Details

Time bar (total: 4.2s)

sample33.0ms

Algorithm
intervals
Results
13.0ms265×body80valid
3.0ms78×body80overflowed
3.0ms8×body640valid
1.0ms8×body320valid
1.0ms2×body1280valid
1.0ms5×body160valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0125
1195
2235
3235

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.8b

Counts
2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (log (+ 1.0 (exp x))) (* x y))
0.8b
(log (+ 1.0 (exp x)))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
8×log-prod
6×add-sqr-sqrt add-cube-cbrt
5×pow1
4×log-div fma-neg prod-diff associate--l+
3×add-exp-log log-pow add-log-exp
2×associate--l- expm1-log1p-u flip3-+ add-cbrt-cube flip-+ log1p-expm1-u distribute-lft-out
1×sub-neg flip3-- diff-log rem-log-exp flip--
Counts
2 → 45
Calls
2 calls:
6.0ms
(- (log (+ 1.0 (exp x))) (* x y))
3.0ms
(log (+ 1.0 (exp x)))

series120.0ms

Counts
2 → 6
Calls
2 calls:
58.0ms
(- (log (+ 1.0 (exp x))) (* x y))
62.0ms
(log (+ 1.0 (exp x)))

simplify55.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 3 (50.0ms)

IterNodesCost
0206339
1587310
21945308
35001281

prune115.0ms

Filtered
51 candidates to 39 candidates (76.5%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New46551
Fresh000
Picked101
Done000
Total47552

Merged error: 0.2b

Counts
52 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (log1p (expm1 (log (+ 1.0 (exp x))))) (* x y))
0.0b
(expm1 (log (+ 1.0 (exp x))))
0.7b
(log1p (expm1 (log (+ 1.0 (exp x)))))
0.8b
(log (+ 1.0 (exp x)))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
7×add-sqr-sqrt add-cube-cbrt add-log-exp
5×pow1 add-exp-log log1p-expm1-u
4×expm1-log1p-u log-prod add-cbrt-cube
3×fma-neg prod-diff
2×log-div log1p-udef diff-log
1×sub-neg expm1-log1p flip3-- flip3-+ log1p-expm1 rem-log-exp log-pow flip-- flip-+ distribute-lft-out expm1-udef
Counts
4 → 60
Calls
4 calls:
3.0ms
(- (log1p (expm1 (log (+ 1.0 (exp x))))) (* x y))
1.0ms
(expm1 (log (+ 1.0 (exp x))))
1.0ms
(log1p (expm1 (log (+ 1.0 (exp x)))))
3.0ms
(log (+ 1.0 (exp x)))

series440.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(- (log1p (expm1 (log (+ 1.0 (exp x))))) (* x y))
101.0ms
(expm1 (log (+ 1.0 (exp x))))
164.0ms
(log1p (expm1 (log (+ 1.0 (exp x)))))
62.0ms
(log (+ 1.0 (exp x)))

simplify64.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 3 (58.0ms)

IterNodesCost
0259476
1707407
22349404
35001378

prune163.0ms

Filtered
72 candidates to 54 candidates (75.0%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New71172
Fresh134
Picked011
Done000
Total72577

Merged error: 0.2b

Counts
77 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.8b
(log (+ 1.0 (exp x)))
1.0b
(cbrt (- (log (+ 1.0 (exp x))) (* x y)))
1.0b
(cbrt (- (log (+ 1.0 (exp x))) (* x y)))
1.0b
(cbrt (- (log (+ 1.0 (exp x))) (* x y)))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
9×cbrt-prod
8×add-sqr-sqrt add-cube-cbrt
6×cbrt-div
5×pow1 add-exp-log
4×expm1-log1p-u log-prod add-cbrt-cube log1p-expm1-u add-log-exp
3×flip3-- pow1/3 flip--
2×log-div
1×flip3-+ rem-log-exp log-pow flip-+ distribute-lft-out
Counts
4 → 62
Calls
4 calls:
3.0ms
(log (+ 1.0 (exp x)))
2.0ms
(cbrt (- (log (+ 1.0 (exp x))) (* x y)))
2.0ms
(cbrt (- (log (+ 1.0 (exp x))) (* x y)))
3.0ms
(cbrt (- (log (+ 1.0 (exp x))) (* x y)))

