Details

Time bar (total: 5.8s)

sample105.0ms

Algorithm
intervals
Results
29.0ms74×body10240exit
23.0ms357×body80valid
20.0ms51×body1280valid
9.0ms36×body640valid
4.0ms21×body320valid
2.0ms17×body160valid

simplify39.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (37.0ms)

IterNodesCost
04716
112416
236516
3137616
4500115

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.0b

localize21.0ms

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)))
3.2b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite50.0ms

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:
14.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
3.0ms
(exp (- (* (+ 1.0 eps) x)))
4.0ms
(exp (- (* (- 1.0 eps) x)))
18.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series309.0ms

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)))
31.0ms
(exp (- (* (- 1.0 eps) x)))
199.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify148.0ms

Algorithm
egg-herbie
Counts
179 → 179
Iterations

Useful iterations: 2 (114.0ms)

IterNodesCost
012853925
145753627
250013589

prune450.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 1 expressions with local error:

5.6b
(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))))

simplify28.0ms

Algorithm
egg-herbie
Counts
13 → 13
Iterations

Useful iterations: 3 (26.0ms)

IterNodesCost
04289
113678
272278
3500275

prune47.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 3 expressions with local error:

0.6b
(expm1 (log1p (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))))
5.6b
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))
9.7b
(log1p (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))

rewrite3.0ms

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:
1.0ms
(expm1 (log1p (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))))
1.0ms
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))
1.0ms
(log1p (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))

series282.0ms

Counts
3 → 9
Calls
3 calls:
144.0ms
(expm1 (log1p (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))))
45.0ms
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))
93.0ms
(log1p (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))

simplify90.0ms

Algorithm
egg-herbie
Counts
41 → 41
Iterations

Useful iterations: 3 (85.0ms)

IterNodesCost
0249372
1848331
23865305
35002297

prune135.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

9.5b
(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
9.5b
(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
9.5b
(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
9.7b
(log1p (* (* (cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))) (cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))) (cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
5×expm1-log1p-u
4×pow1 add-exp-log add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3
1×log1p-udef log1p-expm1
Counts
4 → 50
Calls
4 calls:
1.0ms
(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
1.0ms
(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
1.0ms
(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
1.0ms
(log1p (* (* (cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))) (cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))) (cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))))

series551.0ms

Counts
4 → 12
Calls
4 calls:
148.0ms
(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
156.0ms
(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
153.0ms
(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
94.0ms
(log1p (* (* (cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))) (cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))) (cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))))

simplify88.0ms

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 3 (78.0ms)

IterNodesCost
0248980
1816863
23284792
35001788

prune254.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

regimes107.0ms

Accuracy

96.5% (0.6b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 16.5b

bsearch141.0ms

Steps
ItersRangePoint
10
0.0016736950671300647
38794610249.56377
3.591957276208114

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04822
15822
25822

end0.0ms

sample2.8s

Algorithm
intervals
Results
794.0ms1929×body10240exit
749.0ms1728×body1280valid
540.0ms10048×body80valid
320.0ms1241×body640valid
109.0ms642×body320valid
35.0ms330×body160valid