Details

Time bar (total: 7.0s)

sample104.0ms

Algorithm
intervals
Results
26.0ms59×body1280valid
26.0ms60×body10240exit
17.0ms322×body80valid
10.0ms42×body640valid
3.0ms21×body320valid
1.0ms13×body160valid

simplify40.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (38.0ms)

IterNodesCost
04716
112416
236516
3137616
4500115

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.9b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (- (* (+ 1.0 eps) x)))
0.0b
(exp (* (- 1.0 eps) x))
0.3b
(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
5.1b
(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)))))

rewrite64.0ms

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:
7.0ms
(exp (- (* (+ 1.0 eps) x)))
8.0ms
(exp (* (- 1.0 eps) x))
47.0ms
(/ (+ 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)))))

series348.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(exp (- (* (+ 1.0 eps) x)))
22.0ms
(exp (* (- 1.0 eps) x))
54.0ms
(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
242.0ms
(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 (30.0ms)

IterNodesCost
0365706
11230610
25001590

prune296.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.4b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(* 0.5 (pow x 2))
2.8b
(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
6.1b
(/ (pow x 3) eps)

rewrite24.0ms

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:
11.0ms
(* 0.5 (pow x 2))
0.0ms
(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
9.0ms
(/ (pow x 3) eps)

series102.0ms

Counts
3 → 9
Calls
3 calls:
26.0ms
(* 0.5 (pow x 2))
54.0ms
(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
23.0ms
(/ (pow x 3) eps)

simplify59.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
0305506
11561465
25001451

prune281.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
1.9b
(/ (pow (* (cbrt x) (cbrt x)) 3) (/ eps x))
2.8b
(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:
4.0ms
(cbrt x)
1.0ms
(cbrt x)
14.0ms
(/ (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))))

series502.0ms

Counts
4 → 12
Calls
4 calls:
184.0ms
(cbrt x)
188.0ms
(cbrt x)
54.0ms
(/ (pow (* (cbrt x) (cbrt x)) 3) (/ eps x))
75.0ms
(fma 1.3877787807814457e-17 (/ (pow (* (cbrt x) (cbrt x)) 3) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))

simplify157.0ms

Algorithm
egg-herbie
Counts
196 → 196
Iterations

Useful iterations: 2 (135.0ms)

IterNodesCost
07211771
143251200
250011152

prune732.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
2.8b
(fma 1.3877787807814457e-17 (/ (pow (* (cbrt x) (log (exp (cbrt x)))) 3) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
13.9b
(log (exp (cbrt x)))

rewrite7.0ms

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 (* (cbrt x) (log (exp (cbrt x)))) 3) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
4.0ms
(log (exp (cbrt x)))

series640.0ms

Counts
4 → 12
Calls
4 calls:
186.0ms
(cbrt x)
188.0ms
(cbrt x)
83.0ms
(fma 1.3877787807814457e-17 (/ (pow (* (cbrt x) (log (exp (cbrt x)))) 3) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
182.0ms
(log (exp (cbrt x)))

simplify60.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
0139339
1329286
21862275
35001275

prune273.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.5b

regimes141.0ms

Accuracy

94.6% (0.9b remaining)

Error of 4.6b against oracle of 3.7b and baseline of 19.8b

bsearch153.0ms

Steps
ItersRangePoint
10
2.966376253514418e-44
3.01453247982213e-27
2.969928030300931e-27

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05135
15735
25735

end0.0ms

sample2.9s

Algorithm
intervals
Results
741.0ms1868×body10240exit
726.0ms1722×body1280valid
542.0ms9981×body80valid
314.0ms1282×body640valid
102.0ms636×body320valid
36.0ms324×body160valid