Details

Time bar (total: 3.8m)

sample115.0ms

Algorithm
intervals
Results
31.0ms55×body640valid
31.0ms93×body10240exit
29.0ms71×body1280valid
5.0ms27×body320valid
5.0ms89×body80valid
2.0ms14×body160valid

simplify19.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
19.0ms
(/ (exp x) (- (exp x) 1))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.4b

localize16.0ms

Local error

Found 2 expressions with local error:

4.2b
(- (exp x) 1)
0.5b
(/ (exp x) (- (exp x) 1))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
29×*-un-lft-identity
21×times-frac
14×add-cube-cbrt
10×difference-of-squares
7×associate-/r*
5×difference-of-sqr-1 distribute-lft-out--
4×add-cbrt-cube add-log-exp
3×add-exp-log associate-/l*
2×pow1 flip3-- associate-/r/ insert-posit16 flip--
1×cbrt-undiv clear-num sub-neg frac-2neg diff-log div-exp div-inv
Counts
2 → 63
Calls
2 calls:
Slowest
17.0ms
(/ (exp x) (- (exp x) 1))
17.0ms
(- (exp x) 1)

series434.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
414.0ms
(/ (exp x) (- (exp x) 1))
20.0ms
(- (exp x) 1)

simplify1.7s

Counts
68 → 69
Calls
68 calls:
Slowest
366.0ms
(/ (* (* (exp x) (exp x)) (exp x)) (* (* (- (exp x) 1) (- (exp x) 1)) (- (exp x) 1)))
202.0ms
(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
76.0ms
(/ (* (cbrt (exp x)) (cbrt (exp x))) (* (cbrt (- (exp x) 1)) (cbrt (- (exp x) 1))))
41.0ms
(+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))
36.0ms
(/ (* (cbrt (exp x)) (cbrt (exp x))) (+ (sqrt (exp x)) 1))

prune543.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize20.0ms

Local error

Found 1 expressions with local error:

0.3b
(* 1/12 x)

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt
3×pow1 *-un-lft-identity add-cbrt-cube associate-*r* associate-*l* add-exp-log add-cube-cbrt
1×pow-prod-down prod-exp *-commutative cbrt-unprod insert-posit16 add-log-exp unswap-sqr
Counts
1 → 19
Calls
1 calls:
Slowest
10.0ms
(* 1/12 x)

series16.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
16.0ms
(* 1/12 x)

simplify210.0ms

Counts
12 → 22
Calls
12 calls:
Slowest
174.0ms
(* (* (* 1/12 1/12) 1/12) (* (* x x) x))
8.0ms
(* (sqrt 1/12) (sqrt x))
4.0ms
(* (sqrt 1/12) (sqrt x))
4.0ms
(+ (log 1/12) (log x))
4.0ms
(* (cbrt 1/12) (cbrt 1/12))

prune173.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.5b

localize46.0ms

Local error

Found 2 expressions with local error:

59.8b
(posit16->real (real->posit16 (* 1/12 x)))
0.3b
(* 1/12 x)

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
4×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
3×associate-*r* associate-*l*
2×insert-posit16 add-log-exp
1×pow-prod-down prod-exp *-commutative cbrt-unprod remove-posit16 unswap-sqr
Counts
2 → 28
Calls
2 calls:
Slowest
5.0ms
(* 1/12 x)
0.0ms
(posit16->real (real->posit16 (* 1/12 x)))

series51.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
27.0ms
(* 1/12 x)
24.0ms
(posit16->real (real->posit16 (* 1/12 x)))

simplify269.0ms

Counts
15 → 34
Calls
15 calls:
Slowest
196.0ms
(* (* (* 1/12 1/12) 1/12) (* (* x x) x))
8.0ms
(+ (log 1/12) (log x))
7.0ms
(* (sqrt 1/12) (sqrt x))
6.0ms
(* (cbrt 1/12) (cbrt 1/12))
6.0ms
(* 1/12 x)

prune687.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.5b

localize40.0ms

Local error

Found 4 expressions with local error:

4.0b
(- (pow (exp x) 3) (pow 1 3))
0.5b
(/ (exp x) (/ (- (pow (exp x) 3) (pow 1 3)) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))))
0.4b
(/ (- (pow (exp x) 3) (pow 1 3)) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))))
0.0b
(pow (exp x) 3)

rewrite322.0ms

Algorithm
rewrite-expression-head
Rules
834×times-frac
818×add-sqr-sqrt
631×*-un-lft-identity
408×difference-of-squares
309×unpow-prod-down cube-prod
308×add-cube-cbrt
171×sqr-pow
111×associate-/r*
102×distribute-lft-out--
37×associate-/l*
18×cube-mult
17×difference-cubes
12×add-cbrt-cube
11×associate-/r/
9×add-exp-log
6×div-inv add-log-exp
5×pow1 flip3-+ flip-+
4×cbrt-undiv pow-pow div-exp insert-posit16
3×pow-unpow exp-prod
2×clear-num frac-2neg flip3-- flip-- associate-/l/
1×pow-to-exp sub-neg diff-log unpow3 div-sub pow-exp rem-cube-cbrt
Counts
4 → 679
Calls
4 calls:
Slowest
147.0ms
(/ (exp x) (/ (- (pow (exp x) 3) (pow 1 3)) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))))
128.0ms
(/ (- (pow (exp x) 3) (pow 1 3)) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))))
24.0ms
(- (pow (exp x) 3) (pow 1 3))
3.0ms
(pow (exp x) 3)

series342.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
133.0ms
(/ (exp x) (/ (- (pow (exp x) 3) (pow 1 3)) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))))
107.0ms
(/ (- (pow (exp x) 3) (pow 1 3)) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))))
71.0ms
(- (pow (exp x) 3) (pow 1 3))
30.0ms
(pow (exp x) 3)

simplify3.6m

Counts
1095 → 691
Calls
1095 calls:
Slowest
755.0ms
(/ (sqrt (exp x)) (/ (+ (sqrt (pow (exp x) 3)) (pow 1 3)) (sqrt (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))))))
681.0ms
(/ (* (* (exp x) (exp x)) (exp x)) (/ (* (* (- (pow (exp x) 3) (pow 1 3)) (- (pow (exp x) 3) (pow 1 3))) (- (pow (exp x) 3) (pow 1 3))) (* (* (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))))))
612.0ms
(/ (* (cbrt (exp x)) (cbrt (exp x))) (/ (+ (pow (sqrt (exp x)) 3) (pow (sqrt 1) 3)) (sqrt (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))))))
604.0ms
(/ (cbrt (exp x)) (/ (- (pow (exp x) 3) (pow 1 3)) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))))
553.0ms
(/ (cbrt (exp x)) (/ (- (exp x) 1) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))))

prune5.4s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.5b

regimes93.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 20.9b

bsearch41.0ms

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.0s2258×body1280valid
657.0ms2624×body10240exit
349.0ms1654×body640valid
169.0ms835×body320valid
152.0ms2807×body80valid
38.0ms447×body160valid