Details

sample33.0ms

Algorithm

intervals

Results

11.0ms	62×	body	1280	valid
7.0ms	188×	body	80	valid
5.0ms	47×	body	640	valid
2.0ms	26×	body	320	valid
1.0ms	22×	body	160	valid

simplify7.0ms

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: 37.5b

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
4.7b	(- (exp x) 1.0)

rewrite35.0ms

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:

23.0ms	(/ (- (exp x) 1.0) x)
10.0ms	(- (exp x) 1.0)

series51.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(/ (- (exp x) 1.0) x)
13.0ms	(- (exp x) 1.0)

simplify78.0ms

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

prune160.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))
0.2b	(* 1/6 (pow x 2))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
8×	`associate-r`
7×	`add-exp-log` `add-log-exp`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`unpow-prod-down` `add-cbrt-cube` `unswap-sqr`
3×	`associate-l` `prod-exp` `sum-log`
2×	`pow1` `unpow2` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `associate-+r+` `flip3-+` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`

Counts

2 → 40

Calls

2 calls:

24.0ms	(+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))
11.0ms	(* 1/6 (pow x 2))

series40.0ms

Counts

2 → 6

Calls

2 calls:

17.0ms	(+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))
23.0ms	(* 1/6 (pow x 2))

simplify34.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	201	231
1	852	202
2	5001	199

prune107.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x)))
0.0b	(pow (exp x) 3)
0.0b	(/ (- (pow (exp x) 3) (pow 1.0 3)) (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x))))
4.6b	(- (pow (exp x) 3) (pow 1.0 3))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

158×	`add-sqr-sqrt`
88×	`*-un-lft-identity`
80×	`difference-of-squares`
75×	`times-frac`
63×	`unpow-prod-down` `cube-prod`
41×	`sqr-pow`
38×	`add-cube-cbrt`
25×	`associate-/l*` `distribute-lft-out--`
8×	`add-log-exp`
7×	`add-cbrt-cube`
6×	`add-exp-log`
5×	`pow1` `difference-cubes`
4×	`pow-pow`
3×	`pow-unpow` `exp-prod` `associate-/r*`
2×	`associate-+l+` `flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `distribute-rgt-in` `cube-mult` `pow-to-exp` `sub-neg` `frac-2neg` `distribute-lft-in` `diff-log` `unpow3` `div-sub` `div-exp` `pow-exp` `clear-num` `sum-log` `div-inv` `rem-cube-cbrt`

Counts

4 → 193

Calls

4 calls:

23.0ms	(+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x)))
4.0ms	(pow (exp x) 3)
109.0ms	(/ (- (pow (exp x) 3) (pow 1.0 3)) (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x))))
30.0ms	(- (pow (exp x) 3) (pow 1.0 3))

series167.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x)))
20.0ms	(pow (exp x) 3)
83.0ms	(/ (- (pow (exp x) 3) (pow 1.0 3)) (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x))))
32.0ms	(- (pow (exp x) 3) (pow 1.0 3))

simplify98.0ms

Algorithm

egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	596	3033
1	2606	2958
2	5002	2879

prune753.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.0b	(+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x)))
0.0b	(/ (- (* (exp (+ x x)) (exp x)) (pow 1.0 3)) (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x))))
4.6b	(- (* (exp (+ x x)) (exp x)) (pow 1.0 3))

rewrite309.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
13×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`times-frac`
10×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`difference-cubes` `exp-sum` `pow3`
4×	`pow1` `associate-/l*`
3×	`flip3-+` `associate-/r*` `flip-+`
2×	`+-commutative` `associate-+l+` `flip3--` `sum-log` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv` `distribute-lft-out`

Counts

4 → 74

Calls

4 calls:

6.0ms	(+ 1.0 (exp x))
23.0ms	(+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x)))
213.0ms	(/ (- (* (exp (+ x x)) (exp x)) (pow 1.0 3)) (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x))))
65.0ms	(- (* (exp (+ x x)) (exp x)) (pow 1.0 3))

series148.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+ 1.0 (exp x))
32.0ms	(+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x)))
78.0ms	(/ (- (* (exp (+ x x)) (exp x)) (pow 1.0 3)) (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x))))
31.0ms	(- (* (exp (+ x x)) (exp x)) (pow 1.0 3))

simplify54.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	414	1132
1	1801	1007
2	5001	992

prune519.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes33.0ms

Accuracy

99% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.8b

bsearch81.0ms

Steps

Iters	Range		Point
10	-569.2304264003914	-2.5612855498029964e-09	-8.498348281129445e-05

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	31
1	43	31

end0.0ms

sample904.0ms

Algorithm

intervals

Results

387.0ms	2195×	body	1280	valid
189.0ms	1670×	body	640	valid
112.0ms	5454×	body	80	valid
63.0ms	861×	body	320	valid
20.0ms	384×	body	160	valid