Details

sample34.0ms

Algorithm

intervals

Results

13.0ms	79×	body	1280	valid
9.0ms	48×	body	640	valid
3.0ms	165×	body	80	valid
2.0ms	28×	body	320	valid
1.0ms	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: 40.2b

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
3.5b	(- (exp x) 1.0)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 52

Calls

2 calls:

6.0ms	(/ (- (exp x) 1.0) x)
4.0ms	(- (exp x) 1.0)

series55.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(/ (- (exp x) 1.0) x)
15.0ms	(- (exp x) 1.0)

simplify80.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	222	329
1	625	311
2	2739	309
3	5001	309

prune116.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize8.0ms

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)
3.7b	(/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) x)

rewrite31.0ms

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)
7.0ms	(* (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)

series155.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ (* (pow x 2) (+ (* x 1/6) 1/2)) x)
67.0ms	(* (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)

simplify67.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 1 (12.0ms)

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

prune205.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (- (exp x) 1.0) (/ 1 x))
3.5b	(- (exp x) 1.0)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
13×	`associate-r`
11×	`add-exp-log` `times-frac`
10×	`add-cube-cbrt`
7×	`add-cbrt-cube`
5×	`associate-l`
4×	`pow1` `prod-exp` `add-log-exp`
3×	`flip3--` `flip--` `unswap-sqr`
2×	`frac-times` `div-exp` `associate-*l/` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
1×	`cbrt-undiv` `sub-neg` `rec-exp` `diff-log` `1-exp` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `div-inv`

Counts

2 → 56

Calls

2 calls:

10.0ms	(* (- (exp x) 1.0) (/ 1 x))
4.0ms	(- (exp x) 1.0)

series57.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(* (- (exp x) 1.0) (/ 1 x))
18.0ms	(- (exp x) 1.0)

simplify37.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	287	345
1	1233	304
2	5001	287

prune105.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite31.0ms

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:

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

series99.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(* (exp x) (exp x))
47.0ms	(/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (+ (exp x) 1.0))
8.0ms	(+ (exp x) 1.0)
31.0ms	(- (* (exp x) (exp x)) (* 1.0 1.0))

simplify63.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	376	823
1	1712	737
2	5001	719

prune203.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes22.0ms

Accuracy

99% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 21.1b

bsearch30.0ms

Steps

Iters	Range		Point
9	-0.11986014733990268	-1.6789357321840064e-10	-0.00013454200281456905

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	10
1	26	10

end0.0ms

sample872.0ms

Algorithm

intervals

Results

393.0ms	2299×	body	1280	valid
173.0ms	1680×	body	640	valid
100.0ms	5443×	body	80	valid
57.0ms	847×	body	320	valid
16.0ms	383×	body	160	valid