Details

Time bar (total: 17.4s)

sample54.0ms

Algorithm
intervals
Results
36.0ms480×body80valid

simplify111.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
07042
125242
2105942
3471342
4500142
done500142

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize24.0ms

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)

rewrite10.1s

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×expm1-log1p-u log1p-expm1-u 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 → 173
Calls
4 calls:
8.8s
(* (/ 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)

series436.0ms

Counts
4 → 10
Calls
4 calls:
72.0ms
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
316.0ms
(* (/ 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)))))
48.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify60.0ms

Counts
183 → 183
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
013665031
150013864
done50013864

prune701.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1.0 5.0) (* (* (* (* (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)))) (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 21.0)) (* (* (/ (cbrt 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)

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
75×add-exp-log add-cbrt-cube
55×associate-*l/
48×associate-*l*
44×prod-exp cbrt-unprod
42×add-sqr-sqrt
38×times-frac
36×pow1 frac-add
33×add-cube-cbrt *-un-lft-identity
22×frac-times associate-*r/ pow-prod-down
14×flip3-+ flip-+
13×sqrt-prod
9×cbrt-undiv div-exp
5×associate-*r*
4×expm1-log1p-u log1p-expm1-u 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 → 179
Calls
4 calls:
595.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
505.0ms
(* (/ 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)))) (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 21.0)) (* (* (/ (cbrt 1.0) (sqrt 21.0)) (pow (fabs x) 6)) (fabs x)))))
58.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
2.0ms
(sqrt PI)

series608.0ms

Counts
4 → 10
Calls
4 calls:
59.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
505.0ms
(* (/ 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)))) (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 21.0)) (* (* (/ (cbrt 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)

simplify69.0ms

Counts
189 → 189
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
014946266
150025295
done50025295

prune1.0s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (pow (fabs x) 3) 0.6666666666666666 (+ (fma 0.2 (pow (fabs x) 5) (* 2.0 (fabs x))) (/ (* 1.0 (pow (fabs x) 7)) 21.0)))
0.0b
(fma 0.2 (pow (fabs x) 5) (* 2.0 (fabs x)))
0.1b
(/ (* 1.0 (pow (fabs x) 7)) 21.0)
0.1b
(* (* 1.0 (fma (pow (fabs x) 3) 0.6666666666666666 (+ (fma 0.2 (pow (fabs x) 5) (* 2.0 (fabs x))) (/ (* 1.0 (pow (fabs x) 7)) 21.0)))) (sqrt (/ 1 PI)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
19×add-exp-log
16×associate-*r*
14×add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube
13×sqrt-prod
12×times-frac
9×pow1
6×prod-exp
4×expm1-log1p-u div-exp cbrt-unprod log1p-expm1-u add-log-exp
3×pow-prod-down associate-/r*
2×cbrt-undiv fma-udef div-inv
1×pow-to-exp frac-2neg sqrt-div associate-*r/ associate-*l* pow-exp clear-num *-commutative associate-/l*
Counts
4 → 79
Calls
4 calls:
0.0ms
(fma (pow (fabs x) 3) 0.6666666666666666 (+ (fma 0.2 (pow (fabs x) 5) (* 2.0 (fabs x))) (/ (* 1.0 (pow (fabs x) 7)) 21.0)))
0.0ms
(fma 0.2 (pow (fabs x) 5) (* 2.0 (fabs x)))
11.0ms
(/ (* 1.0 (pow (fabs x) 7)) 21.0)
25.0ms
(* (* 1.0 (fma (pow (fabs x) 3) 0.6666666666666666 (+ (fma 0.2 (pow (fabs x) 5) (* 2.0 (fabs x))) (/ (* 1.0 (pow (fabs x) 7)) 21.0)))) (sqrt (/ 1 PI)))

series643.0ms

Counts
4 → 12
Calls
4 calls:
193.0ms
(fma (pow (fabs x) 3) 0.6666666666666666 (+ (fma 0.2 (pow (fabs x) 5) (* 2.0 (fabs x))) (/ (* 1.0 (pow (fabs x) 7)) 21.0)))
78.0ms
(fma 0.2 (pow (fabs x) 5) (* 2.0 (fabs x)))
67.0ms
(/ (* 1.0 (pow (fabs x) 7)) 21.0)
304.0ms
(* (* 1.0 (fma (pow (fabs x) 3) 0.6666666666666666 (+ (fma 0.2 (pow (fabs x) 5) (* 2.0 (fabs x))) (/ (* 1.0 (pow (fabs x) 7)) 21.0)))) (sqrt (/ 1 PI)))

simplify50.0ms

Counts
91 → 91
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
03801208
117571046
250021032
done50021032

prune373.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt PI)
1.0b
(cbrt PI)
1.0b
(cbrt PI)
1.0b
(* (cbrt PI) (cbrt PI))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 81
Calls
4 calls:
1.0ms
(cbrt PI)
1.0ms
(cbrt PI)
1.0ms
(cbrt PI)
10.0ms
(* (cbrt PI) (cbrt PI))

series0.0ms

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

simplify71.0ms

Counts
85 → 85
Iterations

Useful iterations: 3 (66.0ms)

IterNodesCost
0153481
1565458
22594435
35002432
done5002432

prune493.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes82.0ms

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
03318
13318
done3318

end0.0ms

sample1.2s

Algorithm
intervals
Results
938.0ms14106×body80valid