Details

Time bar (total: 6.9s)

sample107.0ms

Algorithm
intervals
Results
27.0ms61×body10240exit
24.0ms56×body1280valid
20.0ms351×body80valid
12.0ms47×body640valid
3.0ms17×body320valid
1.0ms9×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

localize17.0ms

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))))
5.8b
(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)))))

rewrite63.0ms

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))
46.0ms
(/ (+ 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)))))

series312.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(exp (- (* (+ 1.0 eps) x)))
23.0ms
(exp (* (- 1.0 eps) x))
41.0ms
(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
223.0ms
(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

prune427.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.2b

localize10.0ms

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))))
4.6b
(/ (pow x 3) eps)

rewrite25.0ms

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:
12.0ms
(* 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)

series89.0ms

Counts
3 → 9
Calls
3 calls:
23.0ms
(* 0.5 (pow x 2))
43.0ms
(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
22.0ms
(/ (pow x 3) eps)

simplify62.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
0305506
11561465
25001451

prune267.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt x)
0.5b
(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:
1.0ms
(cbrt x)
1.0ms
(cbrt x)
16.0ms
(/ (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))))

series458.0ms

Counts
4 → 12
Calls
4 calls:
173.0ms
(cbrt x)
173.0ms
(cbrt x)
42.0ms
(/ (pow (* (cbrt x) (cbrt x)) 3) (/ eps x))
70.0ms
(fma 1.3877787807814457e-17 (/ (pow (* (cbrt x) (cbrt x)) 3) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))

simplify152.0ms

Algorithm
egg-herbie
Counts
196 → 196
Iterations

Useful iterations: 2 (135.0ms)

IterNodesCost
07211771
143251200
250011152

prune564.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.9b

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt x)
0.5b
(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))))
11.8b
(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)))

series592.0ms

Counts
4 → 12
Calls
4 calls:
177.0ms
(cbrt x)
174.0ms
(cbrt x)
72.0ms
(fma 1.3877787807814457e-17 (/ (pow (* (cbrt x) (log (exp (cbrt x)))) 3) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
169.0ms
(log (exp (cbrt x)))

simplify59.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
0139339
1329286
21862275
35001275

prune270.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.9b

regimes148.0ms

Accuracy

96.2% (0.6b remaining)

Error of 4.4b against oracle of 3.7b and baseline of 20.2b

bsearch149.0ms

Steps
ItersRangePoint
9
1.5996814978684195e-06
74.54631513443616
1.0169468758567441

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05645
16245
26245

end0.0ms

sample3.0s

Algorithm
intervals
Results
795.0ms1973×body10240exit
724.0ms1666×body1280valid
559.0ms10178×body80valid
340.0ms1338×body640valid
109.0ms633×body320valid
33.0ms303×body160valid