Details

Time bar (total: 7.1s)

sample55.0ms

Algorithm
intervals
Results
20.0ms67×body1280valid
10.0ms48×body640valid
6.0ms164×body80valid
4.0ms29×body320valid
2.0ms19×body160valid

simplify18.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
056
1106
2136
3156
done156

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- (exp x) 1.0) x)
5.5b
(- (exp x) 1.0)

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt *-un-lft-identity
19×add-cube-cbrt
15×times-frac
prod-diff
associate-/l* distribute-lft-out-- difference-of-squares
add-exp-log add-cbrt-cube add-log-exp
fma-neg associate-/r*
pow1 expm1-log1p-u flip3-- flip-- log1p-expm1-u associate-/l/
cbrt-undiv sub-neg frac-2neg diff-log div-sub div-exp clear-num div-inv
Counts
2 → 68
Calls
2 calls:
53.0ms
(/ (- (exp x) 1.0) x)
13.0ms
(- (exp x) 1.0)

series96.0ms

Counts
2 → 6
Calls
2 calls:
68.0ms
(/ (- (exp x) 1.0) x)
27.0ms
(- (exp x) 1.0)

simplify852.0ms

Counts
74 → 74
Iterations

Useful iterations: done (848.0ms)

IterNodesCost
0127854
1297748
21007667
done5000648

prune248.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 1 expressions with local error:

0.1b
(fma 1/6 (* x x) (fma 1/2 x 1))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
1 → 10
Calls
1 calls:
1.0ms
(fma 1/6 (* x x) (fma 1/2 x 1))

series38.0ms

Counts
1 → 3
Calls
1 calls:
38.0ms
(fma 1/6 (* x x) (fma 1/2 x 1))

simplify786.0ms

Counts
13 → 13
Iterations

Useful iterations: 3 (174.0ms)

IterNodesCost
023158
143152
2137134
3785107
done5000107

prune51.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 1 expressions with local error:

0.1b
(fma 1/6 (* x x) (fma 1/2 x 1))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
1 → 10
Calls
1 calls:
0.0ms
(fma 1/6 (* x x) (fma 1/2 x 1))

series23.0ms

Counts
1 → 3
Calls
1 calls:
23.0ms
(fma 1/6 (* x x) (fma 1/2 x 1))

simplify1.2s

Counts
13 → 13
Iterations

Useful iterations: 3 (163.0ms)

IterNodesCost
023158
143152
2137134
3785107
done5000107

prune86.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma x 1/6 1/2)
0.1b
(fma x 1/6 1/2)
10.4b
(sqrt (fma x (fma x 1/6 1/2) 1))
10.4b
(sqrt (fma x (fma x 1/6 1/2) 1))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt
pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
rem-sqrt-square sqrt-pow1 pow1/2 fma-udef
Counts
4 → 50
Calls
4 calls:
0.0ms
(fma x 1/6 1/2)
1.0ms
(fma x 1/6 1/2)
3.0ms
(sqrt (fma x (fma x 1/6 1/2) 1))
3.0ms
(sqrt (fma x (fma x 1/6 1/2) 1))

series287.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(fma x 1/6 1/2)
38.0ms
(fma x 1/6 1/2)
82.0ms
(sqrt (fma x (fma x 1/6 1/2) 1))
117.0ms
(sqrt (fma x (fma x 1/6 1/2) 1))

simplify1.1s

Counts
62 → 62
Iterations

Useful iterations: done (1.1s)

IterNodesCost
058634
1119552
2364524
31617516
done5001512

prune212.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

regimes33.0ms

Accuracy

98.6% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.3b

bsearch38.0ms

Steps
ItersRangePoint
6
-0.00015980627971116164
-1.4411493588155298e-05
-0.0001304505555650203

simplify8.0ms

Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
02030
12428
22528
done2528

end0.0ms

sample1.9s

Algorithm
intervals
Results
741.0ms2250×body1280valid
434.0ms1643×body640valid
242.0ms5388×body80valid
109.0ms844×body320valid
38.0ms439×body160valid