Details

sample98.0ms

Algorithm

intervals

Results

57.0ms	88×	body	5120	exit
19.0ms	274×	body	80	valid
4.0ms	5×	body	1280	valid
2.0ms	6×	body	640	valid
2.0ms	7×	body	320	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	5
1	19	5
2	23	5
3	23	5

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: 0.3b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.0b	(- (log (+ 1.0 (exp x))) (* x y))
0.3b	(log (+ 1.0 (exp x)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-cube-cbrt` `log-prod`
6×	`pow1` `add-log-exp`
4×	`add-exp-log` `log-div` `fma-neg` `prod-diff` `associate--l+`
3×	`expm1-log1p-u` `fma-def` `flip3-+` `log-pow` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out`
2×	`associate--l-`
1×	`+-commutative` `sub-neg` `flip3--` `diff-log` `rem-log-exp` `sum-log` `flip--`

Counts

3 → 62

Calls

3 calls:

3.0ms	(+ 1.0 (exp x))
6.0ms	(- (log (+ 1.0 (exp x))) (* x y))
4.0ms	(log (+ 1.0 (exp x)))

series127.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(+ 1.0 (exp x))
58.0ms	(- (log (+ 1.0 (exp x))) (* x y))
62.0ms	(log (+ 1.0 (exp x)))

simplify57.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (51.0ms)

Iter	Nodes	Cost
0	236	404
1	702	369
2	2284	367
3	5002	340

prune160.0ms

Filtered

71 candidates to 54 candidates (76.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	68	3	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	3	72

Merged error: 0b

Counts

72 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.0b	(+ 1.0 (exp x))
1.0b	(log (sqrt (+ 1.0 (exp x))))
1.0b	(log (sqrt (+ 1.0 (exp x))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
14×	`log-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt`
8×	`pow1` `sqrt-prod` `add-log-exp`
6×	`add-exp-log` `fma-def` `log-pow`
4×	`expm1-log1p-u` `log-div` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out`
2×	`+-commutative` `sqrt-pow1` `pow1/2` `rem-log-exp` `sum-log`

Counts

4 → 78

Calls

4 calls:

3.0ms	(+ 1.0 (exp x))
3.0ms	(+ 1.0 (exp x))
4.0ms	(log (sqrt (+ 1.0 (exp x))))
4.0ms	(log (sqrt (+ 1.0 (exp x))))

series219.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+ 1.0 (exp x))
7.0ms	(+ 1.0 (exp x))
100.0ms	(log (sqrt (+ 1.0 (exp x))))
105.0ms	(log (sqrt (+ 1.0 (exp x))))

simplify42.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 3 (35.0ms)

Iter	Nodes	Cost
0	165	504
1	423	460
2	1201	448
3	5002	438

prune211.0ms

Filtered

90 candidates to 68 candidates (75.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	90	3	93

Merged error: 0b

Counts

93 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (* (cbrt (- (log (+ 1.0 (exp x))) (* x y))) (cbrt (- (log (+ 1.0 (exp x))) (* x y)))) (cbrt (- (log (+ 1.0 (exp x))) (* x y))))
1.1b	(cbrt (- (log (+ 1.0 (exp x))) (* x y)))
1.1b	(cbrt (- (log (+ 1.0 (exp x))) (* x y)))
1.1b	(cbrt (- (log (+ 1.0 (exp x))) (* x y)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-div`
30×	`flip3--` `flip--`
28×	`frac-times`
23×	`pow1`
14×	`associate-*l/`
13×	`cbrt-prod`
12×	`pow1/3`
11×	`add-sqr-sqrt`
9×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `pow-prod-up`
8×	`associate-*r/`
6×	`pow-plus` `associate-r`
5×	`pow-prod-down` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`prod-exp` `pow-sqr` `cbrt-unprod`
2×	`pow2` `unswap-sqr`
1×	`associate-l` `pow3` `*-commutative`

Counts

4 → 108

Calls

4 calls:

14.0ms	(* (* (cbrt (- (log (+ 1.0 (exp x))) (* x y))) (cbrt (- (log (+ 1.0 (exp x))) (* x y)))) (cbrt (- (log (+ 1.0 (exp x))) (* x y))))
2.0ms	(cbrt (- (log (+ 1.0 (exp x))) (* x y)))
2.0ms	(cbrt (- (log (+ 1.0 (exp x))) (* x y)))
3.0ms	(cbrt (- (log (+ 1.0 (exp x))) (* x y)))

series1.1s

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (* (cbrt (- (log (+ 1.0 (exp x))) (* x y))) (cbrt (- (log (+ 1.0 (exp x))) (* x y)))) (cbrt (- (log (+ 1.0 (exp x))) (* x y))))
442.0ms	(cbrt (- (log (+ 1.0 (exp x))) (* x y)))
309.0ms	(cbrt (- (log (+ 1.0 (exp x))) (* x y)))
302.0ms	(cbrt (- (log (+ 1.0 (exp x))) (* x y)))

simplify62.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	457	2712
1	1669	2425
2	5001	2290

prune313.0ms

Filtered

120 candidates to 86 candidates (71.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	120	3	123

Merged error: 0b

Counts

123 → 3

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 1/2 (pow x 2) (+ x 2.0))
0.0b	(- (log (fma 1/2 (pow x 2) (+ x 2.0))) (* x y))
8.8b	(log (fma 1/2 (pow x 2) (+ x 2.0)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `log-prod`
4×	`add-exp-log` `fma-neg` `prod-diff` `add-log-exp`
3×	`expm1-log1p-u` `associate--l+` `log-pow` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--` `fma-udef`

Counts

3 → 49

Calls

3 calls:

1.0ms	(fma 1/2 (pow x 2) (+ x 2.0))
6.0ms	(- (log (fma 1/2 (pow x 2) (+ x 2.0))) (* x y))
2.0ms	(log (fma 1/2 (pow x 2) (+ x 2.0)))

series153.0ms

Counts

3 → 9

Calls

3 calls:

16.0ms	(fma 1/2 (pow x 2) (+ x 2.0))
75.0ms	(- (log (fma 1/2 (pow x 2) (+ x 2.0))) (* x y))
62.0ms	(log (fma 1/2 (pow x 2) (+ x 2.0)))

simplify85.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 3 (79.0ms)

Iter	Nodes	Cost
0	229	423
1	763	380
2	3267	376
3	5001	356

prune119.0ms

Filtered

58 candidates to 46 candidates (79.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	58	0	58
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	58	3	61

Merged error: 0b

Counts

61 → 3

regimes65.0ms

Accuracy

0% (0.8b remaining)

Error of 1.1b against oracle of 0.3b and baseline of 1.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	11
1	13	11

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.2s	2491×	body	5120	exit
417.0ms	8485×	body	80	valid
79.0ms	241×	body	640	valid
71.0ms	128×	body	1280	valid
34.0ms	180×	body	320	valid
13.0ms	110×	body	160	valid