Details

Time bar (total: 5.8s)

sample101.0ms

Algorithm
intervals
Results
34.0ms223×body10240exit
33.0ms101×body1280valid
16.0ms91×body640valid
3.0ms32×body320valid
1.0ms16×body160valid
1.0ms16×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: 0.0b

localize8.0ms

Local error

Found 2 expressions with local error:

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

series90.0ms

Counts
2 → 6
Calls
2 calls:
21.0ms
(fma 1 1 (exp (+ x x)))
69.0ms
(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

simplify88.0ms

Algorithm
egg-herbie
Counts
46 → 46
Iterations

Useful iterations: 3 (83.0ms)

IterNodesCost
0150395
1512351
22464344
35002343

prune116.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(log1p (expm1 (/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))))
0.0b
(expm1 (/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x)))))
0.0b
(fma 1 1 (exp (+ x x)))
0.0b
(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
6×add-exp-log add-cbrt-cube
5×log1p-expm1-u
4×pow1 expm1-log1p-u add-log-exp
3×associate-/r* associate-/l*
2×expm1-udef
1×cbrt-undiv log1p-udef expm1-log1p frac-2neg div-sub log1p-expm1 div-exp clear-num fma-udef div-inv
Counts
4 → 62
Calls
4 calls:
0.0ms
(log1p (expm1 (/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))))
0.0ms
(expm1 (/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x)))))
0.0ms
(fma 1 1 (exp (+ x x)))
5.0ms
(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

series360.0ms

Counts
4 → 12
Calls
4 calls:
183.0ms
(log1p (expm1 (/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))))
85.0ms
(expm1 (/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x)))))
27.0ms
(fma 1 1 (exp (+ x x)))
66.0ms
(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

simplify85.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 3 (79.0ms)

IterNodesCost
0190626
1623553
22844544
35002542

prune194.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite15.0ms

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×log1p-expm1-u
4×pow1 expm1-log1p-u unpow-prod-down cube-prod 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
(expm1 (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
(log1p (expm1 (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))
13.0ms
(* 1/3 (pow x 3))

series256.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(expm1 (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))
52.0ms
(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
130.0ms
(log1p (expm1 (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))
37.0ms
(* 1/3 (pow x 3))

simplify212.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 3 (206.0ms)

IterNodesCost
0192411
1745360
24643359
35001358

prune188.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (expm1 (+ x x)))
0.0b
(fma 1 1 (exp (+ x x)))
0.1b
(/ (fma 1 1 (exp (+ x x))) (sqrt (expm1 (+ x x))))
0.1b
(/ (sqrt (expm1 (+ x x))) (/ (fma 1 1 (exp (+ x x))) (sqrt (expm1 (+ x x)))))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
276×times-frac
158×add-sqr-sqrt
157×add-cube-cbrt *-un-lft-identity
147×sqrt-prod
28×associate-/r*
11×add-exp-log add-cbrt-cube
9×div-inv associate-/l*
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
2×frac-2neg clear-num
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/ fma-udef
Counts
4 → 243
Calls
4 calls:
1.0ms
(sqrt (expm1 (+ x x)))
0.0ms
(fma 1 1 (exp (+ x x)))
6.0ms
(/ (fma 1 1 (exp (+ x x))) (sqrt (expm1 (+ x x))))
18.0ms
(/ (sqrt (expm1 (+ x x))) (/ (fma 1 1 (exp (+ x x))) (sqrt (expm1 (+ x x)))))

series214.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(sqrt (expm1 (+ x x)))
22.0ms
(fma 1 1 (exp (+ x x)))
87.0ms
(/ (fma 1 1 (exp (+ x x))) (sqrt (expm1 (+ x x))))
72.0ms
(/ (sqrt (expm1 (+ x x))) (/ (fma 1 1 (exp (+ x x))) (sqrt (expm1 (+ x x)))))

simplify100.0ms

Algorithm
egg-herbie
Counts
255 → 255
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
06514659
131694057
250013993

prune470.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes19.0ms

Accuracy

0% (0.0b 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
0138
1158
2158

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.2s7493×body10240exit
959.0ms3275×body1280valid
440.0ms2445×body640valid
143.0ms1254×body320valid
48.0ms627×body160valid
14.0ms399×body80valid