Details

Time bar (total: 7.5s)

sample126.0ms

Algorithm
intervals
Results
36.0ms349×body80valid
28.0ms55×body1280valid
26.0ms46×body10240exit
13.0ms38×body640valid
4.0ms19×body320valid
0.0ms2×body160valid

simplify37.0ms

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: 26.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 1.0 eps) 1.0)
0.0b
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
0.0b
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
1.2b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
80×exp-neg frac-times
63×add-sqr-sqrt
60×neg-sub0 exp-diff
55×*-un-lft-identity
49×add-cube-cbrt
40×associate-*r/ prod-diff associate-*l/
38×times-frac
32×flip3-- flip--
30×flip3-+ flip-+
20×un-div-inv
14×fma-neg
10×associate-*l*
8×pow1 add-cbrt-cube add-log-exp
6×add-exp-log associate-*r*
4×expm1-log1p-u log1p-expm1-u div-inv difference-of-squares
2×sub-neg diff-log pow-prod-down prod-exp *-commutative cbrt-unprod distribute-lft-out-- unswap-sqr
1×distribute-lft-out
Counts
4 → 228
Calls
4 calls:
14.0ms
(- (/ 1.0 eps) 1.0)
32.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
40.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
30.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series324.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(- (/ 1.0 eps) 1.0)
45.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
51.0ms
(* (- (/ 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)))))

simplify68.0ms

Algorithm
egg-herbie
Counts
240 → 240
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
014574705
150024253

prune740.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 1 expressions with local error:

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:
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

prune48.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 4 expressions with local error:

6.8b
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))
11.4b
(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
11.4b
(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
11.4b
(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3
1×fma-udef
Counts
4 → 49
Calls
4 calls:
0.0ms
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))
0.0ms
(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
0.0ms
(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)))))

series483.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))
150.0ms
(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
147.0ms
(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
149.0ms
(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))

simplify76.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 3 (68.0ms)

IterNodesCost
0190752
1639693
22777627
35001621

prune255.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

11.4b
(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
11.4b
(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
11.4b
(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
11.4b
(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u pow1/3 add-cbrt-cube log1p-expm1-u add-log-exp
Counts
4 → 52
Calls
4 calls:
0.0ms
(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
0.0ms
(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
0.0ms
(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)))))

series591.0ms

Counts
4 → 12
Calls
4 calls:
149.0ms
(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
151.0ms
(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
149.0ms
(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
142.0ms
(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))

simplify66.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
0176884
1578820
22267732
35001732

prune290.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

regimes94.0ms

Accuracy

96.2% (0.6b remaining)

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

bsearch167.0ms

Steps
ItersRangePoint
9
0.08251057621007524
71346.30170445908
335.02122944782855

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05427
16727
26727

end0.0ms

sample3.9s

Algorithm
intervals
Results
1.1s10117×body80valid
922.0ms1815×body10240exit
912.0ms1738×body1280valid
428.0ms1267×body640valid
152.0ms644×body320valid
56.0ms331×body160valid