Details

Time bar (total: 17.0s)

sample46.0ms

Algorithm
intervals
Results
20.0ms83×body1280valid
7.0ms42×body640valid
5.0ms160×body80valid
2.0ms24×body320valid
1.0ms21×body160valid

simplify8.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
056
1106
2136
3156
done156

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.6b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- (exp x) 1.0) x)
5.8b
(- (exp x) 1.0)

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt *-un-lft-identity
15×times-frac
12×add-cube-cbrt
5×associate-/l* distribute-lft-out-- difference-of-squares
4×add-exp-log add-cbrt-cube add-log-exp
3×associate-/r*
2×pow1 flip3-- flip-- associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-sub div-exp clear-num div-inv
Counts
2 → 52
Calls
2 calls:
53.0ms
(/ (- (exp x) 1.0) x)
18.0ms
(- (exp x) 1.0)

series80.0ms

Counts
2 → 6
Calls
2 calls:
59.0ms
(/ (- (exp x) 1.0) x)
21.0ms
(- (exp x) 1.0)

simplify2.3s

Counts
58 → 58
Iterations

Useful iterations: 3 (853.0ms)

IterNodesCost
099596
1227572
2802544
34675537
done5002537

prune155.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ 1/2 (* 1/6 x))
0.1b
(* x (+ 1/2 (* 1/6 x)))
0.3b
(* 1/6 x)

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
7×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×associate-*r* associate-*l*
5×add-log-exp
2×flip3-+ associate-*r/ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ unswap-sqr
1×+-commutative distribute-rgt-in distribute-lft-in sum-log
Counts
3 → 51
Calls
3 calls:
10.0ms
(+ 1/2 (* 1/6 x))
29.0ms
(* x (+ 1/2 (* 1/6 x)))
14.0ms
(* 1/6 x)

series163.0ms

Counts
3 → 9
Calls
3 calls:
44.0ms
(+ 1/2 (* 1/6 x))
102.0ms
(* x (+ 1/2 (* 1/6 x)))
17.0ms
(* 1/6 x)

simplify554.0ms

Counts
60 → 60
Iterations

Useful iterations: done (553.0ms)

IterNodesCost
078480
1227445
2936405
done5000399

prune164.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (exp x))
0.0b
(+ (sqrt (exp x)) (sqrt 1.0))
0.0b
(* (+ (sqrt (exp x)) (sqrt 1.0)) (/ (- (sqrt (exp x)) (sqrt 1.0)) x))
5.6b
(- (sqrt (exp x)) (sqrt 1.0))

rewrite193.0ms

Algorithm
rewrite-expression-head
Rules
58×add-sqr-sqrt
44×*-un-lft-identity
31×associate-*r* sqrt-prod
28×times-frac
20×add-cube-cbrt
16×difference-of-squares
9×add-exp-log add-cbrt-cube
8×distribute-lft-out-- add-log-exp
7×pow1
5×associate-*l*
4×sqrt-pow1 distribute-lft-out
3×exp-prod flip3-+ flip-+
2×frac-times associate-*l/ prod-exp cbrt-unprod unswap-sqr
1×cbrt-undiv +-commutative sub-neg rem-sqrt-square flip3-- pow1/2 diff-log associate-*r/ div-exp pow-prod-down sum-log *-commutative flip-- div-inv
Counts
4 → 103
Calls
4 calls:
8.0ms
(sqrt (exp x))
21.0ms
(+ (sqrt (exp x)) (sqrt 1.0))
119.0ms
(* (+ (sqrt (exp x)) (sqrt 1.0)) (/ (- (sqrt (exp x)) (sqrt 1.0)) x))
37.0ms
(- (sqrt (exp x)) (sqrt 1.0))

series323.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(sqrt (exp x))
53.0ms
(+ (sqrt (exp x)) (sqrt 1.0))
198.0ms
(* (+ (sqrt (exp x)) (sqrt 1.0)) (/ (- (sqrt (exp x)) (sqrt 1.0)) x))
58.0ms
(- (sqrt (exp x)) (sqrt 1.0))

simplify3.7s

Counts
115 → 115
Iterations

Useful iterations: done (3.7s)

