Details

Time bar (total: 6.7s)

sample34.0ms

Algorithm
intervals
Results
14.0ms65×body1280valid
6.0ms61×body640valid
3.0ms173×body80valid
2.0ms27×body320valid
1.0ms16×body160valid

simplify8.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
056
1106
2136
3156
done156

prune1.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.5b

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- (exp x) 1.0) x)
5.2b
(- (exp x) 1.0)

rewrite39.0ms

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:
25.0ms
(/ (- (exp x) 1.0) x)
12.0ms
(- (exp x) 1.0)

series59.0ms

Counts
2 → 6
Calls
2 calls:
40.0ms
(/ (- (exp x) 1.0) x)
19.0ms
(- (exp x) 1.0)

simplify1.3s

Counts
74 → 74
Iterations

Useful iterations: done (1.3s)

IterNodesCost
0127854
1281745
2612665
31785619
done5001605

prune128.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma x (fma 1/6 x 1/2) 1)
0.1b
(fma 1/6 x 1/2)

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
2 → 20
Calls
2 calls:
0.0ms
(fma x (fma 1/6 x 1/2) 1)
0.0ms
(fma 1/6 x 1/2)

series57.0ms

Counts
2 → 6
Calls
2 calls:
22.0ms
(fma x (fma 1/6 x 1/2) 1)
35.0ms
(fma 1/6 x 1/2)

simplify1.8s

Counts
26 → 26
Iterations

Useful iterations: 3 (53.0ms)

IterNodesCost
033213
153204
2114176
3381175
41753175
done5001175

prune50.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (exp x))
0.0b
(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x)))
0.0b
(/ (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x))) x)
5.1b
(- (exp (+ x x)) (* 1.0 1.0))

rewrite298.0ms

Algorithm
rewrite-expression-head
Rules
178×times-frac
139×*-un-lft-identity
107×add-sqr-sqrt
85×add-cube-cbrt
44×difference-of-squares
31×associate-/l*
27×distribute-lft-out
24×exp-sum
11×add-exp-log add-cbrt-cube
10×associate-/r/
add-log-exp
associate-/r*
flip3-+ flip-+ div-inv
pow1 cbrt-undiv expm1-log1p-u fma-neg div-exp prod-diff log1p-expm1-u
fma-def div-sub associate-/l/
flip3-- frac-2neg clear-num flip--
+-commutative sub-neg diff-log sum-log
Counts
4 → 214
Calls
4 calls:
6.0ms
(+ 1.0 (exp x))
115.0ms
(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x)))
111.0ms
(/ (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x))) x)
56.0ms
(- (exp (+ x x)) (* 1.0 1.0))

series140.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(+ 1.0 (exp x))
42.0ms
(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x)))
67.0ms
(/ (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x))) x)
23.0ms
(- (exp (+ x x)) (* 1.0 1.0))

simplify1.3s

Counts
226 → 226
Iterations

Useful iterations: done (1.3s)

IterNodesCost
03194871
17714677
223444400
done50024386

prune468.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes14.0ms

Accuracy

98.7% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.3b

bsearch30.0ms

Steps
ItersRangePoint
9
-24.13061144907697
-3.152803306627408e-07
-0.00012153975327080831

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01826
12126
done2126

end0.0ms

sample873.0ms

Algorithm
intervals
Results
369.0ms2257×body1280valid
169.0ms1651×body640valid
99.0ms5476×body80valid
54.0ms843×body320valid
17.0ms406×body160valid