Details

Time bar (total: 14.3s)

sample46.0ms

Algorithm
intervals
Results
14.0ms65×body1280valid
9.0ms62×body640valid
5.0ms182×body80valid
4.0ms33×body320valid
1.0ms12×body160valid

simplify13.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
056
1106
2136
3156
done156

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.5b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- (exp x) 1.0) x)
3.8b
(- (exp x) 1.0)

rewrite45.0ms

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-cbrt-cube add-exp-log add-log-exp
3×associate-/r*
2×pow1 flip3-- flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg diff-log div-sub div-exp div-inv
Counts
2 → 52
Calls
2 calls:
33.0ms
(/ (- (exp x) 1.0) x)
9.0ms
(- (exp x) 1.0)

series96.0ms

Counts
2 → 6
Calls
2 calls:
68.0ms
(/ (- (exp x) 1.0) x)
28.0ms
(- (exp x) 1.0)

simplify2.1s

Counts
58 → 58
Iterations

Useful iterations: 3 (867.0ms)

IterNodesCost
099596
1227572
2817544
34953537
done5000537

prune261.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 3 expressions with local error:

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

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
7×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
6×associate-*r* associate-*l*
5×add-log-exp
2×flip3-+ pow-prod-down prod-exp associate-*r/ *-commutative cbrt-unprod flip-+ unswap-sqr
1×distribute-rgt-in +-commutative sum-log distribute-lft-in
Counts
3 → 51
Calls
3 calls:
6.0ms
(+ (* x 1/6) 1/2)
33.0ms
(* x (+ (* x 1/6) 1/2))
9.0ms
(* x 1/6)

series170.0ms

Counts
3 → 9
Calls
3 calls:
41.0ms
(+ (* x 1/6) 1/2)
114.0ms
(* x (+ (* x 1/6) 1/2))
16.0ms
(* x 1/6)

simplify604.0ms

Counts
60 → 60
Iterations

Useful iterations: done (602.0ms)

IterNodesCost
078480
1226445
2898407
done5001399

prune179.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (exp x) 3)
0.0b
(/ (- (pow (exp x) 3) (pow 1.0 3)) (* x (+ (* 1.0 (+ (exp x) 1.0)) (exp (+ x x)))))
0.0b
(* x (+ (* 1.0 (+ (exp x) 1.0)) (exp (+ x x))))
3.7b
(- (pow (exp x) 3) (pow 1.0 3))

rewrite214.0ms

Algorithm
rewrite-expression-head
Rules
86×add-sqr-sqrt
48×difference-of-squares
42×*-un-lft-identity
39×unpow-prod-down cube-prod
25×times-frac associate-/l* sqr-pow
15×distribute-lft-out--
12×add-cbrt-cube add-cube-cbrt
11×add-exp-log
7×pow1
6×add-log-exp
4×pow-pow associate-*r/
3×difference-cubes pow-unpow exp-prod associate-*r* associate-*l*
2×cbrt-undiv flip3-+ flip3-- div-exp prod-exp associate-/r/ cbrt-unprod flip-+ flip-- associate-/l/
1×distribute-rgt-in cube-mult pow-to-exp clear-num associate-/r* sub-neg frac-2neg distribute-lft-in diff-log unpow3 div-sub pow-prod-down pow-exp *-commutative div-inv rem-cube-cbrt unswap-sqr
Counts
4 → 152
Calls
4 calls:
4.0ms
(pow (exp x) 3)
86.0ms
(/ (- (pow (exp x) 3) (pow 1.0 3)) (* x (+ (* 1.0 (+ (exp x) 1.0)) (exp (+ x x)))))
83.0ms
(* x (+ (* 1.0 (+ (exp x) 1.0)) (exp (+ x x))))
36.0ms
(- (pow (exp x) 3) (pow 1.0 3))

series382.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(pow (exp x) 3)
185.0ms
(/ (- (pow (exp x) 3) (pow 1.0 3)) (* x (+ (* 1.0 (+ (exp x) 1.0)) (exp (+ x x)))))
110.0ms
(* x (+ (* 1.0 (+ (exp x) 1.0)) (exp (+ x x))))
62.0ms
(- (pow (exp x) 3) (pow 1.0 3))

simplify2.4s

Counts
164 → 164
Iterations

Useful iterations: 2 (735.0ms)

