Details

Time bar (total: 5.7s)

sample106.0ms

Algorithm
intervals
Results
28.0ms72×body10240exit
24.0ms49×body1280valid
16.0ms311×body80valid
13.0ms52×body640valid
4.0ms20×body320valid
1.0ms9×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: 30.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
0.0b
(+ 1.0 (/ 1.0 eps))
0.0b
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
2.6b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite189.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
80×exp-neg frac-times
60×neg-sub0 exp-diff
40×associate-*r/ associate-*l/
31×flip3-- flip3-+ flip-- flip-+
20×un-div-inv
18×add-sqr-sqrt
15×*-un-lft-identity
10×associate-*l*
9×add-cube-cbrt
8×pow1 add-cbrt-cube add-log-exp
6×add-exp-log associate-*r*
4×expm1-log1p-u log1p-expm1-u
3×fma-def
2×pow-prod-down prod-exp *-commutative cbrt-unprod distribute-lft-out difference-of-squares unswap-sqr
1×+-commutative sub-neg times-frac fma-neg diff-log prod-diff sum-log distribute-lft-out--
Counts
4 → 176
Calls
4 calls:
68.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
11.0ms
(+ 1.0 (/ 1.0 eps))
51.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
48.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series302.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
26.0ms
(+ 1.0 (/ 1.0 eps))
48.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
179.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify150.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 2 (115.0ms)

IterNodesCost
013044088
147513782
250013764

prune482.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.8b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b
(- 2.0 (* 1.0 (pow x 2)))
6.8b
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

rewrite7.0ms

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:
6.0ms
(- 2.0 (* 1.0 (pow x 2)))
0.0ms
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

series89.0ms

Counts
2 → 6
Calls
2 calls:
50.0ms
(- 2.0 (* 1.0 (pow x 2)))
39.0ms
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

simplify68.0ms

Algorithm
egg-herbie
Counts
36 → 36
Iterations

Useful iterations: 3 (64.0ms)

IterNodesCost
0126221
1412193
22139191
35001171

prune103.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.8b

localize13.0ms

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)
3.1b
(cbrt (pow (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))) 3))
6.8b
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

rewrite17.0ms

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:
6.0ms
(- 2.0 (* 1.0 (pow x 2)))
6.0ms
(pow (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))) 3)
2.0ms
(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))))

series187.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(- 2.0 (* 1.0 (pow x 2)))
60.0ms
(pow (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))) 3)
35.0ms
(cbrt (pow (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))) 3))
35.0ms
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

simplify41.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0250677
1907626
25001618

prune218.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.8b

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b
(* 12.0 (pow x 2))
7.0b
(fma (pow x 3) 8.0 (- 8.0 (* 12.0 (pow x 2))))
10.0b
(cbrt (fma (pow x 3) 8.0 (- 8.0 (* 12.0 (pow x 2)))))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
8×add-exp-log associate-*r*
7×add-cube-cbrt *-un-lft-identity
5×add-cbrt-cube
4×unpow-prod-down unswap-sqr
3×pow1 cbrt-prod expm1-log1p-u associate-*l* prod-exp log1p-expm1-u add-log-exp
2×unpow2 sqr-pow
1×pow-to-exp pow1/3 pow-exp *-commutative cbrt-unprod fma-udef
Counts
3 → 52
Calls
3 calls:
12.0ms
(* 12.0 (pow x 2))
0.0ms
(fma (pow x 3) 8.0 (- 8.0 (* 12.0 (pow x 2))))
1.0ms
(cbrt (fma (pow x 3) 8.0 (- 8.0 (* 12.0 (pow x 2)))))

series335.0ms

Counts
3 → 9
Calls
3 calls:
160.0ms
(* 12.0 (pow x 2))
34.0ms
(fma (pow x 3) 8.0 (- 8.0 (* 12.0 (pow x 2))))
141.0ms
(cbrt (fma (pow x 3) 8.0 (- 8.0 (* 12.0 (pow x 2)))))

simplify36.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0285418
1997377
25001355

prune161.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.8b

regimes70.0ms

Accuracy

96.7% (0.5b remaining)

Error of 1.0b against oracle of 0.5b and baseline of 17.1b

bsearch103.0ms

Steps
ItersRangePoint
7
345.8824083588705
6330.810310882262
358.4659228440807

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05033
15633
25633

end0.0ms

sample2.9s

Algorithm
intervals
Results
769.0ms1953×body10240exit
731.0ms1715×body1280valid
528.0ms9905×body80valid
320.0ms1284×body640valid
100.0ms633×body320valid
33.0ms317×body160valid