Details

Time bar (total: 12.3s)

sample45.0ms

Algorithm
intervals
Results
15.0ms65×body1280valid
10.0ms62×body640valid
5.0ms182×body80valid
3.0ms33×body320valid
1.0ms12×body160valid

simplify12.0ms

Counts
1 → 1
Iterations
IterNodes
done15
315
213
110
05

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.5b

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite32.0ms

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:
21.0ms
(/ (- (exp x) 1.0) x)
9.0ms
(- (exp x) 1.0)

series75.0ms

Counts
2 → 6
Calls
2 calls:
40.0ms
(/ (- (exp x) 1.0) x)
36.0ms
(- (exp x) 1.0)

simplify2.0s

Counts
58 → 58
Iterations
IterNodes
done5000
34953
2817
1227
099

prune223.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 3 expressions with local error:

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

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:
12.0ms
(+ 1/2 (* 1/6 x))
25.0ms
(* x (+ 1/2 (* 1/6 x)))
11.0ms
(* 1/6 x)

series154.0ms

Counts
3 → 9
Calls
3 calls:
38.0ms
(+ 1/2 (* 1/6 x))
90.0ms
(* x (+ 1/2 (* 1/6 x)))
25.0ms
(* 1/6 x)

simplify545.0ms

Counts
60 → 60
Iterations
IterNodes
done5000
2936
1227
078

prune220.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite224.0ms

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:
111.0ms
(/ (- (pow (exp x) 3) (pow 1.0 3)) (* x (+ (* 1.0 1.0) (* (exp x) (+ 1.0 (exp x))))))
12.0ms
(pow (exp x) 3)
36.0ms
(* x (+ (* 1.0 1.0) (* (exp x) (+ 1.0 (exp x)))))
52.0ms
(- (pow (exp x) 3) (pow 1.0 3))

series454.0ms

Counts
4 → 12
Calls
4 calls:
230.0ms
(/ (- (pow (exp x) 3) (pow 1.0 3)) (* x (+ (* 1.0 1.0) (* (exp x) (+ 1.0 (exp x))))))
27.0ms
(pow (exp x) 3)
149.0ms
(* x (+ (* 1.0 1.0) (* (exp x) (+ 1.0 (exp x)))))
47.0ms
(- (pow (exp x) 3) (pow 1.0 3))

simplify2.4s

Counts
164 → 164
Iterations
IterNodes
done5000
23528
1647
0218

prune762.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- (pow 1.0 4) (* (* (+ 1.0 (exp x)) (+ 1.0 (exp x))) (exp (+ x x)))) x)
0.0b
(* (+ 1.0 (exp x)) (+ 1.0 (exp x)))
0.0b
(/ (- (pow (exp x) 3) (pow 1.0 3)) (* (- (pow 1.0 4) (* (* (+ 1.0 (exp x)) (+ 1.0 (exp x))) (exp (+ x x)))) x))
3.7b
(- (pow (exp x) 3) (pow 1.0 3))

rewrite295.0ms

Algorithm
rewrite-expression-head
Rules
88×add-sqr-sqrt
56×*-un-lft-identity
48×difference-of-squares
36×unpow-prod-down cube-prod
25×times-frac associate-/l*
24×sqr-pow
15×distribute-lft-out--
13×pow1 add-cbrt-cube add-exp-log
12×add-cube-cbrt
7×associate-*r* associate-*l*
6×flip3-+ swap-sqr associate-*l/ flip-+ distribute-lft-out add-log-exp
4×frac-times flip3-- flip--
3×difference-cubes prod-exp cbrt-unprod
2×cbrt-undiv div-exp pow-prod-down associate-*r/ associate-/r/ *-commutative unswap-sqr associate-/l/
1×pow2 distribute-rgt-in clear-num associate-/r* sub-neg frac-2neg distribute-lft-in pow-plus diff-log div-sub pow-sqr pow-prod-up div-inv
Counts
4 → 164
Calls
4 calls:
45.0ms
(* (- (pow 1.0 4) (* (* (+ 1.0 (exp x)) (+ 1.0 (exp x))) (exp (+ x x)))) x)
68.0ms
(* (+ 1.0 (exp x)) (+ 1.0 (exp x)))
141.0ms
(/ (- (pow (exp x) 3) (pow 1.0 3)) (* (- (pow 1.0 4) (* (* (+ 1.0 (exp x)) (+ 1.0 (exp x))) (exp (+ x x)))) x))
29.0ms
(- (pow (exp x) 3) (pow 1.0 3))

series774.0ms

Counts
4 → 12
Calls
4 calls:
241.0ms
(* (- (pow 1.0 4) (* (* (+ 1.0 (exp x)) (+ 1.0 (exp x))) (exp (+ x x)))) x)
37.0ms
(* (+ 1.0 (exp x)) (+ 1.0 (exp x)))
425.0ms
(/ (- (pow (exp x) 3) (pow 1.0 3)) (* (- (pow 1.0 4) (* (* (+ 1.0 (exp x)) (+ 1.0 (exp x))) (exp (+ x x)))) x))
71.0ms
(- (pow (exp x) 3) (pow 1.0 3))

simplify507.0ms

Counts
176 → 176
Iterations
IterNodes
done5000
1729
0259

prune1.1s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes59.0ms

Accuracy

98.8% (0.2b remaining)

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

bsearch54.0ms

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

simplify10.0ms

Iterations
IterNodes
done56
256
155
041

end0.0ms

sample2.1s

Algorithm
intervals
Results
784.0ms2317×body1280valid
626.0ms5413×body80valid
299.0ms1622×body640valid
112.0ms833×body320valid
31.0ms402×body160valid