Details

Time bar (total: 5.0s)

sample98.0ms

Algorithm
intervals
Results
40.0ms235×body10240exit
29.0ms99×body1280valid
14.0ms80×body640valid
4.0ms41×body320valid
1.0ms20×body160valid
1.0ms16×body80valid

simplify45.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 7 (43.0ms)

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: 1.0b

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))))

rewrite3.0ms

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)))
2.0ms
(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

series89.0ms

Counts
2 → 6
Calls
2 calls:
20.0ms
(fma 1 1 (exp (+ x x)))
69.0ms
(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

simplify74.0ms

Algorithm
egg-herbie
Counts
46 → 46
Iterations

Useful iterations: 3 (69.0ms)

IterNodesCost
0150395
1512351
22464344
35002343

prune121.0ms

Filtered
46 candidates to 39 candidates (84.8%)
Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.9b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(exp (log1p (exp (* 2 x))))
1.0b
(log1p (exp (* 2 x)))
1.0b
(/ (expm1 (+ x x)) (exp (log1p (exp (* 2 x)))))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
5×add-cbrt-cube
4×add-exp-log expm1-log1p-u add-log-exp
3×pow1 exp-prod associate-/r* log1p-expm1-u associate-/l*
2×log1p-udef rem-exp-log
1×cbrt-undiv frac-2neg div-sub log1p-expm1 div-exp clear-num div-inv expm1-udef
Counts
3 → 55
Calls
3 calls:
1.0ms
(exp (log1p (exp (* 2 x))))
0.0ms
(log1p (exp (* 2 x)))
3.0ms
(/ (expm1 (+ x x)) (exp (log1p (exp (* 2 x)))))

series272.0ms

Counts
3 → 9
Calls
3 calls:
78.0ms
(exp (log1p (exp (* 2 x))))
57.0ms
(log1p (exp (* 2 x)))
137.0ms
(/ (expm1 (+ x x)) (exp (log1p (exp (* 2 x)))))

simplify70.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 3 (64.0ms)

IterNodesCost
0182523
1556477
22509465
35001451

prune166.0ms

Filtered
64 candidates to 50 candidates (78.1%)
Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.9b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma 1 1 (exp (+ x x)))
0.2b
(/ 1 (/ (fma 1 1 (exp (+ x x))) (expm1 (+ x x))))
1.0b
(/ (fma 1 1 (exp (+ x x))) (expm1 (+ x x)))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
53×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×add-exp-log associate-/r*
10×add-cbrt-cube
8×div-exp
6×div-inv associate-/l*
4×pow1 cbrt-undiv
3×expm1-log1p-u log1p-expm1-u add-log-exp
2×rec-exp frac-2neg 1-exp clear-num
1×pow-flip associate-/r/ fma-udef inv-pow
Counts
3 → 117
Calls
3 calls:
0.0ms
(fma 1 1 (exp (+ x x)))
5.0ms
(/ 1 (/ (fma 1 1 (exp (+ x x))) (expm1 (+ x x))))
2.0ms
(/ (fma 1 1 (exp (+ x x))) (expm1 (+ x x)))

series162.0ms

Counts
3 → 9
Calls
3 calls:
21.0ms
(fma 1 1 (exp (+ x x)))
71.0ms
(/ 1 (/ (fma 1 1 (exp (+ x x))) (expm1 (+ x x))))
70.0ms
(/ (fma 1 1 (exp (+ x x))) (expm1 (+ x x)))

simplify51.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
03871449
117421257
250011169

prune224.0ms

Filtered
126 candidates to 75 candidates (59.5%)
Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.9b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
0.0b
(- x (* 1/3 (pow x 3)))
0.1b
(* 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:
0.0ms
(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
2.0ms
(- x (* 1/3 (pow x 3)))
7.0ms
(* 1/3 (pow x 3))

series176.0ms

Counts
3 → 9
Calls
3 calls:
55.0ms
(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
80.0ms
(- x (* 1/3 (pow x 3)))
40.0ms
(* 1/3 (pow x 3))

simplify48.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0206338
1835292
25002292

prune173.0ms

Filtered
72 candidates to 48 candidates (66.7%)
Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.9b

regimes17.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0157
1177
2177

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.2s7461×body10240exit
980.0ms3297×body1280valid
445.0ms2459×body640valid
124.0ms1141×body320valid
45.0ms666×body160valid
16.0ms437×body80valid