Details

sample79.0ms

Algorithm

intervals

Results

55.0ms	192×	body	1280	valid
5.0ms	238×	body	80	valid
5.0ms	30×	body	640	valid
2.0ms	19×	body	320	valid
1.0ms	10×	body	160	valid

simplify221.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	5
1	26	5
2	41	5
3	55	5
4	67	5
5	104	5
6	161	5
7	344	5
8	1454	5
9	5001	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
3.6b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
18×	`prod-diff`
16×	`add-cube-cbrt`
11×	`associate-+l+`
9×	`add-log-exp`
5×	`fma-def`
4×	`frac-add`
3×	`flip3--` `fma-neg` `flip--` `distribute-lft-out--`
2×	`pow1` `add-exp-log` `neg-sub0` `exp-neg` `expm1-log1p-u` `sub-neg` `exp-diff` `diff-log` `sum-log` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `associate-+l-` `flip3-+` `flip-+`

Counts

2 → 65

Calls

2 calls:

11.0ms	(- (exp x) 2.0)
55.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series70.0ms

Counts

2 → 6

Calls

2 calls:

13.0ms	(- (exp x) 2.0)
57.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify33.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	282	506
1	1008	381
2	5001	367

prune152.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
0.1b	(* 1/12 (pow x 4))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
7×	`add-exp-log` `associate-r`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`unpow-prod-down` `add-cbrt-cube`
3×	`associate-l` `prod-exp` `unswap-sqr`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

2 → 37

Calls

2 calls:

0.0ms	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
13.0ms	(* 1/12 (pow x 4))

series162.0ms

Counts

2 → 6

Calls

2 calls:

124.0ms	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
38.0ms	(* 1/12 (pow x 4))

simplify84.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	123	177
1	469	163
2	2175	160
3	5002	160

prune103.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (exp x) 2.0) (exp x))
0.0b	(fma (- 2.0) 2.0 (exp (+ x x)))
0.0b	(/ (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (* (+ (exp x) 2.0) (exp x)))
4.2b	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-cbrt-cube`
10×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-exp-log`
8×	`add-cube-cbrt`
6×	`pow1`
4×	`expm1-log1p-u` `associate-l` `associate-*l/` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `associate-r` `associate-/l*`
2×	`cbrt-undiv` `flip3-+` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+` `fma-udef`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `div-inv` `distribute-lft-out` `unswap-sqr`

Counts

4 → 68

Calls

4 calls:

36.0ms	(* (+ (exp x) 2.0) (exp x))
0.0ms	(fma (- 2.0) 2.0 (exp (+ x x)))
17.0ms	(/ (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (* (+ (exp x) 2.0) (exp x)))
0.0ms	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

series376.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (+ (exp x) 2.0) (exp x))
43.0ms	(fma (- 2.0) 2.0 (exp (+ x x)))
214.0ms	(/ (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (* (+ (exp x) 2.0) (exp x)))
96.0ms	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

simplify41.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	309	842
1	1272	718
2	5002	714

prune221.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (exp x) (exp x)) (* 2.0 2.0))
0.0b	(* (- (* (exp x) (exp x)) (* 2.0 2.0)) (exp x))
0.0b	(* (exp x) (exp x))
4.2b	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
18×	`exp-prod`
16×	`add-cube-cbrt` `*-un-lft-identity`
13×	`pow1`
8×	`add-cbrt-cube`
7×	`associate-l`
6×	`associate-r` `add-log-exp`
5×	`add-exp-log` `pow-prod-down`
4×	`expm1-log1p-u` `pow-sqr` `pow-prod-up` `log1p-expm1-u`
3×	`swap-sqr`
2×	`flip3--` `associate-l/` `prod-exp` `-commutative` `flip--` `cbrt-unprod` `difference-of-squares` `unswap-sqr`
1×	`pow2` `sub-neg` `pow-plus` `fma-neg` `diff-log` `prod-diff` `fma-udef`

Counts

4 → 86

Calls

4 calls:

16.0ms	(- (* (exp x) (exp x)) (* 2.0 2.0))
64.0ms	(* (- (* (exp x) (exp x)) (* 2.0 2.0)) (exp x))
20.0ms	(* (exp x) (exp x))
0.0ms	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

series174.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(- (* (exp x) (exp x)) (* 2.0 2.0))
43.0ms	(* (- (* (exp x) (exp x)) (* 2.0 2.0)) (exp x))
13.0ms	(* (exp x) (exp x))
94.0ms	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

simplify47.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	322	627
1	1349	531
2	5002	512

prune289.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes12.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	5
1	11	5

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.9s	5638×	body	1280	valid
231.0ms	1254×	body	640	valid
196.0ms	7951×	body	80	valid
69.0ms	651×	body	320	valid
23.0ms	284×	body	160	valid