Details

sample157.0ms

Algorithm

intervals

Results

47.0ms	370×	body	80	valid
36.0ms	57×	body	10240	exit
26.0ms	43×	body	1280	valid
21.0ms	44×	body	640	valid
6.0ms	21×	body	320	valid
2.0ms	8×	body	160	valid

simplify36.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (35.0ms)

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

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 26.8b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
0.1b	(exp (- (* (+ 1.0 eps) x)))
0.1b	(exp (- (* (- 1.0 eps) x)))
1.5b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
78×	`exp-neg`
76×	`frac-times`
59×	`neg-sub0` `exp-diff`
38×	`associate-r/` `associate-l/`
31×	`flip3--` `flip--`
27×	`flip3-+` `flip-+`
19×	`un-div-inv`
15×	`add-sqr-sqrt`
12×	`exp-prod`
10×	`*-un-lft-identity` `add-log-exp`
8×	`add-cube-cbrt`
6×	`pow1` `associate-l` `add-cbrt-cube`
5×	`add-exp-log`
4×	`rem-exp-log`
3×	`associate-r`
2×	`distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in` `neg-log` `difference-of-squares`
1×	`sub-neg` `times-frac` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 157

Calls

4 calls:

43.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
3.0ms	(exp (- (* (+ 1.0 eps) x)))
4.0ms	(exp (- (* (- 1.0 eps) x)))
27.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series306.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
31.0ms	(exp (- (* (+ 1.0 eps) x)))
27.0ms	(exp (- (* (- 1.0 eps) x)))
199.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify135.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (100.0ms)

Iter	Nodes	Cost
0	1169	3874
1	4198	3608
2	5002	3593

prune430.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.7b

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 0.6666666666666667 (pow x 3))
7.4b	(- (+ (* 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))
30.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

series77.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(* 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

prune129.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.7b

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 0.6666666666666667 (pow x 3))
7.4b	(+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (pow x 2))))

rewrite15.0ms

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` `associate-+r+` `sum-log` `sqr-pow`
1×	`+-commutative` `cube-mult` `pow-to-exp` `associate-+r-` `sub-neg` `flip3-+` `diff-log` `unpow3` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`

Counts

2 → 46

Calls

2 calls:

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

series77.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(* 0.6666666666666667 (pow x 3))
42.0ms	(+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (pow x 2))))

simplify34.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	203	267
1	840	244
2	5002	243

prune128.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 0.6666666666666667 (pow x 3))
0.5b	(exp (log (+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (pow x 2))))))
7.4b	(+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (pow x 2))))
11.4b	(log (+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (pow x 2)))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

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

series200.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* 0.6666666666666667 (pow x 3))
38.0ms	(exp (log (+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (pow x 2))))))
42.0ms	(+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (pow x 2))))
85.0ms	(log (+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (pow x 2)))))

simplify49.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	326	684
1	1309	624
2	5001	606

prune236.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.7b

regimes99.0ms

Accuracy

96.3% (0.6b remaining)

Error of 1.1b against oracle of 0.5b and baseline of 16.0b

bsearch135.0ms

Steps

Iters	Range		Point
7	231.08097083698556	22857.716182190634	254.14528551610528

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	38
1	63	38
2	63	38

end0.0ms

sample4.6s

Algorithm

intervals

Results

1.3s	10091×	body	80	valid
1.2s	1870×	body	10240	exit
1.0s	1692×	body	1280	valid
523.0ms	1292×	body	640	valid
185.0ms	643×	body	320	valid
76.0ms	357×	body	160	valid