Details

sample55.0ms

Algorithm

intervals

Results

28.0ms	70×	body	10240	exit
10.0ms	265×	body	80	valid
3.0ms	11×	body	640	valid
2.0ms	4×	body	1280	valid
1.0ms	8×	body	320	valid
0.0ms	3×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize11.0ms

Local error

Found 3 expressions with local error:

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

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

series131.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(- (log (+ 1.0 (exp x))) (* x y))
13.0ms	(+ 1.0 (exp x))
61.0ms	(log (+ 1.0 (exp x)))

simplify62.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (56.0ms)

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

prune177.0ms

Filtered

71 candidates to 54 candidates (76.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (log (+ 1.0 (exp x))))
0.0b	(+ 1.0 (exp x))
0.0b	(expm1 (log1p (log (+ 1.0 (exp x)))))
1.0b	(log (+ 1.0 (exp x)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

0.0ms	(log1p (log (+ 1.0 (exp x))))
3.0ms	(+ 1.0 (exp x))
0.0ms	(expm1 (log1p (log (+ 1.0 (exp x)))))
3.0ms	(log (+ 1.0 (exp x)))

series448.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(log1p (log (+ 1.0 (exp x))))
11.0ms	(+ 1.0 (exp x))
224.0ms	(expm1 (log1p (log (+ 1.0 (exp x)))))
62.0ms	(log (+ 1.0 (exp x)))

simplify79.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (74.0ms)

Iter	Nodes	Cost
0	251	370
1	777	332
2	2932	322
3	5001	321

prune190.0ms

Filtered

68 candidates to 49 candidates (72.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.0b	(+ 1.0 (exp x))
1.7b	(log (sqrt (+ 1.0 (exp x))))
1.7b	(log (sqrt (+ 1.0 (exp x))))

rewrite15.0ms

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

series223.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+ 1.0 (exp x))
8.0ms	(+ 1.0 (exp x))
102.0ms	(log (sqrt (+ 1.0 (exp x))))
105.0ms	(log (sqrt (+ 1.0 (exp x))))

simplify46.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 3 (39.0ms)

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

prune276.0ms

Filtered

90 candidates to 68 candidates (75.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x 0.5 (log 2.0))
0.0b	(+ (fma x 0.5 (log 2.0)) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))))
0.0b	(- (+ (fma x 0.5 (log 2.0)) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))) (* x y))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

172×	`associate-+r+`
171×	`prod-diff`
152×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
144×	`times-frac`
86×	`distribute-rgt-in` `distribute-lft-in`
54×	`unpow-prod-down`
18×	`unpow2` `sqr-pow`
10×	`add-log-exp`
6×	`div-inv`
3×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `fma-def` `fma-neg` `add-cbrt-cube` `log1p-expm1-u`
2×	`diff-log` `sum-log` `fma-udef`
1×	`+-commutative` `associate-+l+` `flip3--` `flip3-+` `associate--l+` `flip--` `flip-+`

Counts

3 → 221

Calls

3 calls:

0.0ms	(fma x 0.5 (log 2.0))
33.0ms	(+ (fma x 0.5 (log 2.0)) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))))
15.0ms	(- (+ (fma x 0.5 (log 2.0)) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))) (* x y))

series308.0ms

Counts

3 → 9

Calls

3 calls:

175.0ms	(fma x 0.5 (log 2.0))
56.0ms	(+ (fma x 0.5 (log 2.0)) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))))
77.0ms	(- (+ (fma x 0.5 (log 2.0)) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))) (* x y))

simplify95.0ms

Algorithm

egg-herbie

Counts

230 → 230

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	1276	3322
1	4558	2635
2	5001	2632

prune872.0ms

Filtered

230 candidates to 161 candidates (70.0%)

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes36.0ms

Accuracy

0% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	7
1	12	7

end0.0ms

sample1.6s

Algorithm

intervals

Results

926.0ms	2344×	body	10240	exit
314.0ms	8425×	body	80	valid
58.0ms	220×	body	640	valid
56.0ms	113×	body	1280	valid
32.0ms	203×	body	320	valid
8.0ms	87×	body	160	valid