Details

sample51.0ms

Algorithm

intervals

Results

23.0ms	89×	body	1280	valid
8.0ms	42×	body	640	valid
8.0ms	169×	body	80	valid
2.0ms	20×	body	320	valid
1.0ms	12×	body	160	valid

simplify60.0ms

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: 30.4b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
3.2b	(- (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)

series47.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(exp (* a x))
35.0ms	(- (exp (* a x)) 1.0)

simplify81.0ms

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

prune91.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 8.2b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(exp (* a x))
0.0b	(exp (* a x))
3.3b	(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))
1.0ms	(fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0))

series107.0ms

Counts

3 → 9

Calls

3 calls:

12.0ms	(exp (* a x))
12.0ms	(exp (* a x))
82.0ms	(fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0))

simplify44.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 2 (11.0ms)

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

prune111.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 8.2b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* a x))
0.0b	(pow (- (exp (* a x)) 1.0) 3)
0.3b	(cbrt (pow (- (exp (* a x)) 1.0) 3))
3.2b	(- (exp (* a x)) 1.0)

rewrite216.0ms

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:

1.0ms	(exp (* a x))
6.0ms	(pow (- (exp (* a x)) 1.0) 3)
201.0ms	(cbrt (pow (- (exp (* a x)) 1.0) 3))
5.0ms	(- (exp (* a x)) 1.0)

series135.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(exp (* a x))
54.0ms	(pow (- (exp (* a x)) 1.0) 3)
35.0ms	(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

prune209.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (* (- (exp (* a x)) 1.0) (- (exp (* a x)) 1.0)))
3.2b	(- (exp (* a x)) 1.0)
3.2b	(- (exp (* a x)) 1.0)
3.2b	(- (exp (* a x)) 1.0)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt` `*-un-lft-identity`
27×	`prod-diff`
25×	`add-cube-cbrt`
10×	`add-log-exp`
9×	`flip3--` `fma-neg` `flip--`
8×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u`
3×	`sub-neg` `diff-log` `distribute-lft-out--` `difference-of-squares`
2×	`associate-r/` `associate-l/`
1×	`cbrt-prod` `pow1/3`

Counts

4 → 103

Calls

4 calls:

9.0ms	(cbrt (* (- (exp (* a x)) 1.0) (- (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)

series224.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(cbrt (* (- (exp (* a x)) 1.0) (- (exp (* a x)) 1.0)))
37.0ms	(- (exp (* a x)) 1.0)
34.0ms	(- (exp (* a x)) 1.0)
38.0ms	(- (exp (* a x)) 1.0)

simplify45.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	282	1101
1	1004	835
2	5001	820

prune273.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 8.2b

regimes305.0ms

Accuracy

93.7% (1.3b remaining)

Error of 9.8b against oracle of 8.4b and baseline of 29.8b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	23
1	29	23

end0.0ms

sample1.5s

Algorithm

intervals

Results

700.0ms	2710×	body	1280	valid
247.0ms	5339×	body	80	valid
236.0ms	1309×	body	640	valid
109.0ms	802×	body	320	valid
44.0ms	419×	body	160	valid