Details

sample54.0ms

Algorithm

intervals

Results

24.0ms	64×	body	10240	exit
12.0ms	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

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: 1.1b

localize7.0ms

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)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 45

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))
55.0ms	(- (log (+ 1.0 (exp x))) (* x y))
65.0ms	(log (+ 1.0 (exp x)))

simplify45.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 3 (41.0ms)

Iter	Nodes	Cost
0	207	322
1	584	301
2	1729	298
3	5001	297

prune127.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

localize12.0ms

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)))))

rewrite21.0ms

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×	`frac-times` `add-cbrt-cube` `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 → 74

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)))))

series642.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(cbrt (+ 1.0 (exp x)))
118.0ms	(cbrt (+ 1.0 (exp x)))
189.0ms	(log (cbrt (+ 1.0 (exp x))))
194.0ms	(log (* (cbrt (+ 1.0 (exp x))) (cbrt (+ 1.0 (exp x)))))

simplify69.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	257	729
1	650	645
2	2159	629
3	5001	629

prune422.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.5b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
10×	`add-exp-log` `add-log-exp`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`associate-r`
6×	`log-prod` `add-cbrt-cube`
5×	`pow1`
4×	`unpow-prod-down` `log-div` `unswap-sqr`
3×	`flip3-+` `associate-l` `prod-exp` `associate--l+` `sum-log` `flip-+`
2×	`associate--l-` `unpow2` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `sub-neg` `associate-+r+` `flip3--` `diff-log` `rem-log-exp` `pow-exp` `log-pow` `*-commutative` `flip--` `cbrt-unprod`

Counts

4 → 71

Calls

4 calls:

5.0ms	(* 1/2 (pow x 2))
7.0ms	(+ (* 1/2 (pow x 2)) (+ x 2.0))
9.0ms	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
7.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

series176.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* 1/2 (pow x 2))
18.0ms	(+ (* 1/2 (pow x 2)) (+ x 2.0))
79.0ms	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
55.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

simplify53.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	371	575
1	1439	529
2	5001	520

prune204.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.5b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

11×	`log-prod`
9×	`pow1`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `add-log-exp`
5×	`log-pow`
4×	`exp-prod` `exp-sum` `add-cbrt-cube`
2×	`log-div` `rem-log-exp`
1×	`sub-neg` `flip3--` `flip3-+` `diff-log` `flip--` `flip-+` `rem-exp-log`

Counts

4 → 55

Calls

4 calls:

9.0ms	(- (exp (log (log (+ (* 1/2 (pow x 2)) (+ x 2.0))))) (* x y))
2.0ms	(log (log (+ (* 1/2 (pow x 2)) (+ x 2.0))))
5.0ms	(exp (log (log (+ (* 1/2 (pow x 2)) (+ x 2.0)))))
10.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

series300.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (exp (log (log (+ (* 1/2 (pow x 2)) (+ x 2.0))))) (* x y))
109.0ms	(log (log (+ (* 1/2 (pow x 2)) (+ x 2.0))))
56.0ms	(exp (log (log (+ (* 1/2 (pow x 2)) (+ x 2.0)))))
55.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

simplify42.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	404	731
1	1440	654
2	5002	617

prune189.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.5b

regimes57.0ms

Accuracy

86.9% (0.2b remaining)

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

bsearch49.0ms

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	44	49
1	44	49

end0.0ms

sample1.6s

Algorithm

intervals

Results

941.0ms	2371×	body	10240	exit
308.0ms	8347×	body	80	valid
72.0ms	263×	body	640	valid
62.0ms	125×	body	1280	valid
29.0ms	190×	body	320	valid
11.0ms	122×	body	160	valid