Details

sample73.0ms

Algorithm

intervals

Results

45.0ms	105×	body	10240	exit
10.0ms	275×	body	80	valid
2.0ms	4×	body	1280	valid
2.0ms	8×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	3×	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: 0.8b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.7b	(log (+ 1.0 (exp x)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 34

Calls

2 calls:

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

series73.0ms

Counts

2 → 6

Calls

2 calls:

8.0ms	(+ 1.0 (exp x))
65.0ms	(log (+ 1.0 (exp x)))

simplify103.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 4 (100.0ms)

Iter	Nodes	Cost
0	137	181
1	364	163
2	1024	163
3	3614	161
4	5001	159

prune101.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp x) 3)
0.7b	(log (+ (pow 1.0 3) (pow (exp x) 3)))
6.2b	(- (* (exp x) (exp x)) (* 1.0 (exp x)))
6.3b	(log (+ (* 1.0 1.0) (- (* (exp x) (exp x)) (* 1.0 (exp x)))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
12×	`log-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`pow1` `unpow-prod-down` `cube-prod`
6×	`add-exp-log` `add-log-exp`
5×	`add-cbrt-cube` `distribute-lft-out`
4×	`expm1-log1p-u` `log-div` `pow-pow` `log1p-expm1-u`
3×	`pow-unpow` `exp-prod`
2×	`flip3-+` `rem-log-exp` `log-pow` `flip-+`
1×	`cube-mult` `pow-to-exp` `sub-neg` `flip3--` `distribute-rgt-out--` `fma-neg` `diff-log` `unpow3` `prod-diff` `pow-exp` `sum-cubes` `flip--` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 83

Calls

4 calls:

2.0ms	(pow (exp x) 3)
13.0ms	(log (+ (pow 1.0 3) (pow (exp x) 3)))
10.0ms	(- (* (exp x) (exp x)) (* 1.0 (exp x)))
19.0ms	(log (+ (* 1.0 1.0) (- (* (exp x) (exp x)) (* 1.0 (exp x)))))

series273.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(pow (exp x) 3)
94.0ms	(log (+ (pow 1.0 3) (pow (exp x) 3)))
48.0ms	(- (* (exp x) (exp x)) (* 1.0 (exp x)))
108.0ms	(log (+ (* 1.0 1.0) (- (* (exp x) (exp x)) (* 1.0 (exp x)))))

simplify66.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	398	699
1	1683	631
2	5001	622

prune314.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (log (fma x (fma 1/2 x 1) 2.0)) (* x y))
7.8b	(log (fma x (fma 1/2 x 1) 2.0))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 39

Calls

2 calls:

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

series151.0ms

Counts

2 → 6

Calls

2 calls:

88.0ms	(- (log (fma x (fma 1/2 x 1) 2.0)) (* x y))
63.0ms	(log (fma x (fma 1/2 x 1) 2.0))

simplify79.0ms

Algorithm

egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 3 (74.0ms)

Iter	Nodes	Cost
0	221	317
1	704	285
2	2781	282
3	5001	264

prune126.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/2 (/ (pow x 2) (pow 2.0 2)))
0.0b	(- (fma x (+ (* 0.25 x) 0.5) (- (log 2.0) (* 1/2 (/ (pow x 2) (pow 2.0 2))))) (* x y))
0.0b	(- (log 2.0) (* 1/2 (/ (pow x 2) (pow 2.0 2))))
8.1b	(fma x (+ (* 0.25 x) 0.5) (- (log 2.0) (* 1/2 (/ (pow x 2) (pow 2.0 2)))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

80×	`times-frac`
77×	`add-sqr-sqrt`
68×	`associate-r`
56×	`unpow-prod-down`
43×	`add-cube-cbrt` `*-un-lft-identity`
27×	`add-exp-log`
24×	`unpow2` `sqr-pow`
17×	`unswap-sqr`
10×	`prod-exp`
9×	`div-exp` `add-cbrt-cube`
8×	`pow1`
7×	`fma-neg` `prod-diff` `add-log-exp`
6×	`pow-to-exp` `pow-exp`
4×	`expm1-log1p-u` `associate--l+` `log1p-expm1-u`
3×	`log-prod` `associate-l`
2×	`sub-neg` `flip3--` `diff-log` `log-pow` `flip--` `cbrt-unprod` `fma-udef`
1×	`cbrt-undiv` `associate-r/` `pow-prod-down` `-commutative` `div-inv`

Counts

4 → 168

Calls

4 calls:

28.0ms	(* 1/2 (/ (pow x 2) (pow 2.0 2)))
3.0ms	(- (fma x (+ (* 0.25 x) 0.5) (- (log 2.0) (* 1/2 (/ (pow x 2) (pow 2.0 2))))) (* x y))
4.0ms	(- (log 2.0) (* 1/2 (/ (pow x 2) (pow 2.0 2))))
0.0ms	(fma x (+ (* 0.25 x) 0.5) (- (log 2.0) (* 1/2 (/ (pow x 2) (pow 2.0 2)))))

series461.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* 1/2 (/ (pow x 2) (pow 2.0 2)))
72.0ms	(- (fma x (+ (* 0.25 x) 0.5) (- (log 2.0) (* 1/2 (/ (pow x 2) (pow 2.0 2))))) (* x y))
275.0ms	(- (log 2.0) (* 1/2 (/ (pow x 2) (pow 2.0 2))))
61.0ms	(fma x (+ (* 0.25 x) 0.5) (- (log 2.0) (* 1/2 (/ (pow x 2) (pow 2.0 2)))))

simplify75.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	742	1374
1	3093	1185
2	5002	1159

prune476.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.4b

regimes45.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	17
1	22	17

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.0s	2497×	body	10240	exit
330.0ms	8451×	body	80	valid
74.0ms	148×	body	1280	valid
71.0ms	268×	body	640	valid
33.0ms	192×	body	320	valid
10.0ms	105×	body	160	valid