	`exp-sum`
10×	`add-log-exp`
9×	`fma-neg`
6×	`log-pow`
5×	`pow1` `exp-prod`
4×	`add-exp-log` `expm1-log1p-u` `sub-neg` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`flip3--` `diff-log` `flip--`
1×	`log-div` `exp-diff` `rem-log-exp`

Counts

4 → 115

Calls

4 calls:

5.0ms	(- (exp (* a x)) 1.0)
5.0ms	(- (exp (* a x)) 1.0)
5.0ms	(- (exp (* a x)) 1.0)
12.0ms	(log (exp (- (exp (* a x)) 1.0)))

series137.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (exp (* a x)) 1.0)
36.0ms	(- (exp (* a x)) 1.0)
32.0ms	(- (exp (* a x)) 1.0)
36.0ms	(log (exp (- (exp (* a x)) 1.0)))

simplify94.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 3 (84.0ms)

Iter	Nodes	Cost
0	225	1029
1	633	701
2	2823	551
3	5001	515

prune320.0ms

Filtered

127 candidates to 73 candidates (57.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.4b

localize16.0ms

Local error

Found 4 expressions with local error:

3.6b	(- (exp (* a x)) 1.0)
3.6b	(- (exp (* a x)) 1.0)
3.7b	(log (sqrt (exp (- (exp (* a x)) 1.0))))
3.7b	(log (sqrt (exp (- (exp (* a x)) 1.0))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt` `*-un-lft-identity`
36×	`add-cube-cbrt` `prod-diff`
34×	`log-prod`
28×	`sqrt-prod`
22×	`exp-sum`
16×	`log-pow`
12×	`sqrt-pow1`
10×	`exp-prod`
8×	`pow1` `add-log-exp`
6×	`add-exp-log` `fma-neg`
4×	`expm1-log1p-u` `sub-neg` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
2×	`log-div` `flip3--` `pow1/2` `exp-diff` `sqrt-div` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 128

Calls

4 calls:

5.0ms	(- (exp (* a x)) 1.0)
5.0ms	(- (exp (* a x)) 1.0)
13.0ms	(log (sqrt (exp (- (exp (* a x)) 1.0))))
14.0ms	(log (sqrt (exp (- (exp (* a x)) 1.0))))

series261.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (exp (* a x)) 1.0)
34.0ms	(- (exp (* a x)) 1.0)
94.0ms	(log (sqrt (exp (- (exp (* a x)) 1.0))))
100.0ms	(log (sqrt (exp (- (exp (* a x)) 1.0))))

simplify110.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 3 (95.0ms)

Iter	Nodes	Cost
0	272	1390
1	738	1068
2	3244	934
3	5001	802

prune379.0ms

Filtered

140 candidates to 80 candidates (57.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.3b

regimes415.0ms

Accuracy

95.5% (0.9b remaining)

Error of 9.4b against oracle of 8.4b and baseline of 29.4b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	85
1	52	85

end0.0ms

sample911.0ms

Algorithm

intervals

Results

422.0ms	2682×	body	1280	valid
130.0ms	1336×	body	640	valid
109.0ms	5531×	body	80	valid
46.0ms	727×	body	320	valid
20.0ms	391×	body	160	valid