Details

Time bar (total: 5.3s)

sample94.0ms

Algorithm
intervals
Results
35.0ms225×body10240exit
26.0ms90×body1280valid
13.0ms77×body640valid
6.0ms53×body320valid
2.0ms23×body160valid
0.0ms13×body80valid

simplify43.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 7 (42.0ms)

IterNodesCost
0159
1249
2329
3449
4639
51799
611849
750017

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma 1 1 (exp (+ x x)))
1.0b
(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
4×add-exp-log add-cbrt-cube
3×associate-/r* associate-/l*
2×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
1×cbrt-undiv frac-2neg div-sub div-exp clear-num fma-udef div-inv expm1-udef
Counts
2 → 40
Calls
2 calls:
0.0ms
(fma 1 1 (exp (+ x x)))
5.0ms
(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

series81.0ms

Counts
2 → 6
Calls
2 calls:
19.0ms
(fma 1 1 (exp (+ x x)))
62.0ms
(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

simplify74.0ms

Algorithm
egg-herbie
Counts
46 → 46
Iterations

Useful iterations: 3 (67.0ms)

IterNodesCost
0150395
1512351
22464344
35002343

prune108.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.5b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(- x (* 1/3 (pow x 3)))
0.0b
(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
0.2b
(* 1/3 (pow x 3))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
12×associate-*r*
9×add-cube-cbrt *-un-lft-identity
8×add-exp-log
5×add-cbrt-cube add-log-exp
4×unpow-prod-down cube-prod unswap-sqr
3×pow1 expm1-log1p-u fma-neg associate-*l* prod-diff prod-exp log1p-expm1-u
2×sqr-pow
1×cube-mult pow-to-exp sub-neg flip3-- diff-log unpow3 pow-exp *-commutative flip-- cbrt-unprod fma-udef
Counts
3 → 63
Calls
3 calls:
6.0ms
(- x (* 1/3 (pow x 3)))
0.0ms
(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
12.0ms
(* 1/3 (pow x 3))

series154.0ms

Counts
3 → 9
Calls
3 calls:
72.0ms
(- x (* 1/3 (pow x 3)))
46.0ms
(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
36.0ms
(* 1/3 (pow x 3))

simplify36.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0206338
1835292
25001292

prune161.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(- x (* 1/3 (pow x 3)))
0.0b
(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
0.1b
(expm1 (log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))
0.2b
(* 1/3 (pow x 3))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
12×associate-*r*
10×add-cube-cbrt *-un-lft-identity
9×add-exp-log
6×add-cbrt-cube add-log-exp
4×pow1 expm1-log1p-u unpow-prod-down cube-prod log1p-expm1-u unswap-sqr
3×fma-neg associate-*l* prod-diff prod-exp
2×sqr-pow
1×cube-mult pow-to-exp sub-neg expm1-log1p flip3-- diff-log unpow3 pow-exp *-commutative flip-- cbrt-unprod fma-udef expm1-udef
Counts
4 → 74
Calls
4 calls:
6.0ms
(- x (* 1/3 (pow x 3)))
0.0ms
(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
0.0ms
(expm1 (log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))
15.0ms
(* 1/3 (pow x 3))

series299.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(- x (* 1/3 (pow x 3)))
52.0ms
(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
142.0ms
(expm1 (log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))
34.0ms
(* 1/3 (pow x 3))

simplify51.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0305475
11203415
25001395

prune232.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(expm1 (log1p (* (sqrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))) (sqrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))))
0.2b
(* 1/3 (pow x 3))
0.2b
(* 1/3 (pow x 3))
0.3b
(* (sqrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))) (sqrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
46×add-sqr-sqrt
30×associate-*r*
20×add-cube-cbrt *-un-lft-identity
19×pow1
18×sqrt-prod
16×add-exp-log
12×associate-*l* unswap-sqr
10×add-cbrt-cube
8×unpow-prod-down sqrt-pow1 pow1/2 cube-prod swap-sqr
7×prod-exp
5×pow-prod-up
4×expm1-log1p-u log1p-expm1-u add-log-exp sqr-pow
3×pow-prod-down pow-sqr *-commutative cbrt-unprod
2×cube-mult pow-to-exp unpow3 pow-exp
1×pow2 expm1-log1p pow-plus sqrt-unprod rem-square-sqrt expm1-udef
Counts
4 → 128
Calls
4 calls:
0.0ms
(expm1 (log1p (* (sqrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))) (sqrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))))
15.0ms
(* 1/3 (pow x 3))
12.0ms
(* 1/3 (pow x 3))
12.0ms
(* (sqrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))) (sqrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))

series267.0ms

Counts
4 → 12
Calls
4 calls:
148.0ms
(expm1 (log1p (* (sqrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))) (sqrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))))
33.0ms
(* 1/3 (pow x 3))
38.0ms
(* 1/3 (pow x 3))
48.0ms
(* (sqrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))) (sqrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))

simplify58.0ms

Algorithm
egg-herbie
Counts
140 → 140
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0323925
11377787
25001740

prune365.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.5b

regimes41.0ms

Accuracy

0% (0.1b remaining)

Error of 0.6b against oracle of 0.5b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0116
1136
2136

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.2s7651×body10240exit
984.0ms3334×body1280valid
422.0ms2401×body640valid
141.0ms1271×body320valid
40.0ms587×body160valid
14.0ms407×body80valid