Details

Time bar (total: 5.7s)

sample104.0ms

Algorithm
intervals
Results
26.0ms66×body10240exit
24.0ms56×body1280valid
20.0ms291×body80valid
13.0ms52×body640valid
3.0ms15×body320valid
1.0ms9×body160valid

simplify38.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (36.0ms)

IterNodesCost
04716
112416
236516
3137616
4500115

prune9.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 31.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (- (* (+ 1.0 eps) x)))
0.0b
(exp (* (- 1.0 eps) x))
0.0b
(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
4.1b
(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)))))

rewrite31.0ms

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:
3.0ms
(exp (- (* (+ 1.0 eps) x)))
3.0ms
(exp (* (- 1.0 eps) x))
23.0ms
(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (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)))))

series475.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(exp (- (* (+ 1.0 eps) x)))
157.0ms
(exp (* (- 1.0 eps) x))
45.0ms
(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
245.0ms
(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)))))

simplify37.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0365706
11230610
25001590

prune281.0ms

Filtered
81 candidates to 62 candidates (76.5%)
Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.5b

localize11.0ms

Local error

Found 2 expressions with local error:

2.6b
(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
4.9b
(/ (pow x 3) eps)

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
27×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×unpow-prod-down cube-prod associate-/l*
7×add-exp-log
4×cube-mult unpow3 add-cbrt-cube sqr-pow
3×div-exp associate-/r*
2×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
1×cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num fma-udef div-inv
Counts
2 → 77
Calls
2 calls:
0.0ms
(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
5.0ms
(/ (pow x 3) eps)

series73.0ms

Counts
2 → 6
Calls
2 calls:
51.0ms
(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
22.0ms
(/ (pow x 3) eps)

simplify39.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0216398
11026377
25002377

prune204.0ms

Filtered
83 candidates to 49 candidates (59.0%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.5b

localize15.0ms

Local error

Found 4 expressions with local error:

1.4b
(/ (* (cbrt (pow x 3)) (cbrt (pow x 3))) (/ eps x))
2.6b
(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))

rewrite16.0ms

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:
10.0ms
(/ (* (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))

series173.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(/ (* (cbrt (pow x 3)) (cbrt (pow x 3))) (/ eps x))
86.0ms
(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))
17.0ms
(cbrt (pow x 3))

simplify80.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
0388603
12652494
25002480

prune333.0ms

Filtered
116 candidates to 80 candidates (69.0%)
Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.7b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (* (log (exp x)) (cbrt (pow x 3))) (/ eps x))
2.4b
(fma 1.3877787807814457e-17 (/ (* (log (exp x)) (cbrt (pow x 3))) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
4.5b
(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))

series145.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(/ (* (log (exp x)) (cbrt (pow x 3))) (/ eps x))
71.0ms
(fma 1.3877787807814457e-17 (/ (* (log (exp x)) (cbrt (pow x 3))) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
8.0ms
(log (exp x))
19.0ms
(cbrt (pow x 3))

simplify79.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
0432603
12707478
25002464

prune319.0ms

Filtered
110 candidates to 80 candidates (72.7%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.2b

regimes146.0ms

Accuracy

96.6% (0.6b remaining)

Error of 2.4b against oracle of 1.8b and baseline of 18.2b

bsearch128.0ms

Steps
ItersRangePoint
8
1.4245899198289959e-07
0.00010219770701537972
1.8493523655100802e-05

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05733
16533
26533

end0.0ms

sample2.8s

Algorithm
intervals
Results
772.0ms1735×body1280valid
772.0ms1893×body10240exit
540.0ms9761×body80valid
319.0ms1268×body640valid
111.0ms658×body320valid
32.0ms297×body160valid