Details

Time bar (total: 7.4s)

sample151.0ms

Algorithm
intervals
Results
48.0ms370×body80valid
34.0ms57×body10240exit
25.0ms43×body1280valid
18.0ms44×body640valid
6.0ms21×body320valid
2.0ms8×body160valid

simplify38.0ms

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: 26.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
0.1b
(exp (- (* (+ 1.0 eps) x)))
0.1b
(exp (* (- 1.0 eps) x))
4.6b
(fma (/ (exp (- (* (+ 1.0 eps) x))) 2.0) (- 1.0 (/ 1.0 eps)) (/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x)))))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity
10×add-log-exp
9×add-cbrt-cube
8×add-exp-log
7×add-sqr-sqrt add-cube-cbrt exp-prod
4×pow1 expm1-log1p-u times-frac log1p-expm1-u associate-/l*
3×rem-exp-log
2×cbrt-undiv exp-to-pow div-exp associate-/l/ distribute-lft-out
1×neg-sub0 distribute-lft-neg-in exp-neg neg-mul-1 distribute-rgt-neg-in frac-2neg flip3-+ exp-diff diff-log neg-log prod-exp clear-num associate-/r* cbrt-unprod flip-+ fma-udef div-inv
Counts
4 → 69
Calls
4 calls:
25.0ms
(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
3.0ms
(exp (- (* (+ 1.0 eps) x)))
3.0ms
(exp (* (- 1.0 eps) x))
0.0ms
(fma (/ (exp (- (* (+ 1.0 eps) x))) 2.0) (- 1.0 (/ 1.0 eps)) (/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x)))))

series328.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
26.0ms
(exp (- (* (+ 1.0 eps) x)))
20.0ms
(exp (* (- 1.0 eps) x))
234.0ms
(fma (/ (exp (- (* (+ 1.0 eps) x))) 2.0) (- 1.0 (/ 1.0 eps)) (/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x)))))

simplify36.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0365706
11230610
25001590

prune293.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.9b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(* 0.5 (pow x 2))
3.9b
(/ (pow x 3) eps)
4.0b
(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
36×times-frac
31×add-cube-cbrt *-un-lft-identity
16×unpow-prod-down
13×add-exp-log
12×cube-prod associate-/l*
8×associate-*r*
7×add-cbrt-cube
6×sqr-pow
4×cube-mult unpow3 unswap-sqr
3×pow1 expm1-log1p-u div-exp associate-*l* prod-exp associate-/r* log1p-expm1-u add-log-exp
2×pow-to-exp pow-exp unpow2
1×cbrt-undiv frac-2neg clear-num *-commutative cbrt-unprod fma-udef div-inv
Counts
3 → 106
Calls
3 calls:
6.0ms
(* 0.5 (pow x 2))
5.0ms
(/ (pow x 3) eps)
0.0ms
(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))

series96.0ms

Counts
3 → 9
Calls
3 calls:
24.0ms
(* 0.5 (pow x 2))
21.0ms
(/ (pow x 3) eps)
51.0ms
(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))

simplify64.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
0305506
11561465
25002451

prune277.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (* (cbrt (pow x 3)) (cbrt (pow x 3))) (/ eps x))
4.0b
(fma 1.3877787807814457e-17 (/ (* (cbrt (pow x 3)) (cbrt (pow x 3))) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
42.7b
(cbrt (pow x 3))
42.7b
(cbrt (pow x 3))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
31×times-frac
24×cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×add-exp-log
13×associate-/r*
12×add-cbrt-cube
6×cbrt-undiv unpow-prod-down cube-prod div-exp
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×div-inv
2×cube-mult pow1/3 unpow3 prod-exp rem-cbrt-cube cbrt-unprod sqr-pow
1×frac-2neg clear-num associate-/r/ fma-udef associate-/l*
Counts
4 → 104
Calls
4 calls:
9.0ms
(/ (* (cbrt (pow x 3)) (cbrt (pow x 3))) (/ eps x))
0.0ms
(fma 1.3877787807814457e-17 (/ (* (cbrt (pow x 3)) (cbrt (pow x 3))) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
1.0ms
(cbrt (pow x 3))
1.0ms
(cbrt (pow x 3))

series168.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(/ (* (cbrt (pow x 3)) (cbrt (pow x 3))) (/ eps x))
84.0ms
(fma 1.3877787807814457e-17 (/ (* (cbrt (pow x 3)) (cbrt (pow x 3))) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
15.0ms
(cbrt (pow x 3))
16.0ms
(cbrt (pow x 3))

simplify78.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
0388603
12652494
25002480

prune329.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (* (log (exp x)) (cbrt (pow x 3))) (/ eps x))
3.8b
(fma 1.3877787807814457e-17 (/ (* (log (exp x)) (cbrt (pow x 3))) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
3.9b
(log (exp x))
42.7b
(cbrt (pow x 3))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
31×times-frac
23×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×add-exp-log
14×add-cbrt-cube
13×associate-/r*
12×cbrt-prod
6×cbrt-undiv div-exp
5×pow1
4×expm1-log1p-u log-pow log1p-expm1-u add-log-exp
3×unpow-prod-down log-prod exp-prod cube-prod div-inv
2×prod-exp cbrt-unprod
1×cube-mult frac-2neg pow1/3 unpow3 rem-log-exp clear-num associate-/r/ rem-cbrt-cube fma-udef associate-/l* sqr-pow
Counts
4 → 98
Calls
4 calls:
8.0ms
(/ (* (log (exp x)) (cbrt (pow x 3))) (/ eps x))
0.0ms
(fma 1.3877787807814457e-17 (/ (* (log (exp x)) (cbrt (pow x 3))) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
1.0ms
(log (exp x))
1.0ms
(cbrt (pow x 3))

series143.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(/ (* (log (exp x)) (cbrt (pow x 3))) (/ eps x))
68.0ms
(fma 1.3877787807814457e-17 (/ (* (log (exp x)) (cbrt (pow x 3))) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
12.0ms
(log (exp x))
17.0ms
(cbrt (pow x 3))

simplify77.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
0432603
12707478
25002464

prune307.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.9b

regimes192.0ms

Accuracy

96.2% (0.6b remaining)

Error of 2.4b against oracle of 1.8b and baseline of 17.4b

bsearch149.0ms

Steps
ItersRangePoint
8
7.373205740752909e-17
2.2219667061302788e-13
8.146015422330596e-14

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05667
16267
26267

end0.0ms

sample4.5s

Algorithm
intervals
Results
1.3s10091×body80valid
1.1s1870×body10240exit
998.0ms1692×body1280valid
510.0ms1292×body640valid
182.0ms643×body320valid
74.0ms357×body160valid