Details

Time bar (total: 6.4s)

sample166.0ms

Algorithm
intervals
Results
52.0ms64×body1280valid
52.0ms352×body80valid
22.0ms42×body640valid
11.0ms79×body80overflowed
8.0ms21×body320valid
2.0ms9×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: 31.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
0.0b
(* (- 1.0 eps) x)
0.0b
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
2.9b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
80×exp-neg frac-times
60×neg-sub0 exp-diff
42×associate-*l/
40×associate-*r/
32×flip3-- flip--
30×flip3-+ flip-+
23×add-sqr-sqrt
20×un-div-inv
16×*-un-lft-identity
15×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 difference-of-squares unswap-sqr
2×distribute-lft-out--
1×sub-neg times-frac fma-neg diff-log prod-diff distribute-lft-out
Counts
4 → 183
Calls
4 calls:
41.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
10.0ms
(* (- 1.0 eps) x)
34.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
28.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series339.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
32.0ms
(* (- 1.0 eps) x)
46.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
212.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify65.0ms

Algorithm
egg-herbie
Counts
195 → 195
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
013724120
150013814

prune499.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b
(- 2.0 (* 1.0 (pow x 2)))
5.8b
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-log-exp
3×fma-neg prod-diff
2×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
1×sub-neg flip3-- diff-log flip-- fma-udef
Counts
2 → 30
Calls
2 calls:
2.0ms
(- 2.0 (* 1.0 (pow x 2)))
0.0ms
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

series97.0ms

Counts
2 → 6
Calls
2 calls:
55.0ms
(- 2.0 (* 1.0 (pow x 2)))
42.0ms
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

simplify71.0ms

Algorithm
egg-herbie
Counts
36 → 36
Iterations

Useful iterations: 3 (62.0ms)

IterNodesCost
0126221
1412193
22139191
35001171

prune95.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

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

series43.0ms

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

simplify106.0ms

Algorithm
egg-herbie
Counts
13 → 13
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
04982
113267
253467
3307667
4500167

prune39.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(- 2.0 (* 1.0 (pow x 2)))
0.0b
(pow (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))) 3)
1.9b
(cbrt (pow (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))) 3))
5.8b
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×unpow-prod-down cube-prod add-log-exp
5×pow1 add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u
3×pow-unpow fma-neg prod-diff
2×cube-mult unpow3 sqr-pow
1×pow-to-exp sub-neg flip3-- pow-pow pow1/3 diff-log pow-exp flip-- rem-cbrt-cube fma-udef rem-cube-cbrt
Counts
4 → 78
Calls
4 calls:
2.0ms
(- 2.0 (* 1.0 (pow x 2)))
1.0ms
(pow (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))) 3)
1.0ms
(cbrt (pow (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))) 3))
0.0ms
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

series204.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(- 2.0 (* 1.0 (pow x 2)))
67.0ms
(pow (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))) 3)
43.0ms
(cbrt (pow (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))) 3))
39.0ms
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

simplify44.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0250677
1907626
25001618

prune218.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

regimes54.0ms

Accuracy

96.4% (0.6b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 16.6b

bsearch202.0ms

Steps
ItersRangePoint
10
1.9435667087631803
128700106451.34695
154.4482937142435

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05628
16928
26928

end0.0ms

sample3.9s

Algorithm
intervals
Results
1.3s1786×body1280valid
1.2s10024×body80valid
599.0ms1253×body640valid
230.0ms1967×body80overflowed
200.0ms590×body320valid
72.0ms321×body160valid