Details

Time bar (total: 6.8s)

sample107.0ms

Algorithm
intervals
Results
26.0ms62×body1280valid
23.0ms63×body10240exit
18.0ms351×body80valid
9.0ms38×body640valid
5.0ms11×body160valid
4.0ms25×body320valid

simplify37.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (36.0ms)

IterNodesCost
04716
112416
236516
3137616
4500115

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
0.0b
(* (- 1.0 eps) x)
0.0b
(* (+ 1.0 eps) x)
4.9b
(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)))))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
18×*-un-lft-identity
16×add-sqr-sqrt
13×add-cbrt-cube
12×add-exp-log
10×add-cube-cbrt
9×associate-*l*
8×pow1
6×associate-*r*
4×expm1-log1p-u times-frac associate-*l/ log1p-expm1-u associate-/l* add-log-exp
3×prod-exp cbrt-unprod distribute-lft-out
2×cbrt-undiv flip3-+ div-exp pow-prod-down *-commutative flip-+ associate-/l/ unswap-sqr
1×flip3-- frac-2neg clear-num associate-/r* flip-- fma-udef div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 84
Calls
4 calls:
44.0ms
(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
20.0ms
(* (- 1.0 eps) x)
22.0ms
(* (+ 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)))))

series367.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
31.0ms
(* (- 1.0 eps) x)
34.0ms
(* (+ 1.0 eps) x)
249.0ms
(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)))))

simplify48.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0462738
11805635
25003628

prune331.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 3.8b

localize10.0ms

Local error

Found 2 expressions with local error:

4.3b
(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
6.7b
(/ (pow x 3) eps)

rewrite12.0ms

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))))
9.0ms
(/ (pow x 3) eps)

series223.0ms

Counts
2 → 6
Calls
2 calls:
199.0ms
(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
24.0ms
(/ (pow x 3) eps)

simplify39.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0216398
11026377
25002377

prune195.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
1.0b
(/ (pow (* (cbrt x) (cbrt x)) 3) (/ eps x))
4.3b
(fma 1.3877787807814457e-17 (/ (pow (* (cbrt x) (cbrt x)) 3) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
185×times-frac
83×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
24×add-exp-log
14×cube-mult unpow-prod-down unpow3 cube-prod sqr-pow
13×associate-/r*
12×div-exp
10×div-inv
9×add-cbrt-cube
8×associate-/l*
6×cbrt-prod
4×pow1 expm1-log1p-u pow-exp log1p-expm1-u add-log-exp
3×cbrt-undiv
2×pow-to-exp pow1/3 prod-exp
1×frac-2neg clear-num associate-/r/ fma-udef
Counts
4 → 184
Calls
4 calls:
1.0ms
(cbrt x)
1.0ms
(cbrt x)
17.0ms
(/ (pow (* (cbrt x) (cbrt x)) 3) (/ eps x))
0.0ms
(fma 1.3877787807814457e-17 (/ (pow (* (cbrt x) (cbrt x)) 3) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))

series493.0ms

Counts
4 → 12
Calls
4 calls:
180.0ms
(cbrt x)
180.0ms
(cbrt x)
48.0ms
(/ (pow (* (cbrt x) (cbrt x)) 3) (/ eps x))
84.0ms
(fma 1.3877787807814457e-17 (/ (pow (* (cbrt x) (cbrt x)) 3) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))

simplify148.0ms

Algorithm
egg-herbie
Counts
196 → 196
Iterations

Useful iterations: 2 (133.0ms)

IterNodesCost
07211771
143251200
250011152

prune559.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
3.8b
(fma 1.3877787807814457e-17 (/ (pow (* (log (exp (cbrt x))) (cbrt x)) 3) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
13.1b
(log (exp (cbrt x)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity
7×log-pow
6×exp-prod
5×pow1
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×log-prod
2×pow1/3
1×rem-log-exp fma-udef
Counts
4 → 56
Calls
4 calls:
1.0ms
(cbrt x)
1.0ms
(cbrt x)
0.0ms
(fma 1.3877787807814457e-17 (/ (pow (* (log (exp (cbrt x))) (cbrt x)) 3) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
7.0ms
(log (exp (cbrt x)))

series622.0ms

Counts
4 → 12
Calls
4 calls:
182.0ms
(cbrt x)
179.0ms
(cbrt x)
79.0ms
(fma 1.3877787807814457e-17 (/ (pow (* (log (exp (cbrt x))) (cbrt x)) 3) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
182.0ms
(log (exp (cbrt x)))

simplify59.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
0139339
1329286
21862275
35001275

prune267.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.6b

regimes85.0ms

Accuracy

96.1% (0.7b remaining)

Error of 4.2b against oracle of 3.5b and baseline of 20.1b

bsearch178.0ms

Steps
ItersRangePoint
11
5.899922635698028e-18
1860724342265.0034
0.07014539269035792

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05543
16143
26143

end0.0ms

sample2.8s

Algorithm
intervals
Results
722.0ms1863×body10240exit
715.0ms1706×body1280valid
530.0ms10124×body80valid
312.0ms1284×body640valid
101.0ms609×body320valid
30.0ms303×body160valid