Details

sample122.0ms

Algorithm

intervals

Results

38.0ms	302×	body	80	valid
34.0ms	50×	body	1280	valid
16.0ms	37×	body	640	valid
8.0ms	27×	body	320	valid
6.0ms	51×	body	80	overflowed
2.0ms	12×	body	160	valid

simplify36.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (34.0ms)

Iter	Nodes	Cost
0	46	16
1	122	16
2	347	16
3	1295	16
4	5001	15

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
0.0b	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
0.0b	(* (- 1.0 eps) x)
3.4b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
80×	`exp-neg` `frac-times`
60×	`neg-sub0` `exp-diff`
42×	`associate-*l/`
40×	`associate-*r/`
32×	`flip3--` `flip--`
30×	`flip3-+` `flip-+`
23×	`add-sqr-sqrt`
20×	`un-div-inv`
16×	`*-un-lft-identity`
15×	`associate-l`
10×	`pow1` `add-cube-cbrt` `add-cbrt-cube`
9×	`associate-r`
8×	`add-exp-log`
6×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `difference-of-squares` `unswap-sqr`
2×	`distribute-lft-out--`
1×	`sub-neg` `times-frac` `diff-log` `distribute-lft-out`

Counts

4 → 173

Calls

4 calls:

32.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
44.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
10.0ms	(* (- 1.0 eps) x)
28.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series324.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
53.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
28.0ms	(* (- 1.0 eps) x)
197.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify153.0ms

Algorithm

egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 2 (115.0ms)

Iter	Nodes	Cost
0	1253	4065
1	4712	3787
2	5001	3778

prune435.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 0.6666666666666667 (pow x 3))
6.4b	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`associate-r`
7×	`add-exp-log` `add-log-exp`
6×	`add-cube-cbrt` `*-un-lft-identity`
4×	`unpow-prod-down` `cube-prod` `add-cbrt-cube` `unswap-sqr`
3×	`associate-l` `prod-exp`
2×	`pow1` `diff-log` `sqr-pow`
1×	`cube-mult` `pow-to-exp` `sub-neg` `flip3--` `unpow3` `pow-exp` `associate--l+` `sum-log` `*-commutative` `flip--` `cbrt-unprod`

Counts

2 → 45

Calls

2 calls:

7.0ms	(* 0.6666666666666667 (pow x 3))
31.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

series77.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(* 0.6666666666666667 (pow x 3))
38.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

simplify34.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	207	270
1	894	242
2	5002	238

prune108.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize13.0ms

Local error

Found 4 expressions with local error:

6.4b	(- (+ (* (* (cbrt (* 0.6666666666666667 (pow x 3))) (cbrt (* 0.6666666666666667 (pow x 3)))) (cbrt (* 0.6666666666666667 (pow x 3)))) 2.0) (* 1.0 (pow x 2)))
43.6b	(cbrt (* 0.6666666666666667 (pow x 3)))
43.6b	(cbrt (* 0.6666666666666667 (pow x 3)))
43.6b	(cbrt (* 0.6666666666666667 (pow x 3)))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`cbrt-prod` `pow1/3`
2×	`diff-log`
1×	`sub-neg` `flip3--` `associate--l+` `sum-log` `flip--`

Counts

4 → 41

Calls

4 calls:

110.0ms	(- (+ (* (* (cbrt (* 0.6666666666666667 (pow x 3))) (cbrt (* 0.6666666666666667 (pow x 3)))) (cbrt (* 0.6666666666666667 (pow x 3)))) 2.0) (* 1.0 (pow x 2)))
2.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))
2.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))
2.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))

series180.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(- (+ (* (* (cbrt (* 0.6666666666666667 (pow x 3))) (cbrt (* 0.6666666666666667 (pow x 3)))) (cbrt (* 0.6666666666666667 (pow x 3)))) 2.0) (* 1.0 (pow x 2)))
40.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))
35.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))
36.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))

simplify71.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 3 (66.0ms)

Iter	Nodes	Cost
0	133	470
1	484	391
2	2180	346
3	5001	327

prune163.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize18.0ms

Local error

Found 4 expressions with local error:

43.6b	(cbrt (* 0.6666666666666667 (pow x 3)))
43.6b	(cbrt (* 0.6666666666666667 (pow x 3)))
43.6b	(cbrt (* 0.6666666666666667 (pow x 3)))
43.6b	(cbrt (* 0.6666666666666667 (pow x 3)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `pow1/3` `add-cbrt-cube` `add-log-exp`

Counts

4 → 36

Calls

4 calls:

2.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))
2.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))
2.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))
2.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))

series150.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))
40.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))
35.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))
39.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))

simplify112.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	36	192
1	80	164
2	122	156
3	218	156
4	761	156
5	2445	156
6	5001	156

prune182.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

regimes47.0ms

Accuracy

96.7% (0.5b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 16.7b

bsearch205.0ms

Steps

Iters	Range		Point
10	6.5383237107547055e-09	649.3281407255394	329.6365001759523

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	60
1	73	60
2	73	60

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.2s	1706×	body	1280	valid
1.2s	9989×	body	80	valid
570.0ms	1231×	body	640	valid
223.0ms	1928×	body	80	overflowed
213.0ms	641×	body	320	valid
65.0ms	305×	body	160	valid