Details

sample44.0ms

Algorithm

intervals

Results

21.0ms	87×	body	1280	valid
8.0ms	51×	body	640	valid
3.0ms	89×	body	80	valid
2.0ms	80×	body	80	overflowed
2.0ms	21×	body	320	valid
1.0ms	8×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	4
1	8	4
2	8	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.4b

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (exp x) (- (exp x) 1.0))
2.1b	(- (exp x) 1.0)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 51

Calls

2 calls:

8.0ms	(/ (exp x) (- (exp x) 1.0))
4.0ms	(- (exp x) 1.0)

series45.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(/ (exp x) (- (exp x) 1.0))
14.0ms	(- (exp x) 1.0)

simplify69.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	180	378
1	542	357
2	2210	354
3	5001	354

prune119.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1/2 (+ (* 1/12 x) (/ 1 x)))
0.0b	(+ (* 1/12 x) (/ 1 x))
0.4b	(* 1/12 x)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 43

Calls

3 calls:

18.0ms	(+ 1/2 (+ (* 1/12 x) (/ 1 x)))
5.0ms	(+ (* 1/12 x) (/ 1 x))
3.0ms	(* 1/12 x)

series69.0ms

Counts

3 → 9

Calls

3 calls:

14.0ms	(+ 1/2 (+ (* 1/12 x) (/ 1 x)))
40.0ms	(+ (* 1/12 x) (/ 1 x))
14.0ms	(* 1/12 x)

simplify112.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	200	216
1	705	205
2	3820	204
3	5002	204

prune78.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (exp x) (/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (+ (exp x) 1.0)))
0.0b	(* (exp x) (exp x))
0.0b	(/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (+ (exp x) 1.0))
2.1b	(- (* (exp x) (exp x)) (* 1.0 1.0))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

146×	`times-frac`
125×	`*-un-lft-identity`
85×	`add-sqr-sqrt`
83×	`add-cube-cbrt`
26×	`associate-/r*`
22×	`difference-of-squares`
21×	`distribute-lft-out`
18×	`exp-prod`
13×	`add-cbrt-cube`
11×	`pow1` `associate-/r/`
9×	`add-exp-log`
7×	`associate-/l*`
6×	`div-inv` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`cbrt-undiv` `div-exp` `pow-prod-down` `pow-sqr` `pow-prod-up`
3×	`swap-sqr` `associate-r` `associate-l`
2×	`flip3--` `frac-2neg` `clear-num` `flip--` `associate-/l/`
1×	`pow2` `sub-neg` `pow-plus` `diff-log` `div-sub` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 194

Calls

4 calls:

21.0ms	(/ (exp x) (/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (+ (exp x) 1.0)))
7.0ms	(* (exp x) (exp x))
27.0ms	(/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (+ (exp x) 1.0))
7.0ms	(- (* (exp x) (exp x)) (* 1.0 1.0))

series165.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(/ (exp x) (/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (+ (exp x) 1.0)))
13.0ms	(* (exp x) (exp x))
52.0ms	(/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (+ (exp x) 1.0))
27.0ms	(- (* (exp x) (exp x)) (* 1.0 1.0))

simplify164.0ms

Algorithm

egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 2 (142.0ms)

Iter	Nodes	Cost
0	697	2666
1	4229	2519
2	5001	2515

prune419.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1/12 x) (/ 1 x))
0.2b	(pow (+ (* 1/12 x) (/ 1 x)) 3)
0.4b	(* 1/12 x)
43.9b	(cbrt (pow (+ (* 1/12 x) (/ 1 x)) 3))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

5.0ms	(+ (* 1/12 x) (/ 1 x))
10.0ms	(pow (+ (* 1/12 x) (/ 1 x)) 3)
3.0ms	(* 1/12 x)
13.0ms	(cbrt (pow (+ (* 1/12 x) (/ 1 x)) 3))

series169.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(+ (* 1/12 x) (/ 1 x))
47.0ms	(pow (+ (* 1/12 x) (/ 1 x)) 3)
13.0ms	(* 1/12 x)
61.0ms	(cbrt (pow (+ (* 1/12 x) (/ 1 x)) 3))

simplify47.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	274	467
1	1193	443
2	5002	434

prune147.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes58.0ms

Accuracy

98.2% (0.4b remaining)

Error of 0.8b against oracle of 0.4b and baseline of 21.4b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	15
1	25	15

end0.0ms

sample1.2s

Algorithm

intervals

Results

528.0ms	2281×	body	1280	valid
252.0ms	1624×	body	640	valid
94.0ms	843×	body	320	valid
85.0ms	2863×	body	80	valid
78.0ms	2606×	body	80	overflowed
27.0ms	393×	body	160	valid