Details

Time bar (total: 7.2s)

sample146.0ms

Algorithm
intervals
Results
50.0ms314×body80valid
40.0ms54×body1280valid
19.0ms39×body640valid
10.0ms71×body80overflowed
6.0ms16×body320valid
3.0ms13×body160valid

simplify38.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (36.0ms)

IterNodesCost
04716
112416
236516
3137616
4500115

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ 1.0 eps) x)
0.0b
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
0.0b
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
3.0b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite125.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
80×exp-neg frac-times
60×neg-sub0 exp-diff
42×associate-*l/
40×associate-*r/
31×flip3-- flip3-+ flip-- flip-+
21×add-sqr-sqrt
20×un-div-inv
16×*-un-lft-identity
14×associate-*l*
10×pow1 add-cube-cbrt add-cbrt-cube
9×associate-*r*
8×add-exp-log
6×add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×distribute-lft-out difference-of-squares
1×sub-neg times-frac fma-neg diff-log prod-diff distribute-lft-out--
Counts
4 → 182
Calls
4 calls:
10.0ms
(* (+ 1.0 eps) x)
31.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
44.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
29.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series311.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(* (+ 1.0 eps) x)
48.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
47.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
191.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify66.0ms

Algorithm
egg-herbie
Counts
194 → 194
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
013754113
150023879

prune510.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize9.0ms

Local error

Found 1 expressions with local error:

6.4b
(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:
0.0ms
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

series37.0ms

Counts
1 → 3
Calls
1 calls:
37.0ms
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

simplify29.0ms

Algorithm
egg-herbie
Counts
13 → 13
Iterations

Useful iterations: 3 (26.0ms)

IterNodesCost
04289
113678
272278
3500275

prune54.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.5b

localize14.0ms

Local error

Found 3 expressions with local error:

0.5b
(expm1 (log1p (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))))
6.4b
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))
11.4b
(log1p (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
4×expm1-log1p-u
3×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube log1p-expm1-u add-log-exp
1×log1p-udef expm1-log1p log1p-expm1 fma-udef expm1-udef
Counts
3 → 32
Calls
3 calls:
0.0ms
(expm1 (log1p (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))))
0.0ms
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))
0.0ms
(log1p (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))

series267.0ms

Counts
3 → 9
Calls
3 calls:
138.0ms
(expm1 (log1p (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))))
41.0ms
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))
87.0ms
(log1p (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))

simplify92.0ms

Algorithm
egg-herbie
Counts
41 → 41
Iterations

Useful iterations: 3 (87.0ms)

IterNodesCost
0249372
1848331
23865305
35002297

prune141.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.5b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x eps) (* 1.0 x))
0.0b
(/ (exp (- (* x eps) (* 1.0 x))) eps)
0.0b
(/ 1 (exp (fma x eps (* 1.0 x))))
3.0b
(fma 1.0 (/ (exp (- (* x eps) (* 1.0 x))) eps) (- (* 1.0 (+ (/ 1 (exp (fma x eps (* 1.0 x)))) (exp (- (* x eps) (* 1.0 x))))) (* 1.0 (/ (exp (- (+ (* x eps) (* 1.0 x)))) eps))))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
30×times-frac
25×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×exp-sum
9×associate-/l*
8×add-cbrt-cube
7×associate-/r*
6×add-exp-log add-log-exp
5×pow1 fma-udef
4×expm1-log1p-u sub-neg pow-flip prod-diff log1p-expm1-u
3×exp-prod div-exp
2×cbrt-undiv frac-2neg clear-num div-inv
1×+-commutative rec-exp fma-def flip3-+ exp-diff 1-exp sum-log flip-+ associate-/l/ inv-pow
Counts
4 → 106
Calls
4 calls:
3.0ms
(+ (* x eps) (* 1.0 x))
16.0ms
(/ (exp (- (* x eps) (* 1.0 x))) eps)
4.0ms
(/ 1 (exp (fma x eps (* 1.0 x))))
0.0ms
(fma 1.0 (/ (exp (- (* x eps) (* 1.0 x))) eps) (- (* 1.0 (+ (/ 1 (exp (fma x eps (* 1.0 x)))) (exp (- (* x eps) (* 1.0 x))))) (* 1.0 (/ (exp (- (+ (* x eps) (* 1.0 x)))) eps))))

series267.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(+ (* x eps) (* 1.0 x))
29.0ms
(/ (exp (- (* x eps) (* 1.0 x))) eps)
21.0ms
(/ 1 (exp (fma x eps (* 1.0 x))))
176.0ms
(fma 1.0 (/ (exp (- (* x eps) (* 1.0 x))) eps) (- (* 1.0 (+ (/ 1 (exp (fma x eps (* 1.0 x)))) (exp (- (* x eps) (* 1.0 x))))) (* 1.0 (/ (exp (- (+ (* x eps) (* 1.0 x)))) eps))))

simplify48.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
04171097
11489980
25002935

prune412.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.5b

regimes109.0ms

Accuracy

96.4% (0.6b remaining)

Error of 1.0b against oracle of 0.5b and baseline of 16.7b

bsearch151.0ms

Steps
ItersRangePoint
7
12.48454705949842
1654.2658435481542
117.76041323671743

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04731
15931
25931

end0.0ms

sample4.3s

Algorithm
intervals
Results
1.5s9782×body80valid
1.3s1727×body1280valid
631.0ms1254×body640valid
284.0ms1896×body80overflowed
242.0ms657×body320valid
89.0ms330×body160valid