Details

Time bar (total: 3.3s)

sample28.0ms

Algorithm
intervals
Results
10.0ms62×body1280valid
4.0ms44×body640valid
3.0ms189×body80valid
2.0ms30×body320valid
1.0ms13×body160valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0103
1133
2153
3153

prune1.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.9b

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- (exp x) 1.0) x)
3.8b
(- (exp x) 1.0)

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt *-un-lft-identity
19×add-cube-cbrt
15×times-frac
9×prod-diff
5×associate-/l* distribute-lft-out-- difference-of-squares
4×add-exp-log add-cbrt-cube add-log-exp
3×fma-neg associate-/r*
2×pow1 expm1-log1p-u flip3-- flip-- log1p-expm1-u associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-sub div-exp clear-num div-inv
Counts
2 → 68
Calls
2 calls:
28.0ms
(/ (- (exp x) 1.0) x)
11.0ms
(- (exp x) 1.0)

series54.0ms

Counts
2 → 6
Calls
2 calls:
38.0ms
(/ (- (exp x) 1.0) x)
16.0ms
(- (exp x) 1.0)

simplify32.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0282468
1919380
25001377

prune134.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma 1/6 (pow x 3) x)
4.9b
(/ (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)) x)
12.8b
(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
5×add-exp-log add-cbrt-cube
3×pow1 expm1-log1p-u associate-/r* log1p-expm1-u associate-/l* add-log-exp
2×fma-udef
1×cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
3 → 49
Calls
3 calls:
0.0ms
(fma 1/6 (pow x 3) x)
5.0ms
(/ (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)) x)
0.0ms
(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

series153.0ms

Counts
3 → 9
Calls
3 calls:
77.0ms
(fma 1/6 (pow x 3) x)
45.0ms
(/ (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)) x)
32.0ms
(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

simplify86.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0140391
1510356
22915356
35002356

prune162.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

12.8b
(fma 1/2 (pow x 2) (* (* (cbrt (fma 1/6 (pow x 3) x)) (cbrt (fma 1/6 (pow x 3) x))) (cbrt (fma 1/6 (pow x 3) x))))
17.5b
(cbrt (fma 1/6 (pow x 3) x))
17.5b
(cbrt (fma 1/6 (pow x 3) x))
17.5b
(cbrt (fma 1/6 (pow x 3) x))

rewrite4.0ms

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 1/2 (pow x 2) (* (* (cbrt (fma 1/6 (pow x 3) x)) (cbrt (fma 1/6 (pow x 3) x))) (cbrt (fma 1/6 (pow x 3) x))))
1.0ms
(cbrt (fma 1/6 (pow x 3) x))
1.0ms
(cbrt (fma 1/6 (pow x 3) x))
1.0ms
(cbrt (fma 1/6 (pow x 3) x))

series377.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(fma 1/2 (pow x 2) (* (* (cbrt (fma 1/6 (pow x 3) x)) (cbrt (fma 1/6 (pow x 3) x))) (cbrt (fma 1/6 (pow x 3) x))))
114.0ms
(cbrt (fma 1/6 (pow x 3) x))
120.0ms
(cbrt (fma 1/6 (pow x 3) x))
115.0ms
(cbrt (fma 1/6 (pow x 3) x))

simplify64.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 3 (57.0ms)

IterNodesCost
0173599
1495548
22018508
35001470

prune234.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

17.5b
(cbrt (fma 1/6 (pow x 3) x))
17.5b
(cbrt (fma 1/2 (pow x 2) (* (* (cbrt (fma 1/6 (pow x 3) x)) (cbrt (fma 1/6 (pow x 3) x))) (cbrt (fma 1/6 (pow x 3) x)))))
17.5b
(cbrt (fma 1/2 (pow x 2) (* (* (cbrt (fma 1/6 (pow x 3) x)) (cbrt (fma 1/6 (pow x 3) x))) (cbrt (fma 1/6 (pow x 3) x)))))
17.5b
(cbrt (fma 1/2 (pow x 2) (* (* (cbrt (fma 1/6 (pow x 3) x)) (cbrt (fma 1/6 (pow x 3) x))) (cbrt (fma 1/6 (pow x 3) x)))))

rewrite4.0ms

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:
1.0ms
(cbrt (fma 1/6 (pow x 3) x))
1.0ms
(cbrt (fma 1/2 (pow x 2) (* (* (cbrt (fma 1/6 (pow x 3) x)) (cbrt (fma 1/6 (pow x 3) x))) (cbrt (fma 1/6 (pow x 3) x)))))
1.0ms
(cbrt (fma 1/2 (pow x 2) (* (* (cbrt (fma 1/6 (pow x 3) x)) (cbrt (fma 1/6 (pow x 3) x))) (cbrt (fma 1/6 (pow x 3) x)))))
1.0ms
(cbrt (fma 1/2 (pow x 2) (* (* (cbrt (fma 1/6 (pow x 3) x)) (cbrt (fma 1/6 (pow x 3) x))) (cbrt (fma 1/6 (pow x 3) x)))))

series508.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(cbrt (fma 1/6 (pow x 3) x))
61.0ms
(cbrt (fma 1/2 (pow x 2) (* (* (cbrt (fma 1/6 (pow x 3) x)) (cbrt (fma 1/6 (pow x 3) x))) (cbrt (fma 1/6 (pow x 3) x)))))
267.0ms
(cbrt (fma 1/2 (pow x 2) (* (* (cbrt (fma 1/6 (pow x 3) x)) (cbrt (fma 1/6 (pow x 3) x))) (cbrt (fma 1/6 (pow x 3) x)))))
65.0ms
(cbrt (fma 1/2 (pow x 2) (* (* (cbrt (fma 1/6 (pow x 3) x)) (cbrt (fma 1/6 (pow x 3) x))) (cbrt (fma 1/6 (pow x 3) x)))))

simplify68.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 3 (57.0ms)

IterNodesCost
01941129
15211034
21944996
35002981

prune303.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

regimes29.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 21.8b

bsearch25.0ms

Steps
ItersRangePoint
7
-0.002950799818357885
-5.931762247777049e-05
-0.00017098774397487554

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02616
12616

end0.0ms

sample909.0ms

Algorithm
intervals
Results
383.0ms2299×body1280valid
178.0ms1668×body640valid
101.0ms5461×body80valid
51.0ms780×body320valid
16.0ms381×body160valid