Details

Time bar (total: 56.2s)

sample165.0ms

Algorithm
intervals
Results
139.0ms443×body80valid

simplify2.6s

Counts
1 → 1

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize76.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt PI)
0.2b
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
0.1b
(* (/ 1 (sqrt PI)) (+ (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
0.1b
(* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))

rewrite10.2s

Algorithm
rewrite-expression-head
Rules
181×add-exp-log
128×prod-exp
107×add-cbrt-cube
70×cbrt-unprod
51×pow1
48×associate-*l*
46×add-sqr-sqrt
40×times-frac
35×*-un-lft-identity pow-prod-down
33×add-cube-cbrt
19×div-exp
15×associate-*l/
14×sqrt-prod
12×frac-add
11×cbrt-undiv
8×rec-exp 1-exp
6×frac-times flip3-+ associate-*r/ flip-+
5×associate-*r* unswap-sqr
4×insert-posit16 add-log-exp
3×*-commutative div-inv
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2
Counts
4 → 187
Calls
4 calls:
Slowest
8.0s
(* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
2.2s
(* (/ 1 (sqrt PI)) (+ (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
66.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
2.0ms
(sqrt PI)

series632.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
453.0ms
(* (/ 1 (sqrt PI)) (+ (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
95.0ms
(* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
83.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify3.5s

Counts
197 → 197

prune3.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize78.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt PI)
0.2b
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
0.1b
(* (/ 1 (sqrt PI)) (+ (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* 1/21 (pow (fabs x) 7))))
0.1b
(* 1/21 (pow (fabs x) 7))

rewrite710.0ms

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt
39×add-exp-log
38×associate-*l*
32×add-cbrt-cube
31×*-un-lft-identity times-frac
29×add-cube-cbrt
19×prod-exp
16×pow1
15×cbrt-unprod
14×sqrt-prod
11×associate-*r*
8×unswap-sqr
7×pow-prod-down
5×div-exp
4×cbrt-undiv unpow-prod-down insert-posit16 add-log-exp
3×*-commutative
2×frac-times flip3-+ associate-*l/ associate-*r/ flip-+ div-inv sqr-pow
1×distribute-rgt-in pow-to-exp rem-sqrt-square rec-exp distribute-lft-in sqrt-pow1 pow1/2 1-exp pow-exp
Counts
4 → 132
Calls
4 calls:
Slowest
642.0ms
(* (/ 1 (sqrt PI)) (+ (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* 1/21 (pow (fabs x) 7))))
45.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
16.0ms
(* 1/21 (pow (fabs x) 7))
2.0ms
(sqrt PI)

series544.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
384.0ms
(* (/ 1 (sqrt PI)) (+ (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* 1/21 (pow (fabs x) 7))))
101.0ms
(* 1/21 (pow (fabs x) 7))
59.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify1.4s

Counts
142 → 142

prune2.4s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize121.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt PI)
0.2b
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
0.1b
(* (/ 1 (sqrt PI)) (+ (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1 (sqrt 21)) (* (/ 1 (sqrt 21)) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))))))
0.1b
(* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x))

rewrite4.1s

Algorithm
rewrite-expression-head
Rules
122×pow1
60×pow-plus pow-prod-up
48×add-exp-log
44×add-cbrt-cube
40×add-sqr-sqrt
38×associate-*l/
36×associate-*l* frac-add
31×times-frac
29×*-un-lft-identity
27×add-cube-cbrt
26×prod-exp
24×cbrt-unprod
22×frac-times associate-*r/
17×pow-prod-down
14×flip3-+ sqrt-prod flip-+
8×pow2 pow-sqr
7×associate-*r*
5×div-exp unswap-sqr
4×cbrt-undiv pow3 insert-posit16 add-log-exp
3×*-commutative
2×div-inv
1×distribute-rgt-in rem-sqrt-square rec-exp distribute-lft-in sqrt-pow1 pow1/2 1-exp
Counts
4 → 191
Calls
4 calls:
Slowest
3.9s
(* (/ 1 (sqrt PI)) (+ (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1 (sqrt 21)) (* (/ 1 (sqrt 21)) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))))))
155.0ms
(* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x))
59.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms
(sqrt PI)

series623.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
499.0ms
(* (/ 1 (sqrt PI)) (+ (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1 (sqrt 21)) (* (/ 1 (sqrt 21)) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))))))
64.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
59.0ms
(* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x))
0.0ms
(sqrt PI)

simplify3.5s

Counts
201 → 201

prune4.4s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

localize109.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt PI)
1.0b
(sqrt PI)
0.4b
(* (fabs x) 2/3)
0.4b
(* (/ 1 (sqrt (sqrt PI))) (/ (+ (* 2 (fabs x)) (+ (* (* (fabs x) (fabs x)) (* (fabs x) 2/3)) (+ (* 1/5 (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (fabs x))) (* (pow (fabs x) 7) 1/21)))) (sqrt (sqrt PI))))

rewrite7.0s

Algorithm
rewrite-expression-head
Rules
139×add-sqr-sqrt
105×sqrt-prod
99×times-frac
58×*-un-lft-identity
46×add-cube-cbrt
34×associate-*r* associate-*l*
29×unswap-sqr
28×add-exp-log
18×add-cbrt-cube
10×pow1
9×prod-exp
8×div-exp
5×cbrt-unprod
4×cbrt-undiv insert-posit16 add-log-exp
2×rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp pow-prod-down *-commutative div-inv
1×frac-times associate-*l/ associate-*r/
Counts
4 → 162
Calls
4 calls:
Slowest
7.0s
(* (/ 1 (sqrt (sqrt PI))) (/ (+ (* 2 (fabs x)) (+ (* (* (fabs x) (fabs x)) (* (fabs x) 2/3)) (+ (* 1/5 (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (fabs x))) (* (pow (fabs x) 7) 1/21)))) (sqrt (sqrt PI))))
10.0ms
(* (fabs x) 2/3)
2.0ms
(sqrt PI)
1.0ms
(sqrt PI)

series401.0ms

Counts
4 → 8
Calls
4 calls:
Slowest
371.0ms
(* (/ 1 (sqrt (sqrt PI))) (/ (+ (* 2 (fabs x)) (+ (* (* (fabs x) (fabs x)) (* (fabs x) 2/3)) (+ (* 1/5 (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (fabs x))) (* (pow (fabs x) 7) 1/21)))) (sqrt (sqrt PI))))
30.0ms
(* (fabs x) 2/3)
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify1.2s

Counts
170 → 170

prune3.2s

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 0b

regimes492.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch11.0ms

end0.0ms

sample5.0s

Algorithm
intervals
Results
4.8s13902×body80valid