Details

Time bar (total: 5.7s)

sample106.0ms

Algorithm
intervals
Results
42.0ms259×body10240exit
35.0ms105×body1280valid
12.0ms68×body640valid
4.0ms36×body320valid
2.0ms30×body160valid
1.0ms17×body80valid

simplify47.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 7 (45.0ms)

IterNodesCost
0159
1249
2329
3449
4639
51799
611849
750017

prune7.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(expm1 (+ x x))
0.0b
(fma 1 1 (exp (+ x x)))
0.5b
(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
5×add-exp-log add-cbrt-cube
4×log1p-expm1-u
3×pow1 expm1-log1p-u associate-/r* associate-/l* add-log-exp
2×expm1-udef
1×cbrt-undiv expm1-log1p frac-2neg div-sub div-exp clear-num fma-udef div-inv
Counts
3 → 51
Calls
3 calls:
0.0ms
(expm1 (+ x x))
0.0ms
(fma 1 1 (exp (+ x x)))
2.0ms
(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

series106.0ms

Counts
3 → 9
Calls
3 calls:
18.0ms
(expm1 (+ x x))
20.0ms
(fma 1 1 (exp (+ x x)))
68.0ms
(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

simplify80.0ms

Algorithm
egg-herbie
Counts
60 → 60
Iterations

Useful iterations: 3 (74.0ms)

IterNodesCost
0164440
1564391
22669384
35001382

prune141.0ms

Filtered
60 candidates to 49 candidates (81.7%)
Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 1 1 (exp (+ x x)))
0.2b
(sqrt (fma 1 1 (exp (+ x x))))
0.6b
(/ (/ (expm1 (* 2 x)) (hypot 1 (exp x))) (sqrt (fma 1 1 (exp (+ x x)))))
0.9b
(/ (expm1 (* 2 x)) (hypot 1 (exp x)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
150×times-frac
91×add-sqr-sqrt
90×add-cube-cbrt *-un-lft-identity
45×sqrt-prod
16×associate-/l*
11×add-exp-log add-cbrt-cube
9×associate-/r* div-inv
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
3×div-sub
2×frac-2neg clear-num expm1-udef
1×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef associate-/l/
Counts
4 → 170
Calls
4 calls:
0.0ms
(fma 1 1 (exp (+ x x)))
1.0ms
(sqrt (fma 1 1 (exp (+ x x))))
7.0ms
(/ (/ (expm1 (* 2 x)) (hypot 1 (exp x))) (sqrt (fma 1 1 (exp (+ x x)))))
2.0ms
(/ (expm1 (* 2 x)) (hypot 1 (exp x)))

series431.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(fma 1 1 (exp (+ x x)))
47.0ms
(sqrt (fma 1 1 (exp (+ x x))))
245.0ms
(/ (/ (expm1 (* 2 x)) (hypot 1 (exp x))) (sqrt (fma 1 1 (exp (+ x x)))))
119.0ms
(/ (expm1 (* 2 x)) (hypot 1 (exp x)))

simplify75.0ms

Algorithm
egg-herbie
Counts
182 → 182
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
07092890
129732548
250012356

prune451.0ms

Filtered
182 candidates to 122 candidates (67.0%)
Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize10.0ms

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))

rewrite11.0ms

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:
2.0ms
(- x (* 1/3 (pow x 3)))
0.0ms
(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
7.0ms
(* 1/3 (pow x 3))

series167.0ms

Counts
3 → 9
Calls
3 calls:
76.0ms
(- x (* 1/3 (pow x 3)))
50.0ms
(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
41.0ms
(* 1/3 (pow x 3))

simplify35.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0206338
1835292
25001292

prune156.0ms

Filtered
72 candidates to 48 candidates (66.7%)
Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
12×associate-*r*
9×add-exp-log
8×add-cube-cbrt *-un-lft-identity
6×add-cbrt-cube
5×expm1-log1p-u
4×pow1 unpow-prod-down cube-prod log1p-expm1-u add-log-exp unswap-sqr
3×associate-*l* prod-exp
2×sqr-pow
1×cube-mult pow-to-exp log1p-udef expm1-log1p unpow3 log1p-expm1 pow-exp *-commutative cbrt-unprod fma-udef expm1-udef
Counts
4 → 65
Calls
4 calls:
0.0ms
(log1p (fma (pow x 5) 2/15 (- 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))))))
6.0ms
(* 1/3 (pow x 3))

series333.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))
54.0ms
(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
150.0ms
(expm1 (log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))
35.0ms
(* 1/3 (pow x 3))

simplify41.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0306465
11191409
25001389

prune208.0ms

Filtered
77 candidates to 56 candidates (72.7%)
Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

regimes40.0ms

Accuracy

0% (0.1b remaining)

Error of 0.7b against oracle of 0.6b and baseline of 0.7b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0116
1136
2136

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.3s7478×body10240exit
987.0ms3246×body1280valid
452.0ms2455×body640valid
143.0ms1216×body320valid
45.0ms634×body160valid
17.0ms449×body80valid