Details

Time bar (total: 34.7s)

sample68.0ms

Algorithm
intervals
Results
45.0ms422×body80valid

simplify107.0ms

Counts
1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize73.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
0.1b
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
0.2b
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0b
(sqrt PI)

rewrite16.0s

Algorithm
rewrite-expression-head
Rules
107×add-exp-log add-cbrt-cube
70×prod-exp cbrt-unprod
51×pow1
48×associate-*l*
42×add-sqr-sqrt
38×times-frac
35×pow-prod-down
33×add-cube-cbrt *-un-lft-identity
15×associate-*l/
13×sqrt-prod
12×frac-add
11×cbrt-undiv div-exp
6×frac-times flip3-+ associate-*r/ flip-+
5×associate-*r*
4×add-log-exp
3×*-commutative div-inv unswap-sqr
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2
Counts
4 → 165
Calls
4 calls:
14.4s
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
1.5s
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
101.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
2.0ms
(sqrt PI)

series668.0ms

Counts
4 → 10
Calls
4 calls:
116.0ms
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
473.0ms
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
78.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify85.0ms

Counts
175 → 175

prune1.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1 (sqrt 21.0)) (* (* (/ 1.0 (sqrt 21.0)) (pow (fabs x) 6)) (fabs x)))
0.1b
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1 (sqrt 21.0)) (* (* (/ 1.0 (sqrt 21.0)) (pow (fabs x) 6)) (fabs x)))))
0.2b
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0b
(sqrt PI)

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
158×add-exp-log
98×prod-exp
62×add-cbrt-cube
59×associate-*l/
57×associate-*l*
48×add-sqr-sqrt
47×times-frac
39×add-cube-cbrt *-un-lft-identity
36×frac-add
32×div-exp cbrt-unprod
23×frac-times associate-*r/
22×sqrt-prod
21×pow1
14×flip3-+ flip-+
10×cbrt-undiv pow-prod-down
8×pow-to-exp rec-exp 1-exp pow-exp
5×associate-*r*
4×add-log-exp
3×*-commutative div-inv unswap-sqr
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2
Counts
4 → 199
Calls
4 calls:
222.0ms
(* (/ 1 (sqrt 21.0)) (* (* (/ 1.0 (sqrt 21.0)) (pow (fabs x) 6)) (fabs x)))
847.0ms
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1 (sqrt 21.0)) (* (* (/ 1.0 (sqrt 21.0)) (pow (fabs x) 6)) (fabs x)))))
95.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
2.0ms
(sqrt PI)

series1.1s

Counts
4 → 10
Calls
4 calls:
245.0ms
(* (/ 1 (sqrt 21.0)) (* (* (/ 1.0 (sqrt 21.0)) (pow (fabs x) 6)) (fabs x)))
760.0ms
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1 (sqrt 21.0)) (* (* (/ 1.0 (sqrt 21.0)) (pow (fabs x) 6)) (fabs x)))))
82.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify111.0ms

Counts
209 → 209

prune1.7s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 3602879701896397.0 18014398509481984.0) (pow (fabs x) 5))
0.1b
(/ (* 1.0 (pow (fabs x) 7)) 21.0)
0.1b
(* (sqrt (/ 1 PI)) (+ (+ (* (/ 6004799503160661.0 9007199254740992.0) (pow (fabs x) 3)) (+ (* (/ 3602879701896397.0 18014398509481984.0) (pow (fabs x) 5)) (* 2.0 (fabs x)))) (/ (* 1.0 (pow (fabs x) 7)) 21.0)))
0.1b
(* (/ 6004799503160661.0 9007199254740992.0) (pow (fabs x) 3))

rewrite909.0ms

Algorithm
rewrite-expression-head
Rules
74×add-sqr-sqrt
42×add-exp-log associate-*l*
39×times-frac
37×*-un-lft-identity
34×add-cube-cbrt
23×associate-*r*
21×add-cbrt-cube
18×unswap-sqr
16×prod-exp sqrt-prod
12×frac-add
10×unpow-prod-down div-exp
7×sqrt-div associate-*l/
6×pow1 frac-times flip3-+ associate-*r/ cbrt-unprod flip-+ sqr-pow
5×pow-to-exp cube-prod pow-exp
4×cbrt-undiv div-inv add-log-exp
3×associate-/r* *-commutative
1×distribute-rgt-in cube-mult frac-2neg distribute-lft-in unpow3 pow-prod-down clear-num distribute-lft-out associate-/l*
Counts
4 → 166
Calls
4 calls:
21.0ms
(* (/ 3602879701896397.0 18014398509481984.0) (pow (fabs x) 5))
12.0ms
(/ (* 1.0 (pow (fabs x) 7)) 21.0)
846.0ms
(* (sqrt (/ 1 PI)) (+ (+ (* (/ 6004799503160661.0 9007199254740992.0) (pow (fabs x) 3)) (+ (* (/ 3602879701896397.0 18014398509481984.0) (pow (fabs x) 5)) (* 2.0 (fabs x)))) (/ (* 1.0 (pow (fabs x) 7)) 21.0)))
23.0ms
(* (/ 6004799503160661.0 9007199254740992.0) (pow (fabs x) 3))