series989.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(log (+ 1.0 (exp x)))
322.0ms
(cbrt (- (log (+ 1.0 (exp x))) (* x y)))
304.0ms
(cbrt (- (log (+ 1.0 (exp x))) (* x y)))
306.0ms
(cbrt (- (log (+ 1.0 (exp x))) (* x y)))

simplify39.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0349970
11259923
25002905

prune250.0ms

Filtered
74 candidates to 67 candidates (90.5%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New74074
Fresh033
Picked011
Done011
Total74579

Merged error: 0.2b

Counts
79 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (log1p (fma (pow x 2) 0.75 (- (fma 1.0 x 1.0) (* 1.0 (/ (pow x 2) (pow 2.0 2)))))) (* x y))
0.2b
(/ (pow x 2) (pow 2.0 2))
7.0b
(fma (pow x 2) 0.75 (- (fma 1.0 x 1.0) (* 1.0 (/ (pow x 2) (pow 2.0 2)))))
8.8b
(log1p (fma (pow x 2) 0.75 (- (fma 1.0 x 1.0) (* 1.0 (/ (pow x 2) (pow 2.0 2))))))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
64×times-frac
54×unpow-prod-down
42×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×unpow2 sqr-pow
16×add-exp-log
9×div-exp
8×associate-/r* associate-/l*
7×add-log-exp
6×pow-to-exp pow-exp add-cbrt-cube
5×expm1-log1p-u
4×pow1 log1p-expm1-u
3×fma-neg prod-diff
2×log1p-udef diff-log
1×cbrt-undiv sub-neg flip3-- frac-2neg log1p-expm1 clear-num flip-- fma-udef div-inv
Counts
4 → 144
Calls
4 calls:
3.0ms
(- (log1p (fma (pow x 2) 0.75 (- (fma 1.0 x 1.0) (* 1.0 (/ (pow x 2) (pow 2.0 2)))))) (* x y))
10.0ms
(/ (pow x 2) (pow 2.0 2))
1.0ms
(fma (pow x 2) 0.75 (- (fma 1.0 x 1.0) (* 1.0 (/ (pow x 2) (pow 2.0 2)))))
1.0ms
(log1p (fma (pow x 2) 0.75 (- (fma 1.0 x 1.0) (* 1.0 (/ (pow x 2) (pow 2.0 2))))))

series350.0ms

Counts
4 → 12
Calls
4 calls:
146.0ms
(- (log1p (fma (pow x 2) 0.75 (- (fma 1.0 x 1.0) (* 1.0 (/ (pow x 2) (pow 2.0 2)))))) (* x y))
43.0ms
(/ (pow x 2) (pow 2.0 2))
48.0ms
(fma (pow x 2) 0.75 (- (fma 1.0 x 1.0) (* 1.0 (/ (pow x 2) (pow 2.0 2)))))
112.0ms
(log1p (fma (pow x 2) 0.75 (- (fma 1.0 x 1.0) (* 1.0 (/ (pow x 2) (pow 2.0 2))))))

simplify69.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
05011267
119451090
250011075

prune368.0ms

Filtered
156 candidates to 94 candidates (60.3%)
Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New1551156
Fresh022
Picked011
Done022
Total1556161

Merged error: 0.2b

Counts
161 → 6

regimes109.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0127
1127

end0.0ms

sample928.0ms

Algorithm
intervals
Results
410.0ms8435×body80valid
104.0ms2435×body80overflowed
71.0ms228×body640valid
68.0ms123×body1280valid
38.0ms201×body320valid
14.0ms122×body160valid

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