Details

sample56.0ms

Algorithm

intervals

Results

26.0ms	64×	body	10240	exit
13.0ms	258×	body	80	valid
3.0ms	6×	body	1280	valid
2.0ms	7×	body	640	valid
2.0ms	11×	body	320	valid
0.0ms	2×	body	160	valid

simplify7.0ms

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: 1.1b

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))
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:

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))
56.0ms	(- (log (+ 1.0 (exp x))) (* x y))
64.0ms	(log (+ 1.0 (exp x)))

simplify62.0ms

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

prune170.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (+ 1.0 (exp x)))
0.7b	(cbrt (+ 1.0 (exp x)))
1.1b	(log (cbrt (+ 1.0 (exp x))))
1.7b	(log (* (cbrt (+ 1.0 (exp x))) (cbrt (+ 1.0 (exp x)))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-div`
14×	`*-un-lft-identity`
13×	`pow1`
12×	`cbrt-prod`
11×	`log-pow`
10×	`log-div`
9×	`flip3-+` `pow1/3` `flip-+`
8×	`add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `log-prod`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`rem-log-exp` `distribute-lft-out`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp`

Counts

4 → 82

Calls

4 calls:

3.0ms	(cbrt (+ 1.0 (exp x)))
3.0ms	(cbrt (+ 1.0 (exp x)))
4.0ms	(log (cbrt (+ 1.0 (exp x))))
9.0ms	(log (* (cbrt (+ 1.0 (exp x))) (cbrt (+ 1.0 (exp x)))))

series634.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(cbrt (+ 1.0 (exp x)))
120.0ms	(cbrt (+ 1.0 (exp x)))
195.0ms	(log (cbrt (+ 1.0 (exp x))))
193.0ms	(log (* (cbrt (+ 1.0 (exp x))) (cbrt (+ 1.0 (exp x)))))

simplify72.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 3 (63.0ms)

Iter	Nodes	Cost
0	271	770
1	701	685
2	2411	670
3	5001	666

prune311.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.5b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 1/2 (pow x 2) (+ x 2.0))
0.0b	(- (log (fma 1/2 (pow x 2) (+ x 2.0))) (* x y))
7.6b	(log (fma 1/2 (pow x 2) (+ x 2.0)))

rewrite7.0ms

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:

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

series145.0ms

Counts

3 → 9

Calls

3 calls:

17.0ms	(fma 1/2 (pow x 2) (+ x 2.0))
77.0ms	(- (log (fma 1/2 (pow x 2) (+ x 2.0))) (* x y))
51.0ms	(log (fma 1/2 (pow x 2) (+ x 2.0)))

simplify84.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 3 (79.0ms)

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

prune162.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (exp (log (log (fma 1/2 (pow x 2) (+ x 2.0))))) (* x y))
0.0b	(log (log (fma 1/2 (pow x 2) (+ x 2.0))))
0.3b	(exp (log (log (fma 1/2 (pow x 2) (+ x 2.0)))))
7.6b	(log (fma 1/2 (pow x 2) (+ x 2.0)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

19×	`log-prod`
12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `exp-sum`
11×	`pow1`
7×	`fma-neg` `prod-diff` `log-pow`
6×	`add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `exp-prod` `add-cbrt-cube` `log1p-expm1-u`
2×	`rem-log-exp`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `rem-exp-log`

Counts

4 → 75

Calls

4 calls:

6.0ms	(- (exp (log (log (fma 1/2 (pow x 2) (+ x 2.0))))) (* x y))
2.0ms	(log (log (fma 1/2 (pow x 2) (+ x 2.0))))
2.0ms	(exp (log (log (fma 1/2 (pow x 2) (+ x 2.0)))))
2.0ms	(log (fma 1/2 (pow x 2) (+ x 2.0)))

series293.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- (exp (log (log (fma 1/2 (pow x 2) (+ x 2.0))))) (* x y))
107.0ms	(log (log (fma 1/2 (pow x 2) (+ x 2.0))))
58.0ms	(exp (log (log (fma 1/2 (pow x 2) (+ x 2.0)))))
50.0ms	(log (fma 1/2 (pow x 2) (+ x 2.0)))

simplify40.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	382	809
1	1323	693
2	5002	666

prune253.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.5b

regimes57.0ms

Accuracy

86.4% (0.2b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 1.9b

bsearch50.0ms

Steps

Iters	Range		Point
8	-0.007295393535134763	-5.1833216364644605e-06	-8.057362563360427e-05

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	46
1	41	46

end0.0ms

sample1.7s

Algorithm

intervals

Results

969.0ms	2371×	body	10240	exit
334.0ms	8347×	body	80	valid
71.0ms	263×	body	640	valid
63.0ms	125×	body	1280	valid
31.0ms	190×	body	320	valid
12.0ms	122×	body	160	valid