series679.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(* (/ 3602879701896397.0 18014398509481984.0) (pow (fabs x) 5))
104.0ms
(/ (* 1.0 (pow (fabs x) 7)) 21.0)
410.0ms
(* (sqrt (/ 1 PI)) (+ (+ (* (/ 6004799503160661.0 9007199254740992.0) (pow (fabs x) 3)) (+ (* (/ 3602879701896397.0 18014398509481984.0) (pow (fabs x) 5)) (* 2.0 (fabs x)))) (/ (* 1.0 (pow (fabs x) 7)) 21.0)))
78.0ms
(* (/ 6004799503160661.0 9007199254740992.0) (pow (fabs x) 3))

simplify70.0ms

Counts
178 → 178

prune1.5s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (pow (fabs x) 7) (sqrt 21.0))
0.1b
(* (/ 1.0 (sqrt 21.0)) (/ (pow (fabs x) 7) (sqrt 21.0)))
0.1b
(* (sqrt (/ 1 PI)) (+ (+ (* (/ 6004799503160661.0 9007199254740992.0) (pow (fabs x) 3)) (+ (* (/ 3602879701896397.0 18014398509481984.0) (pow (fabs x) 5)) (* 2.0 (fabs x)))) (* (/ 1.0 (sqrt 21.0)) (/ (pow (fabs x) 7) (sqrt 21.0)))))
0.1b
(* (/ 6004799503160661.0 9007199254740992.0) (pow (fabs x) 3))

rewrite922.0ms

Algorithm
rewrite-expression-head
Rules
188×add-sqr-sqrt
158×times-frac
94×*-un-lft-identity
93×add-cube-cbrt
86×sqrt-prod
61×associate-*r*
51×associate-*l*
50×unpow-prod-down
48×add-exp-log
36×frac-add
33×unswap-sqr
25×add-cbrt-cube
23×frac-times associate-*r/ associate-*l/
22×sqr-pow
16×div-exp
15×sqrt-div prod-exp
14×flip3-+ flip-+
8×pow1
7×cbrt-unprod associate-/l*
6×cbrt-undiv associate-/r*
5×pow-to-exp cube-prod pow-exp div-inv
4×add-log-exp
3×*-commutative
2×pow-prod-down
1×distribute-rgt-in cube-mult frac-2neg distribute-lft-in unpow3 clear-num
Counts
4 → 297
Calls
4 calls:
21.0ms
(/ (pow (fabs x) 7) (sqrt 21.0))
82.0ms
(* (/ 1.0 (sqrt 21.0)) (/ (pow (fabs x) 7) (sqrt 21.0)))
753.0ms
(* (sqrt (/ 1 PI)) (+ (+ (* (/ 6004799503160661.0 9007199254740992.0) (pow (fabs x) 3)) (+ (* (/ 3602879701896397.0 18014398509481984.0) (pow (fabs x) 5)) (* 2.0 (fabs x)))) (* (/ 1.0 (sqrt 21.0)) (/ (pow (fabs x) 7) (sqrt 21.0)))))
36.0ms
(* (/ 6004799503160661.0 9007199254740992.0) (pow (fabs x) 3))

series1.1s

Counts
4 → 12
Calls
4 calls:
164.0ms
(/ (pow (fabs x) 7) (sqrt 21.0))
271.0ms
(* (/ 1.0 (sqrt 21.0)) (/ (pow (fabs x) 7) (sqrt 21.0)))
607.0ms
(* (sqrt (/ 1 PI)) (+ (+ (* (/ 6004799503160661.0 9007199254740992.0) (pow (fabs x) 3)) (+ (* (/ 3602879701896397.0 18014398509481984.0) (pow (fabs x) 5)) (* 2.0 (fabs x)))) (* (/ 1.0 (sqrt 21.0)) (/ (pow (fabs x) 7) (sqrt 21.0)))))
77.0ms
(* (/ 6004799503160661.0 9007199254740992.0) (pow (fabs x) 3))

simplify104.0ms

Counts
309 → 309

prune2.6s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes240.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify72.0ms

end0.0ms

sample4.2s

Algorithm
intervals
Results
3.8s14061×body80valid