Details

sample51.0ms

Algorithm

intervals

Results

25.0ms	63×	body	10240	exit
10.0ms	269×	body	80	valid
2.0ms	9×	body	640	valid
2.0ms	3×	body	1280	valid
1.0ms	4×	body	320	valid
0.0ms	4×	body	160	valid

simplify6.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (log (+ 1.0 (exp x))) (* x y))
0.0b	(+ 1.0 (exp x))
0.5b	(log (+ 1.0 (exp x)))

rewrite13.0ms

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:

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

series128.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(- (log (+ 1.0 (exp x))) (* x y))
8.0ms	(+ 1.0 (exp x))
63.0ms	(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

prune166.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.5b	(log (+ 1.0 (exp x)))
0.7b	(sqrt (log (+ 1.0 (exp x))))
0.7b	(sqrt (log (+ 1.0 (exp x))))
0.7b	(* (sqrt (log (+ 1.0 (exp x)))) (sqrt (log (+ 1.0 (exp x)))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

34×	`sqrt-prod`
30×	`pow1`
29×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
15×	`add-cube-cbrt`
11×	`swap-sqr`
10×	`sqrt-pow1` `pow1/2`
9×	`log-pow`
7×	`add-exp-log` `associate-r` `associate-l`
6×	`add-cbrt-cube`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log-prod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square` `log-div`
1×	`pow2` `flip3-+` `pow-plus` `sqrt-unprod` `rem-log-exp` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out`

Counts

4 → 105

Calls

4 calls:

3.0ms	(log (+ 1.0 (exp x)))
5.0ms	(sqrt (log (+ 1.0 (exp x))))
5.0ms	(sqrt (log (+ 1.0 (exp x))))
10.0ms	(* (sqrt (log (+ 1.0 (exp x)))) (sqrt (log (+ 1.0 (exp x)))))

series334.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(log (+ 1.0 (exp x)))
103.0ms	(sqrt (log (+ 1.0 (exp x))))
104.0ms	(sqrt (log (+ 1.0 (exp x))))
62.0ms	(* (sqrt (log (+ 1.0 (exp x)))) (sqrt (log (+ 1.0 (exp x)))))

simplify165.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 3 (156.0ms)

Iter	Nodes	Cost
0	241	700
1	837	631
2	4232	605
3	5001	601

prune241.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(log (+ (exp x) 1.0))
0.5b	(log (+ (exp x) 1.0))
0.7b	(* (- (log (+ (exp x) 1.0)) (* x y)) (fma x y (log (+ (exp x) 1.0))))
10.8b	(/ (* (- (log (+ (exp x) 1.0)) (* x y)) (fma x y (log (+ (exp x) 1.0)))) (fma x y (log (+ (exp x) 1.0))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
13×	`add-exp-log`
12×	`add-sqr-sqrt`
11×	`add-cbrt-cube`
10×	`add-cube-cbrt`
8×	`pow1` `log-prod`
4×	`expm1-log1p-u` `log-div` `associate-*l/` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `associate-r` `associate-l` `associate-/r*`
2×	`cbrt-undiv` `flip3--` `flip3-+` `div-exp` `rem-log-exp` `prod-exp` `log-pow` `flip--` `cbrt-unprod` `flip-+` `fma-udef` `associate-/l/` `distribute-lft-out`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

4 → 83

Calls

4 calls:

3.0ms	(log (+ (exp x) 1.0))
3.0ms	(log (+ (exp x) 1.0))
10.0ms	(* (- (log (+ (exp x) 1.0)) (* x y)) (fma x y (log (+ (exp x) 1.0))))
8.0ms	(/ (* (- (log (+ (exp x) 1.0)) (* x y)) (fma x y (log (+ (exp x) 1.0)))) (fma x y (log (+ (exp x) 1.0))))

series345.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(log (+ (exp x) 1.0))
65.0ms	(log (+ (exp x) 1.0))
159.0ms	(* (- (log (+ (exp x) 1.0)) (* x y)) (fma x y (log (+ (exp x) 1.0))))
62.0ms	(/ (* (- (log (+ (exp x) 1.0)) (* x y)) (fma x y (log (+ (exp x) 1.0)))) (fma x y (log (+ (exp x) 1.0))))

simplify56.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	363	967
1	1721	777
2	5001	775

prune285.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (log (fma 1/2 (pow x 2) (+ x 2.0))) (* x y))
0.0b	(fma 1/2 (pow x 2) (+ x 2.0))
8.0b	(log (fma 1/2 (pow x 2) (+ x 2.0)))

rewrite6.0ms

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:

4.0ms	(- (log (fma 1/2 (pow x 2) (+ x 2.0))) (* x y))
0.0ms	(fma 1/2 (pow x 2) (+ x 2.0))
1.0ms	(log (fma 1/2 (pow x 2) (+ x 2.0)))

series149.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(- (log (fma 1/2 (pow x 2) (+ x 2.0))) (* x y))
17.0ms	(fma 1/2 (pow x 2) (+ x 2.0))
54.0ms	(log (fma 1/2 (pow x 2) (+ x 2.0)))

simplify86.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 3 (80.0ms)

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

prune165.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes36.0ms

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	12	11
1	12	11

end0.0ms

sample1.7s

Algorithm

intervals

Results

996.0ms	2478×	body	10240	exit
323.0ms	8410×	body	80	valid
77.0ms	293×	body	640	valid
64.0ms	130×	body	1280	valid
28.0ms	177×	body	320	valid
9.0ms	98×	body	160	valid