IterNodesCost
02223312
16533127
236222922
done50022922

prune693.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize60.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (pow (exp x) 3) (pow 1.0 3)) (* (* x (sqrt (+ (* 1.0 (+ (exp x) 1.0)) (exp (+ x x))))) (sqrt (+ (* 1.0 (+ (exp x) 1.0)) (exp (+ x x))))))
0.3b
(* x (sqrt (+ (* 1.0 (+ (exp x) 1.0)) (exp (+ x x)))))
0.3b
(* (* x (sqrt (+ (* 1.0 (+ (exp x) 1.0)) (exp (+ x x))))) (sqrt (+ (* 1.0 (+ (exp x) 1.0)) (exp (+ x x)))))
3.7b
(- (pow (exp x) 3) (pow 1.0 3))

rewrite652.0ms

Algorithm
rewrite-expression-head
Rules
87×add-sqr-sqrt
48×difference-of-squares
41×*-un-lft-identity
36×unpow-prod-down cube-prod
26×sqrt-div
25×times-frac associate-/l*
24×sqr-pow
20×add-cbrt-cube add-exp-log
18×associate-*r/
15×distribute-lft-out--
13×flip3-+ flip-+
12×associate-*r*
11×pow1 add-cube-cbrt
8×frac-times associate-/r/
7×prod-exp sqrt-prod cbrt-unprod
6×add-log-exp
4×associate-*l* pow-prod-down associate-*l/
3×difference-cubes cbrt-undiv div-exp
2×flip3-- *-commutative flip-- unswap-sqr associate-/l/
1×clear-num associate-/r* sub-neg frac-2neg diff-log div-sub div-inv
Counts
4 → 165
Calls
4 calls:
256.0ms
(/ (- (pow (exp x) 3) (pow 1.0 3)) (* (* x (sqrt (+ (* 1.0 (+ (exp x) 1.0)) (exp (+ x x))))) (sqrt (+ (* 1.0 (+ (exp x) 1.0)) (exp (+ x x))))))
103.0ms
(* x (sqrt (+ (* 1.0 (+ (exp x) 1.0)) (exp (+ x x)))))
235.0ms
(* (* x (sqrt (+ (* 1.0 (+ (exp x) 1.0)) (exp (+ x x))))) (sqrt (+ (* 1.0 (+ (exp x) 1.0)) (exp (+ x x)))))
51.0ms
(- (pow (exp x) 3) (pow 1.0 3))

series622.0ms

Counts
4 → 12
Calls
4 calls:
216.0ms
(/ (- (pow (exp x) 3) (pow 1.0 3)) (* (* x (sqrt (+ (* 1.0 (+ (exp x) 1.0)) (exp (+ x x))))) (sqrt (+ (* 1.0 (+ (exp x) 1.0)) (exp (+ x x))))))
230.0ms
(* x (sqrt (+ (* 1.0 (+ (exp x) 1.0)) (exp (+ x x)))))
132.0ms
(* (* x (sqrt (+ (* 1.0 (+ (exp x) 1.0)) (exp (+ x x))))) (sqrt (+ (* 1.0 (+ (exp x) 1.0)) (exp (+ x x)))))
44.0ms
(- (pow (exp x) 3) (pow 1.0 3))

simplify2.4s

Counts
177 → 177
Iterations

Useful iterations: 2 (957.0ms)

IterNodesCost
02656058
17444780
246994320
done50014320

prune894.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

regimes63.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.2b

bsearch59.0ms

Steps
ItersRangePoint
8
-0.00181011214377754
-1.6902992745682556e-06
-0.00016704963527402913

simplify15.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03471
14871
done4871

end0.0ms

sample2.1s

Algorithm
intervals
Results
702.0ms5413×body80valid
694.0ms2317×body1280valid
320.0ms1622×body640valid
135.0ms833×body320valid
31.0ms402×body160valid