Details

sample34.0ms

Algorithm

intervals

Results

12.0ms	74×	body	1280	valid
5.0ms	53×	body	640	valid
5.0ms	27×	body	320	valid
4.0ms	195×	body	80	valid
0.0ms	11×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	3
1	13	3
2	15	3
3	15	3

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.0b

localize4.0ms

Local error

Found 1 expressions with local error:

3.3b	(- (exp x) 1.0)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
1×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 14

Calls

1 calls:

4.0ms

(- (exp x) 1.0)

series14.0ms

Counts

1 → 3

Calls

1 calls:

14.0ms

(- (exp x) 1.0)

simplify54.0ms

Algorithm

egg-herbie

Counts

17 → 17

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	81	72
1	185	67
2	499	66
3	1399	66
4	5002	66

prune37.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (pow x 2) (+ (* x 1/6) 1/2)) x)
0.0b	(* (pow x 2) (+ (* x 1/6) 1/2))
0.3b	(* x 1/6)
2.8b	(/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) x)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
17×	`add-cube-cbrt` `*-un-lft-identity`
13×	`add-exp-log`
11×	`associate-l`
10×	`add-cbrt-cube`
9×	`times-frac`
6×	`pow1` `associate-r` `add-log-exp`
5×	`unswap-sqr`
4×	`unpow-prod-down` `prod-exp`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `associate-r/` `-commutative` `cbrt-unprod` `associate-/l/` `unpow2` `sqr-pow`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `frac-2neg` `div-exp` `pow-prod-down` `pow-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 91

Calls

4 calls:

8.0ms	(+ (* (pow x 2) (+ (* x 1/6) 1/2)) x)
8.0ms	(* (pow x 2) (+ (* x 1/6) 1/2))
3.0ms	(* x 1/6)
10.0ms	(/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) x)

series154.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* (pow x 2) (+ (* x 1/6) 1/2)) x)
66.0ms	(* (pow x 2) (+ (* x 1/6) 1/2))
13.0ms	(* x 1/6)
48.0ms	(/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) x)

simplify65.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	390	685
1	2030	628
2	5002	628

prune196.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

2.8b	(/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) x)
2.8b	(/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) x)
11.1b	(sqrt (/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) x))
11.1b	(sqrt (/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) x))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
38×	`times-frac`
34×	`add-cube-cbrt` `*-un-lft-identity`
26×	`sqrt-prod`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `associate-/r` `associate-/l`
4×	`rem-sqrt-square` `div-inv` `associate-/l/` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `div-exp` `clear-num` `flip-+`

Counts

4 → 108

Calls

4 calls:

10.0ms	(/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) x)
10.0ms	(/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) x)
7.0ms	(sqrt (/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) x))
7.0ms	(sqrt (/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) x))

series296.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) x)
43.0ms	(/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) x)
99.0ms	(sqrt (/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) x))
104.0ms	(sqrt (/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) x))

simplify43.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	249	1314
1	978	1204
2	5001	1184

prune349.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp x) 1.0)
0.0b	(/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (+ (exp x) 1.0))
0.0b	(* (exp x) (exp x))
3.2b	(- (* (exp x) (exp x)) (* 1.0 1.0))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

36×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
24×	`add-cube-cbrt`
18×	`exp-prod`
16×	`times-frac`
11×	`pow1`
8×	`add-cbrt-cube` `add-log-exp`
6×	`add-exp-log` `distribute-lft-out` `difference-of-squares`
4×	`pow-prod-down` `associate-/r` `pow-sqr` `pow-prod-up` `associate-/l`
3×	`swap-sqr` `associate-r` `associate-l`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `pow2` `sub-neg` `frac-2neg` `pow-plus` `diff-log` `div-sub` `div-exp` `prod-exp` `clear-num` `sum-log` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 100

Calls

4 calls:

4.0ms	(+ (exp x) 1.0)
11.0ms	(/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (+ (exp x) 1.0))
10.0ms	(* (exp x) (exp x))
6.0ms	(- (* (exp x) (exp x)) (* 1.0 1.0))

series99.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+ (exp x) 1.0)
52.0ms	(/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (+ (exp x) 1.0))
13.0ms	(* (exp x) (exp x))
25.0ms	(- (* (exp x) (exp x)) (* 1.0 1.0))

simplify54.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	376	824
1	1712	737
2	5001	719

prune194.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes18.0ms

Accuracy

99% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.3b

bsearch33.0ms

Steps

Iters	Range		Point
10	-402.67606408878214	-8.303200230518375e-17	-0.00019132623240596211

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	15
1	26	15

end0.0ms

sample884.0ms

Algorithm

intervals

Results

389.0ms	2337×	body	1280	valid
179.0ms	1670×	body	640	valid
101.0ms	5512×	body	80	valid
53.0ms	786×	body	320	valid
17.0ms	391×	body	160	valid