Details

sample32.0ms

Algorithm

intervals

Results

12.0ms	70×	body	1280	valid
4.0ms	39×	body	640	valid
4.0ms	171×	body	80	valid
2.0ms	35×	body	320	valid
1.0ms	13×	body	160	valid

simplify62.0ms

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: 29.7b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
4.3b	(- (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)

series49.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(exp (* a x))
37.0ms	(- (exp (* a x)) 1.0)

simplify84.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (80.0ms)

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

prune91.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.9b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(exp (* a x))
4.2b	(log (exp (- (exp (* a x)) 1.0)))
4.3b	(- (exp (* a x)) 1.0)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 71

Calls

3 calls:

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

series82.0ms

Counts

3 → 9

Calls

3 calls:

12.0ms	(exp (* a x))
36.0ms	(log (exp (- (exp (* a x)) 1.0)))
33.0ms	(- (exp (* a x)) 1.0)

simplify94.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 3 (88.0ms)

Iter	Nodes	Cost
0	236	562
1	667	396
2	2936	322
3	5002	304

prune141.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.9b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cbrt (- (exp (* a x)) 1.0)) (cbrt (- (exp (* a x)) 1.0)))
4.3b	(- (exp (* a x)) 1.0)
4.3b	(- (exp (* a x)) 1.0)
4.3b	(- (exp (* a x)) 1.0)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
53×	`*-un-lft-identity`
33×	`add-cube-cbrt`
28×	`cbrt-prod`
27×	`prod-diff`
12×	`cbrt-div`
11×	`pow1`
10×	`swap-sqr` `add-log-exp`
9×	`flip3--` `fma-neg` `flip--` `distribute-lft-out--`
8×	`associate-r` `associate-l`
7×	`difference-of-squares`
6×	`add-exp-log` `pow1/3`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `unswap-sqr`
3×	`sub-neg` `diff-log`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 142

Calls

4 calls:

26.0ms	(* (cbrt (- (exp (* a x)) 1.0)) (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)

series217.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(* (cbrt (- (exp (* a x)) 1.0)) (cbrt (- (exp (* a x)) 1.0)))
37.0ms	(- (exp (* a x)) 1.0)
33.0ms	(- (exp (* a x)) 1.0)
37.0ms	(- (exp (* a x)) 1.0)

simplify48.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	307	1503
1	1077	1228
2	5002	1137

prune352.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.9b

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ (exp (* a x)) 1.0))
4.2b	(- (* (exp (* a x)) (exp (* a x))) (* 1.0 1.0))
4.2b	(- (* (exp (* a x)) (exp (* a x))) (* 1.0 1.0))
4.3b	(- (exp (* a x)) 1.0)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

3.0ms	(cbrt (+ (exp (* a x)) 1.0))
6.0ms	(- (* (exp (* a x)) (exp (* a x))) (* 1.0 1.0))
6.0ms	(- (* (exp (* a x)) (exp (* a x))) (* 1.0 1.0))
5.0ms	(- (exp (* a x)) 1.0)

series252.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(cbrt (+ (exp (* a x)) 1.0))
45.0ms	(- (* (exp (* a x)) (exp (* a x))) (* 1.0 1.0))
48.0ms	(- (* (exp (* a x)) (exp (* a x))) (* 1.0 1.0))
35.0ms	(- (exp (* a x)) 1.0)

simplify50.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	318	767
1	1211	607
2	5002	593

prune304.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.9b

regimes368.0ms

Accuracy

94.5% (1.2b remaining)

Error of 9.1b against oracle of 7.9b and baseline of 29.4b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	61
1	42	61

end0.0ms

sample966.0ms

Algorithm

intervals

Results

454.0ms	2729×	body	1280	valid
128.0ms	1239×	body	640	valid
119.0ms	5499×	body	80	valid
56.0ms	782×	body	320	valid
19.0ms	400×	body	160	valid