Details

Time bar (total: 3.7s)

sample33.0ms

Algorithm
intervals
Results
12.0ms262×body80valid
4.0ms7×body1280valid
3.0ms83×body80overflowed
2.0ms7×body640valid
1.0ms7×body320valid
0.0ms2×body160valid

simplify6.0ms

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 3 expressions with local error:

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

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity
8×add-sqr-sqrt add-cube-cbrt log-prod
6×pow1 add-log-exp
4×add-exp-log log-div fma-neg prod-diff associate--l+
3×expm1-log1p-u fma-def flip3-+ log-pow add-cbrt-cube flip-+ log1p-expm1-u distribute-lft-out
2×associate--l-
1×+-commutative sub-neg flip3-- diff-log rem-log-exp sum-log flip--
Counts
3 → 62
Calls
3 calls:
6.0ms
(- (log (+ 1.0 (exp x))) (* x y))
3.0ms
(+ 1.0 (exp x))
3.0ms
(log (+ 1.0 (exp x)))

series129.0ms

Counts
3 → 9
Calls
3 calls:
59.0ms
(- (log (+ 1.0 (exp x))) (* x y))
7.0ms
(+ 1.0 (exp x))
62.0ms
(log (+ 1.0 (exp x)))

simplify57.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 3 (52.0ms)

IterNodesCost
0236404
1702369
22284367
35002340

prune132.0ms

Filtered
71 candidates to 54 candidates (76.1%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New68371
Fresh000
Picked101
Done000
Total69372

Merged error: 0.4b

Counts
72 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.9b
(cbrt (+ 1.0 (exp x)))
0.9b
(cbrt (+ 1.0 (exp x)))
0.9b
(cbrt (+ 1.0 (exp x)))
1.4b
(log (* (cbrt (+ 1.0 (exp x))) (cbrt (+ 1.0 (exp x)))))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-div
13×*-un-lft-identity
12×pow1 cbrt-prod
9×flip3-+ pow1/3 log-pow flip-+
8×log-div
7×add-exp-log add-sqr-sqrt add-cube-cbrt
4×expm1-log1p-u frac-times add-cbrt-cube log1p-expm1-u add-log-exp
3×distribute-lft-out
2×associate-*r/ rem-log-exp pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 log-prod pow-plus prod-exp
Counts
4 → 77
Calls
4 calls:
3.0ms
(cbrt (+ 1.0 (exp x)))
7.0ms
(cbrt (+ 1.0 (exp x)))
3.0ms
(cbrt (+ 1.0 (exp x)))
9.0ms
(log (* (cbrt (+ 1.0 (exp x))) (cbrt (+ 1.0 (exp x)))))

series565.0ms

Counts
4 → 12
Calls
4 calls:
133.0ms
(cbrt (+ 1.0 (exp x)))
129.0ms
(cbrt (+ 1.0 (exp x)))
117.0ms
(cbrt (+ 1.0 (exp x)))
186.0ms
(log (* (cbrt (+ 1.0 (exp x))) (cbrt (+ 1.0 (exp x)))))

simplify59.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 3 (51.0ms)

IterNodesCost
0222715
1535641
21820619
35002612

prune244.0ms

Filtered
89 candidates to 72 candidates (80.9%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New89089
Fresh022
Picked011
Done000
Total89392

Merged error: 0.4b

Counts
92 → 3

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma 1/2 (pow x 2) (+ x 2.0))
0.0b
(- (log (fma 1/2 (pow x 2) (+ x 2.0))) (* x y))
8.0b
(log (fma 1/2 (pow x 2) (+ x 2.0)))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×pow1 log-prod
4×add-exp-log fma-neg prod-diff add-log-exp
3×expm1-log1p-u associate--l+ log-pow add-cbrt-cube log1p-expm1-u
1×sub-neg flip3-- diff-log rem-log-exp flip-- fma-udef
Counts
3 → 49
Calls
3 calls:
1.0ms
(fma 1/2 (pow x 2) (+ x 2.0))
3.0ms
(- (log (fma 1/2 (pow x 2) (+ x 2.0))) (* x y))
1.0ms
(log (fma 1/2 (pow x 2) (+ x 2.0)))

series145.0ms

Counts
3 → 9
Calls
3 calls:
16.0ms
(fma 1/2 (pow x 2) (+ x 2.0))
75.0ms
(- (log (fma 1/2 (pow x 2) (+ x 2.0))) (* x y))
53.0ms
(log (fma 1/2 (pow x 2) (+ x 2.0)))

simplify83.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 3 (77.0ms)