IterNodesCost
01521629
13771491
228621371
done50011234

prune316.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (pow (sqrt (exp x)) 3) (pow (sqrt 1.0) 3)) (+ (exp x) (+ 1.0 (* (sqrt (exp x)) (sqrt 1.0)))))
0.0b
(* (+ (sqrt (exp x)) (sqrt 1.0)) (/ (/ (- (pow (sqrt (exp x)) 3) (pow (sqrt 1.0) 3)) (+ (exp x) (+ 1.0 (* (sqrt (exp x)) (sqrt 1.0))))) x))
0.0b
(pow (sqrt (exp x)) 3)
5.5b
(- (pow (sqrt (exp x)) 3) (pow (sqrt 1.0) 3))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
1520×add-sqr-sqrt
1393×times-frac
1153×*-un-lft-identity
648×difference-of-squares
610×associate-*r*
584×sqrt-prod
582×unpow-prod-down cube-prod
431×add-cube-cbrt
217×sqr-pow
199×distribute-lft-out
162×distribute-lft-out--
49×associate-/l*
18×difference-cubes
16×add-exp-log add-cbrt-cube
8×pow1 associate-/r/
6×pow-pow flip3-+ flip-+ add-log-exp
5×associate-*l* div-inv
4×cbrt-undiv sqrt-pow1 div-exp associate-/r*
3×pow-unpow exp-prod prod-exp cbrt-unprod unswap-sqr
2×frac-times flip3-- associate-*l/ flip-- associate-/l/
1×cube-mult pow-to-exp sub-neg frac-2neg pow1/2 diff-log unpow3 div-sub associate-*r/ pow-prod-down pow-exp clear-num *-commutative sqrt-pow2 rem-cube-cbrt
Counts
4 → 997
Calls
4 calls:
193.0ms
(/ (- (pow (sqrt (exp x)) 3) (pow (sqrt 1.0) 3)) (+ (exp x) (+ 1.0 (* (sqrt (exp x)) (sqrt 1.0)))))
671.0ms
(* (+ (sqrt (exp x)) (sqrt 1.0)) (/ (/ (- (pow (sqrt (exp x)) 3) (pow (sqrt 1.0) 3)) (+ (exp x) (+ 1.0 (* (sqrt (exp x)) (sqrt 1.0))))) x))
8.0ms
(pow (sqrt (exp x)) 3)
58.0ms
(- (pow (sqrt (exp x)) 3) (pow (sqrt 1.0) 3))

series1.9s

Counts
4 → 12
Calls
4 calls:
578.0ms
(/ (- (pow (sqrt (exp x)) 3) (pow (sqrt 1.0) 3)) (+ (exp x) (+ 1.0 (* (sqrt (exp x)) (sqrt 1.0)))))
1.1s
(* (+ (sqrt (exp x)) (sqrt 1.0)) (/ (/ (- (pow (sqrt (exp x)) 3) (pow (sqrt 1.0) 3)) (+ (exp x) (+ 1.0 (* (sqrt (exp x)) (sqrt 1.0))))) x))
36.0ms
(pow (sqrt (exp x)) 3)
153.0ms
(- (pow (sqrt (exp x)) 3) (pow (sqrt 1.0) 3))

simplify1.7s

Counts
1009 → 1009
Iterations

Useful iterations: done (1.6s)

IterNodesCost
075834025
1241831592
done500031124

prune2.1s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes60.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 21.1b

bsearch56.0ms

Steps
ItersRangePoint
10
-911936.9907706906
-4.3470241882695893e-07
-0.00021407398444296693

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02644
13744
done3744

end0.0ms

sample1.8s

Algorithm
intervals
Results
890.0ms2301×body1280valid
329.0ms1666×body640valid
181.0ms5337×body80valid
97.0ms810×body320valid
36.0ms438×body160valid