Details

sample80.0ms

Algorithm

intervals

Results

42.0ms	80×	body	10240	exit
21.0ms	277×	body	80	valid
2.0ms	3×	body	1280	valid
2.0ms	5×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	2×	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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.0b	(- (log (+ 1.0 (exp x))) (* x y))
0.8b	(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:

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

series128.0ms

Counts

3 → 9

Calls

3 calls:

8.0ms	(+ 1.0 (exp x))
58.0ms	(- (log (+ 1.0 (exp x))) (* x y))
63.0ms	(log (+ 1.0 (exp x)))

simplify60.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (54.0ms)

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

prune163.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 (exp x)))
0.0b	(sqrt (+ 1.0 (exp x)))
1.4b	(log (sqrt (+ 1.0 (exp x))))
1.4b	(log (sqrt (+ 1.0 (exp x))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

5.0ms	(sqrt (+ 1.0 (exp x)))
7.0ms	(sqrt (+ 1.0 (exp x)))
3.0ms	(log (sqrt (+ 1.0 (exp x))))
3.0ms	(log (sqrt (+ 1.0 (exp x))))

series266.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(sqrt (+ 1.0 (exp x)))
30.0ms	(sqrt (+ 1.0 (exp x)))
100.0ms	(log (sqrt (+ 1.0 (exp x))))
103.0ms	(log (sqrt (+ 1.0 (exp x))))

simplify55.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	172	598
1	486	558
2	1684	540
3	5002	522

prune262.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 (exp x)))
0.7b	(* (sqrt (sqrt (+ 1.0 (exp x)))) (sqrt (sqrt (+ 1.0 (exp x)))))
1.4b	(log (* (sqrt (sqrt (+ 1.0 (exp x)))) (sqrt (sqrt (+ 1.0 (exp x))))))
1.4b	(log (sqrt (+ 1.0 (exp x))))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

90×	`sqrt-prod`
66×	`sqrt-pow1`
54×	`pow1`
52×	`add-sqr-sqrt` `sqrt-div`
37×	`*-un-lft-identity`
34×	`pow1/2`
25×	`log-pow`
19×	`add-cube-cbrt`
18×	`swap-sqr` `pow-prod-up`
14×	`flip3-+` `flip-+`
10×	`add-exp-log` `log-div` `associate-r` `associate-l` `pow-prod-down` `pow-sqr`
9×	`unswap-sqr`
8×	`frac-times` `log-prod` `distribute-lft-out`
6×	`add-cbrt-cube`
4×	`expm1-log1p-u` `associate-r/` `associate-l/` `log1p-expm1-u` `add-log-exp`
3×	`rem-log-exp`
2×	`pow2` `pow-plus` `prod-exp`
1×	`rem-sqrt-square` `sqrt-unprod` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `hypot-def`

Counts

4 → 173

Calls

4 calls:

5.0ms	(sqrt (+ 1.0 (exp x)))
32.0ms	(* (sqrt (sqrt (+ 1.0 (exp x)))) (sqrt (sqrt (+ 1.0 (exp x)))))
15.0ms	(log (* (sqrt (sqrt (+ 1.0 (exp x)))) (sqrt (sqrt (+ 1.0 (exp x))))))
3.0ms	(log (sqrt (+ 1.0 (exp x))))

series266.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(sqrt (+ 1.0 (exp x)))
33.0ms	(* (sqrt (sqrt (+ 1.0 (exp x)))) (sqrt (sqrt (+ 1.0 (exp x)))))
100.0ms	(log (* (sqrt (sqrt (+ 1.0 (exp x)))) (sqrt (sqrt (+ 1.0 (exp x))))))
103.0ms	(log (sqrt (+ 1.0 (exp x))))

simplify51.0ms

Algorithm

egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	339	1260
1	1213	1166
2	5001	1134

prune419.0ms

Pruning

4 alts after pruning (1 fresh and 3 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))
6.8b	(log (fma 1/2 (pow x 2) (+ x 2.0)))

rewrite5.0ms

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)))

series144.0ms

Counts

3 → 9

Calls

3 calls:

74.0ms	(- (log (fma 1/2 (pow x 2) (+ x 2.0))) (* x y))
17.0ms	(fma 1/2 (pow x 2) (+ x 2.0))
53.0ms	(log (fma 1/2 (pow x 2) (+ x 2.0)))

simplify84.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 3 (78.0ms)

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

prune156.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.2b

regimes66.0ms

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	16	17
1	16	17

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.2s	2366×	body	10240	exit
648.0ms	8487×	body	80	valid
86.0ms	239×	body	640	valid
58.0ms	93×	body	1280	valid
42.0ms	169×	body	320	valid
17.0ms	107×	body	160	valid