IterNodesCost
0229423
1763380
23267376
35001356

prune128.0ms

Filtered
58 candidates to 46 candidates (79.3%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New56258
Fresh101
Picked101
Done011
Total58361

Merged error: 0.4b

Counts
61 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (fma x (+ (* 0.25 x) 0.5) (- (log 2.0) (* 1/2 (/ (pow x 2) (pow 2.0 2))))) (* x y))
0.0b
(- (log 2.0) (* 1/2 (/ (pow x 2) (pow 2.0 2))))
0.0b
(* 1/2 (/ (pow x 2) (pow 2.0 2)))
8.4b
(fma x (+ (* 0.25 x) 0.5) (- (log 2.0) (* 1/2 (/ (pow x 2) (pow 2.0 2)))))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
80×times-frac
77×add-sqr-sqrt
68×associate-*r*
56×unpow-prod-down
43×add-cube-cbrt *-un-lft-identity
27×add-exp-log
24×unpow2 sqr-pow
17×unswap-sqr
10×prod-exp
9×div-exp add-cbrt-cube
8×pow1
7×fma-neg prod-diff add-log-exp
6×pow-to-exp pow-exp
4×expm1-log1p-u associate--l+ log1p-expm1-u
3×log-prod associate-*l*
2×sub-neg flip3-- diff-log log-pow flip-- cbrt-unprod fma-udef
1×cbrt-undiv associate-*r/ pow-prod-down *-commutative div-inv
Counts
4 → 168
Calls
4 calls:
3.0ms
(- (fma x (+ (* 0.25 x) 0.5) (- (log 2.0) (* 1/2 (/ (pow x 2) (pow 2.0 2))))) (* x y))
4.0ms
(- (log 2.0) (* 1/2 (/ (pow x 2) (pow 2.0 2))))
23.0ms
(* 1/2 (/ (pow x 2) (pow 2.0 2)))
1.0ms
(fma x (+ (* 0.25 x) 0.5) (- (log 2.0) (* 1/2 (/ (pow x 2) (pow 2.0 2)))))

series458.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(- (fma x (+ (* 0.25 x) 0.5) (- (log 2.0) (* 1/2 (/ (pow x 2) (pow 2.0 2))))) (* x y))
273.0ms
(- (log 2.0) (* 1/2 (/ (pow x 2) (pow 2.0 2))))
48.0ms
(* 1/2 (/ (pow x 2) (pow 2.0 2)))
61.0ms
(fma x (+ (* 0.25 x) 0.5) (- (log 2.0) (* 1/2 (/ (pow x 2) (pow 2.0 2)))))

simplify77.0ms

Algorithm
egg-herbie
Counts
180 → 180
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
07421374
130931185
250011159

prune419.0ms

Filtered
180 candidates to 119 candidates (66.1%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1791180
Fresh011
Picked011
Done011
Total1794183

Merged error: 0.4b

Counts
183 → 4

regimes45.0ms

Accuracy

80.6% (0.3b remaining)

Error of 0.6b against oracle of 0.3b and baseline of 1.9b

bsearch50.0ms

Steps
ItersRangePoint
6
-7888799.454350161
-902290.5721441875
-915233.3327664499

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03626
13626

end0.0ms

sample903.0ms

Algorithm
intervals
Results
383.0ms8397×body80valid
96.0ms2466×body80overflowed
82.0ms261×body640valid
78.0ms140×body1280valid
30.0ms167×body320valid
13.0ms117×body160valid