Details

Time bar (total: 16.8s)

sample54.0ms

Algorithm
intervals
Results
37.0ms480×body80valid

simplify105.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
06942
123142
290042
3375342
4500142
done500142

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize25.0ms

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)))))
0.1b
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0b
(sqrt PI)

rewrite9.9s

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:
8.7s
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
1.1s
(* (/ 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)))))
59.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms
(sqrt PI)

series441.0ms

Counts
4 → 10
Calls
4 calls:
74.0ms
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
323.0ms
(* (/ 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)))))
44.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify64.0ms

Counts
175 → 175
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
013384947
150014034
done50014034

prune855.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite588.0ms

Algorithm
rewrite-expression-head
Rules
54×associate-*l/
37×add-sqr-sqrt
36×associate-*l* frac-add
35×pow1 add-exp-log add-cbrt-cube
29×times-frac
27×add-cube-cbrt *-un-lft-identity
22×frac-times associate-*r/
17×prod-exp cbrt-unprod
14×flip3-+ flip-+
13×sqrt-prod
10×pow-prod-down
7×associate-*r*
6×pow-plus pow-prod-up
4×cbrt-undiv div-exp add-log-exp unswap-sqr
3×*-commutative
2×pow2 pow-sqr div-inv
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 pow3
Counts
4 → 151
Calls
4 calls:
18.0ms
(* (* (fabs x) (fabs x)) (fabs x))
503.0ms
(* (/ 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)))))
59.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms
(sqrt PI)

series527.0ms

Counts
4 → 10
Calls
4 calls:
26.0ms
(* (* (fabs x) (fabs x)) (fabs x))
458.0ms
(* (/ 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)))))
43.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify70.0ms

Counts
161 → 161
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
012335351
150014795
done50014795

prune804.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 0.2 (pow (fabs x) 5))
0.1b
(/ (* 1.0 (pow (fabs x) 7)) 21.0)
0.1b
(* 0.6666666666666666 (pow (fabs x) 3))
0.1b
(* (sqrt (/ 1 PI)) (+ (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 0.2 (pow (fabs x) 5)) (* 2.0 (fabs x)))) (/ (* 1.0 (pow (fabs x) 7)) 21.0)))

rewrite324.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
26×add-exp-log
25×*-un-lft-identity
23×associate-*r*
22×add-cube-cbrt associate-*l*
16×sqrt-prod
15×add-cbrt-cube
14×times-frac
11×unswap-sqr
10×prod-exp
8×unpow-prod-down
6×pow1
5×sqrt-div
4×frac-times flip3-+ cube-prod associate-*r/ div-exp frac-add cbrt-unprod flip-+ add-log-exp sqr-pow
3×pow-to-exp pow-exp associate-/r* *-commutative
2×cbrt-undiv div-inv
1×distribute-rgt-in cube-mult frac-2neg distribute-lft-in unpow3 pow-prod-down associate-*l/ clear-num distribute-lft-out associate-/l*
Counts
4 → 125
Calls
4 calls:
11.0ms
(* 0.2 (pow (fabs x) 5))
12.0ms
(/ (* 1.0 (pow (fabs x) 7)) 21.0)
12.0ms
(* 0.6666666666666666 (pow (fabs x) 3))
285.0ms
(* (sqrt (/ 1 PI)) (+ (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 0.2 (pow (fabs x) 5)) (* 2.0 (fabs x)))) (/ (* 1.0 (pow (fabs x) 7)) 21.0)))

series449.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(* 0.2 (pow (fabs x) 5))
71.0ms
(/ (* 1.0 (pow (fabs x) 7)) 21.0)
41.0ms
(* 0.6666666666666666 (pow (fabs x) 3))
277.0ms
(* (sqrt (/ 1 PI)) (+ (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 0.2 (pow (fabs x) 5)) (* 2.0 (fabs x)))) (/ (* 1.0 (pow (fabs x) 7)) 21.0)))

simplify93.0ms

Counts
137 → 137
Iterations

Useful iterations: 1 (19.0ms)

IterNodesCost
07441724
135591604
250011604
done50011604

prune540.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt PI)
1.0b
(* (cbrt PI) (cbrt PI))
1.0b
(/ 1 (sqrt (* (cbrt PI) (cbrt PI))))
1.0b
(sqrt (* (cbrt PI) (cbrt PI)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
28×pow1
22×add-cube-cbrt *-un-lft-identity
19×cbrt-prod pow1/3
18×sqrt-pow1
12×times-frac
11×pow-flip
10×add-exp-log
6×swap-sqr associate-*r* associate-*l* pow-prod-down pow-sqr pow-prod-up add-cbrt-cube
5×sqrt-prod
4×associate-/r* add-log-exp unswap-sqr
3×pow2 pow-plus associate-/l*
2×pow1/2 div-exp
1×cbrt-undiv rem-sqrt-square rec-exp frac-2neg 1-exp prod-exp clear-num *-commutative cbrt-unprod div-inv inv-pow
Counts
4 → 115
Calls
4 calls:
1.0ms
(cbrt PI)
10.0ms
(* (cbrt PI) (cbrt PI))
15.0ms
(/ 1 (sqrt (* (cbrt PI) (cbrt PI))))
8.0ms
(sqrt (* (cbrt PI) (cbrt PI)))

series0.0ms

Counts
4 → 4
Calls
4 calls:
0.0ms
(cbrt PI)
0.0ms
(* (cbrt PI) (cbrt PI))
0.0ms
(/ 1 (sqrt (* (cbrt PI) (cbrt PI))))
0.0ms
(sqrt (* (cbrt PI) (cbrt PI)))

simplify140.0ms

Counts
119 → 119
Iterations

Useful iterations: 3 (133.0ms)

IterNodesCost
0247706
1876647
24260542
35002537
done5002537

prune438.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes102.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03920
13920
done3920

end0.0ms

sample1.2s

Algorithm
intervals
Results
979.0ms14106×body80valid