Details

sample55.0ms

Algorithm

intervals

Results

28.0ms	67×	body	10240	exit
13.0ms	271×	body	80	valid
2.0ms	7×	body	640	valid
1.0ms	5×	body	320	valid
1.0ms	1×	body	1280	valid
0.0ms	4×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

8×	`log-prod` `*-un-lft-identity`
4×	`add-sqr-sqrt` `add-cube-cbrt` `log-div` `associate--l+`
3×	`pow1` `add-exp-log` `add-log-exp`
2×	`associate--l-` `flip3-+` `add-cbrt-cube` `flip-+` `distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `log-pow` `flip--`

Counts

2 → 33

Calls

2 calls:

5.0ms	(- (log (+ 1.0 (exp x))) (* x y))
3.0ms	(log (+ 1.0 (exp x)))

series115.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(- (log (+ 1.0 (exp x))) (* x y))
62.0ms	(log (+ 1.0 (exp x)))

simplify44.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 3 (40.0ms)

Iter	Nodes	Cost
0	180	262
1	479	246
2	1456	243
3	5001	242

prune94.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b

(+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))))

0.0b

(- (+ (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))) (* 0.5 x)) (* x y))

0.0b

(+ (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))) (* 0.5 x))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-log-exp`
7×	`sum-log`
4×	`add-sqr-sqrt` `add-cube-cbrt` `associate-+l+` `associate-+r+` `*-un-lft-identity`
3×	`pow1` `add-exp-log` `sub-neg` `log-prod` `diff-log` `add-cbrt-cube`
2×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `flip3-+` `flip-+`
1×	`flip3--` `associate--l+` `flip--`

Counts

3 → 46

Calls

3 calls:

4.0ms

(+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))))

63.0ms

(- (+ (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))) (* 0.5 x)) (* x y))

16.0ms

(+ (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))) (* 0.5 x))

series643.0ms

Counts

3 → 9

Calls

3 calls:

513.0ms

(+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))))

73.0ms

(- (+ (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))) (* 0.5 x)) (* x y))

57.0ms

(+ (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))) (* 0.5 x))

simplify42.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	271	625
1	1051	590
2	5002	570

prune180.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (log (+ (exp x) 1.0)) (* x y))
0.5b	(log (+ (exp x) 1.0))
0.7b	(pow (- (log (+ (exp x) 1.0)) (* x y)) 3)
14.7b	(cbrt (pow (- (log (+ (exp x) 1.0)) (* x y)) 3))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
12×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt`
8×	`log-prod`
6×	`pow1` `add-exp-log` `unpow-prod-down` `cube-prod`
5×	`add-cbrt-cube` `add-log-exp`
4×	`cube-div` `log-div` `associate--l+`
3×	`pow-unpow` `flip3--` `flip--`
2×	`associate--l-` `cube-mult` `cbrt-div` `flip3-+` `unpow3` `flip-+` `distribute-lft-out` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `pow-pow` `pow1/3` `diff-log` `rem-log-exp` `pow-exp` `log-pow` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 81

Calls

4 calls:

6.0ms	(- (log (+ (exp x) 1.0)) (* x y))
3.0ms	(log (+ (exp x) 1.0))
4.0ms	(pow (- (log (+ (exp x) 1.0)) (* x y)) 3)
4.0ms	(cbrt (pow (- (log (+ (exp x) 1.0)) (* x y)) 3))

series300.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(- (log (+ (exp x) 1.0)) (* x y))
61.0ms	(log (+ (exp x) 1.0))
124.0ms	(pow (- (log (+ (exp x) 1.0)) (* x y)) 3)
61.0ms	(cbrt (pow (- (log (+ (exp x) 1.0)) (* x y)) 3))

simplify51.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	362	798
1	1354	753
2	5001	741

prune203.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow (log 2.0) 2)
1.0b	(pow (log 2.0) 2)
1.0b	(pow (log 2.0) 3)
8.0b	(cbrt (+ (* 1.5 (* (pow (log 2.0) 2) x)) (+ (pow (log 2.0) 3) (* (pow x 2) (+ (* 0.75 (log 2.0)) (* 0.375 (pow (log 2.0) 2)))))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity`
11×	`pow1`
9×	`pow-unpow`
7×	`add-exp-log`
5×	`add-cbrt-cube`
4×	`cube-prod` `log-pow` `add-log-exp`
3×	`cbrt-prod` `pow-to-exp` `pow-pow` `pow-exp` `sqr-pow`
2×	`cbrt-div` `unpow2`
1×	`cube-mult` `flip3-+` `pow1/3` `unpow3` `flip-+` `rem-cube-cbrt`

Counts

4 → 76

Calls

4 calls:

1.0ms	(pow (log 2.0) 2)
1.0ms	(pow (log 2.0) 2)
1.0ms	(pow (log 2.0) 3)
31.0ms	(cbrt (+ (* 1.5 (* (pow (log 2.0) 2) x)) (+ (pow (log 2.0) 3) (* (pow x 2) (+ (* 0.75 (log 2.0)) (* 0.375 (pow (log 2.0) 2)))))))

series621.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(pow (log 2.0) 2)
0.0ms	(pow (log 2.0) 2)
0.0ms	(pow (log 2.0) 3)
621.0ms	(cbrt (+ (* 1.5 (* (pow (log 2.0) 2) x)) (+ (pow (log 2.0) 3) (* (pow x 2) (+ (* 0.75 (log 2.0)) (* 0.375 (pow (log 2.0) 2)))))))

simplify73.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	400	849
1	2011	777
2	5002	771

prune213.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

regimes82.0ms

Accuracy

0% (0.2b remaining)

Error of 0.6b against oracle of 0.3b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	5
1	10	5

end0.0ms

sample1.7s

Algorithm

intervals

Results

997.0ms	2440×	body	10240	exit
320.0ms	8379×	body	80	valid
75.0ms	271×	body	640	valid
50.0ms	100×	body	1280	valid
31.0ms	190×	body	320	valid
12.0ms	123×	body	160	valid