Details

Time bar (total: 5.6s)

sample106.0ms

Algorithm
intervals
Results
25.0ms61×body10240exit
23.0ms44×body1280valid
18.0ms321×body80valid
15.0ms58×body640valid
5.0ms26×body320valid
1.0ms11×body160valid

simplify38.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (36.0ms)

IterNodesCost
04716
112416
236516
3137616
4500115

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.6b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
0.0b
(exp (- (* (+ 1.0 eps) x)))
0.0b
(exp (- (* (- 1.0 eps) x)))
2.7b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
78×exp-neg
76×frac-times
59×neg-sub0 exp-diff
38×associate-*r/ associate-*l/
31×flip3-- flip--
27×flip3-+ flip-+
19×un-div-inv
15×add-sqr-sqrt
12×exp-prod
10×*-un-lft-identity add-log-exp
8×add-cube-cbrt
6×pow1 associate-*l* add-cbrt-cube
5×add-exp-log
4×expm1-log1p-u log1p-expm1-u rem-exp-log
3×associate-*r*
2×distribute-lft-neg-in neg-mul-1 distribute-rgt-neg-in neg-log difference-of-squares
1×sub-neg times-frac fma-neg diff-log prod-diff pow-prod-down prod-exp *-commutative cbrt-unprod distribute-lft-out-- unswap-sqr
Counts
4 → 167
Calls
4 calls:
13.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
3.0ms
(exp (- (* (+ 1.0 eps) x)))
4.0ms
(exp (- (* (- 1.0 eps) x)))
17.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series312.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
26.0ms
(exp (- (* (+ 1.0 eps) x)))
27.0ms
(exp (- (* (- 1.0 eps) x)))
205.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify140.0ms

Algorithm
egg-herbie
Counts
179 → 179
Iterations

Useful iterations: 2 (107.0ms)

IterNodesCost
012853925
145753627
250013589

prune489.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.6b

localize10.0ms

Local error

Found 1 expressions with local error:

6.8b
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
1×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
1 → 10
Calls
1 calls:
1.0ms
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

series43.0ms

Counts
1 → 3
Calls
1 calls:
42.0ms
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

simplify30.0ms

Algorithm
egg-herbie
Counts
13 → 13
Iterations

Useful iterations: 3 (27.0ms)

IterNodesCost
04289
113678
272278
3500275

prune51.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize8.0ms

Local error

Found 1 expressions with local error:

0.0b
(fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
1×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
1 → 10
Calls
1 calls:
1.0ms
(fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)

series40.0ms

Counts
1 → 3
Calls
1 calls:
40.0ms
(fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)

simplify121.0ms

Algorithm
egg-herbie
Counts
13 → 13
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
04982
113267
253467
3307667
4500167

prune47.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)
0.8b
(* (sqrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)) (sqrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)))
5.4b
(sqrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0))
5.4b
(sqrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
24×sqrt-prod
21×pow1
14×add-cube-cbrt *-un-lft-identity
10×sqrt-pow1 pow1/2
8×swap-sqr
6×add-exp-log associate-*r* associate-*l* add-cbrt-cube
5×pow-prod-up
4×expm1-log1p-u log1p-expm1-u add-log-exp unswap-sqr
3×pow-prod-down pow-sqr
2×rem-sqrt-square
1×pow2 pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod fma-udef
Counts
4 → 91
Calls
4 calls:
1.0ms
(fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)
6.0ms
(* (sqrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)) (sqrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)))
1.0ms
(sqrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0))
2.0ms
(sqrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0))

series340.0ms

Counts
4 → 12
Calls
4 calls:
174.0ms
(fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)
39.0ms
(* (sqrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)) (sqrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)))
61.0ms
(sqrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0))
65.0ms
(sqrt (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0))

simplify181.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
0181721
1656625
24112593
35001593

prune247.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.5b

regimes98.0ms

Accuracy

96.7% (0.5b remaining)

Error of 1.0b against oracle of 0.5b and baseline of 16.4b

bsearch135.0ms

Steps
ItersRangePoint
9
1.5006309519768893e-05
674.2754902356271
295.27480666079055

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04530
15730
25730

end0.0ms

sample3.1s

Algorithm
intervals
Results
837.0ms1932×body10240exit
820.0ms1769×body1280valid
589.0ms9961×body80valid
345.0ms1255×body640valid
110.0ms602×body320valid
38.0ms328×body160valid