Details

sample30.0ms

Algorithm

intervals

Results

12.0ms	87×	body	1280	valid
4.0ms	43×	body	640	valid
3.0ms	164×	body	80	valid
1.0ms	15×	body	320	valid
1.0ms	16×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.8b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
4.4b	(- (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)

series46.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(exp (* a x))
34.0ms	(- (exp (* a x)) 1.0)

simplify88.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (79.0ms)

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

prune90.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 7.3b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* a x))
0.0b	(exp (- (exp (* a x)) 1.0))
4.4b	(- (exp (* a x)) 1.0)
4.4b	(log (exp (- (exp (* a x)) 1.0)))

rewrite34.0ms

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:

1.0ms	(exp (* a x))
11.0ms	(exp (- (exp (* a x)) 1.0))
5.0ms	(- (exp (* a x)) 1.0)
14.0ms	(log (exp (- (exp (* a x)) 1.0)))

series118.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(exp (* a x))
35.0ms	(exp (- (exp (* a x)) 1.0))
37.0ms	(- (exp (* a x)) 1.0)
34.0ms	(log (exp (- (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	720	594
2	3168	484
3	5001	483

prune198.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 7.3b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(exp (* a x))
0.0b	(exp (* a x))
4.4b	(fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-log-exp`
3×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u`
2×	`exp-prod` `exp-to-pow` `rem-exp-log`
1×	`fma-udef`

Counts

3 → 34

Calls

3 calls:

1.0ms	(exp (* a x))
1.0ms	(exp (* a x))
0.0ms	(fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0))

series105.0ms

Counts

3 → 9

Calls

3 calls:

12.0ms	(exp (* a x))
12.0ms	(exp (* a x))
81.0ms	(fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0))

simplify41.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	91	211
1	311	177
2	1202	176
3	5001	176

prune106.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 7.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0)))
4.4b	(fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0))
4.4b	(fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0))
4.4b	(fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `fma-udef`
1×	`pow1/3`

Counts

4 → 43

Calls

4 calls:

0.0ms	(cbrt (fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0)))
0.0ms	(fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0))
0.0ms	(fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0))
0.0ms	(fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0))

series386.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(cbrt (fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0)))
79.0ms	(fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0))
96.0ms	(fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0))
78.0ms	(fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0))

simplify60.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 3 (54.0ms)

Iter	Nodes	Cost
0	132	566
1	440	389
2	1877	377
3	5002	352

prune204.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.3b

regimes280.0ms

Accuracy

94.3% (1.2b remaining)

Error of 9.5b against oracle of 8.4b and baseline of 29.2b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	13
1	24	13

end0.0ms

sample907.0ms

Algorithm

intervals

Results

425.0ms	2760×	body	1280	valid
126.0ms	1273×	body	640	valid
102.0ms	5437×	body	80	valid
50.0ms	771×	body	320	valid
18.0ms	418×	body	160	valid