Details

Time bar (total: 7.1s)

sample104.0ms

Algorithm
intervals
Results
28.0ms67×body10240exit
22.0ms330×body80valid
20.0ms46×body1280valid
12.0ms47×body640valid
4.0ms22×body320valid
1.0ms7×body160valid

simplify39.0ms

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: 29.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ 1.0 eps) x)
0.0b
(* (- 1.0 eps) x)
0.0b
(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
3.2b
(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)))))

rewrite27.0ms

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:
6.0ms
(* (+ 1.0 eps) x)
6.0ms
(* (- 1.0 eps) x)
12.0ms
(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
1.0ms
(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)))))

series327.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(* (+ 1.0 eps) x)
31.0ms
(* (- 1.0 eps) x)
43.0ms
(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
226.0ms
(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
25002628

prune312.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 3.3b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(* 0.5 (pow x 2))
4.1b
(/ (pow x 3) eps)
4.6b
(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))

rewrite15.0ms

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:
5.0ms
(* 0.5 (pow x 2))
5.0ms
(/ (pow x 3) eps)
1.0ms
(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))

series92.0ms

Counts
3 → 9
Calls
3 calls:
23.0ms
(* 0.5 (pow x 2))
20.0ms
(/ (pow x 3) eps)
48.0ms
(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))

simplify58.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
0305506
11561465
25002451

prune237.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.3b

localize15.0ms

Local error

Found 4 expressions with local error:

4.6b
(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
12.5b
(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
12.5b
(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
12.5b
(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3
1×fma-udef
Counts
4 → 49
Calls
4 calls:
1.0ms
(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
1.0ms
(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
1.0ms
(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
1.0ms
(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))

series1.1s

Counts
4 → 12
Calls
4 calls:
51.0ms
(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
361.0ms
(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
365.0ms
(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
361.0ms
(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))

simplify49.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 3 (42.0ms)

IterNodesCost
0123615
1351557
21616548
35001542

prune247.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 3.3b

localize19.0ms

Local error

Found 4 expressions with local error:

4.6b
(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
4.6b
(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
12.5b
(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
12.5b
(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
6×cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
2×pow1/3 fma-udef
Counts
4 → 46
Calls
4 calls:
1.0ms
(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
1.0ms
(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
1.0ms
(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
1.0ms
(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))

series827.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
52.0ms
(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
362.0ms
(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
367.0ms
(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))

simplify49.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 3 (42.0ms)

IterNodesCost
0123550
1351494
21616488
35001484

prune271.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 3.2b

regimes97.0ms

Accuracy

96.2% (0.6b remaining)

Error of 5.3b against oracle of 4.7b and baseline of 20.5b

bsearch172.0ms

Steps
ItersRangePoint
11
1.648961095024041e-05
5.175139968754377e+19
0.8925960409309325

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05437
16037
26037

end0.0ms

sample2.9s

Algorithm
intervals
Results
810.0ms1933×body10240exit
742.0ms1697×body1280valid
581.0ms10153×body80valid
337.0ms1295×body640valid
110.0ms625×body320valid
34.0ms306×body160valid