Details

Time bar (total: 33.4s)

sample146.0ms

Algorithm
intervals
Results
123.0ms471×body80valid

simplify1.3s

Counts
1 → 1
Iterations
IterNodes
done2017
42017
31250
2261
175
028

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize107.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* (* (fabs x) (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)))))
0.2b
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
1.0b
(sqrt PI)

rewrite1.9s

Algorithm
rewrite-expression-head
Rules
62×pow1
43×add-exp-log
40×add-sqr-sqrt
39×add-cbrt-cube
36×associate-*l*
31×times-frac
29×*-un-lft-identity
27×add-cube-cbrt
22×prod-exp
21×pow-plus pow-prod-up
20×cbrt-unprod
14×associate-*l/ sqrt-prod
13×pow-prod-down
12×frac-add
7×associate-*r*
6×frac-times flip3-+ associate-*r/ flip-+
5×div-exp unswap-sqr
4×pow2 expm1-log1p-u cbrt-undiv pow-sqr insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative
2×pow3 div-inv
1×distribute-rgt-in rem-sqrt-square rec-exp distribute-lft-in sqrt-pow1 pow1/2 1-exp
Counts
4 → 162
Calls
4 calls:
51.0ms
(* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x))
1.8s
(* (/ 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)))))
65.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
2.0ms
(sqrt PI)

series457.0ms

Counts
4 → 10
Calls
4 calls:
49.0ms
(* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x))
356.0ms
(* (/ 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)))))
52.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify1.7s

Counts
172 → 172
Iterations
IterNodes
done2002
22002
11053
0306

prune2.9s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize95.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* (* (fabs x) (fabs x)) (fabs x)) (sqrt (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)) (sqrt (fabs x))) (sqrt (fabs x))) (fabs x)) (fabs x)) (fabs x)))))
0.2b
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
1.0b
(sqrt PI)

rewrite3.3s

Algorithm
rewrite-expression-head
Rules
62×pow1
43×add-exp-log
41×add-sqr-sqrt
39×add-cbrt-cube
36×associate-*l*
31×times-frac
30×*-un-lft-identity pow-prod-up
28×add-cube-cbrt
22×prod-exp
20×cbrt-unprod
17×sqrt-prod
14×associate-*l/
13×pow-prod-down
12×pow-plus frac-add
10×sqrt-pow1 pow1/2 associate-*r*
6×frac-times flip3-+ associate-*r/ flip-+
5×div-exp unswap-sqr
4×pow2 expm1-log1p-u cbrt-undiv pow-sqr insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative
2×pow3 div-inv
1×distribute-rgt-in rem-sqrt-square rec-exp distribute-lft-in 1-exp
Counts
4 → 165
Calls
4 calls:
61.0ms
(* (* (* (fabs x) (fabs x)) (fabs x)) (sqrt (fabs x)))
3.2s
(* (/ 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)) (sqrt (fabs x))) (sqrt (fabs x))) (fabs x)) (fabs x)) (fabs x)))))
46.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
2.0ms
(sqrt PI)

series513.0ms

Counts
4 → 10
Calls
4 calls:
64.0ms
(* (* (* (fabs x) (fabs x)) (fabs x)) (sqrt (fabs x)))
377.0ms
(* (/ 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)) (sqrt (fabs x))) (sqrt (fabs x))) (fabs x)) (fabs x)) (fabs x)))))
72.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify1.5s

Counts
175 → 175
Iterations
IterNodes
done2003
22003
11135
0322

prune3.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize75.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (fma 1/21 (* (* (fabs x) (* (fabs x) (fabs x))) (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x)))) (fma 2 (fabs x) (fma (* (fabs x) (* (fabs x) (fabs x))) 2/3 (/ (* (* (fabs x) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) 5)))) (sqrt (sqrt PI)))
0.3b
(* (/ 1 (sqrt (sqrt PI))) (/ (fma 1/21 (* (* (fabs x) (* (fabs x) (fabs x))) (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x)))) (fma 2 (fabs x) (fma (* (fabs x) (* (fabs x) (fabs x))) 2/3 (/ (* (* (fabs x) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) 5)))) (sqrt (sqrt PI))))
1.0b
(sqrt PI)
1.0b
(sqrt PI)

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
157×add-sqr-sqrt
141×sqrt-prod
126×times-frac
78×*-un-lft-identity
66×add-cube-cbrt
31×associate-*r* associate-*l*
28×add-exp-log unswap-sqr
18×add-cbrt-cube
9×associate-/r* div-exp
8×pow1 prod-exp
5×cbrt-undiv
4×expm1-log1p-u cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×div-inv associate-/l*
2×rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp
1×frac-times clear-num frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 203
Calls
4 calls:
11.0ms
(/ (fma 1/21 (* (* (fabs x) (* (fabs x) (fabs x))) (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x)))) (fma 2 (fabs x) (fma (* (fabs x) (* (fabs x) (fabs x))) 2/3 (/ (* (* (fabs x) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) 5)))) (sqrt (sqrt PI)))
51.0ms
(* (/ 1 (sqrt (sqrt PI))) (/ (fma 1/21 (* (* (fabs x) (* (fabs x) (fabs x))) (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x)))) (fma 2 (fabs x) (fma (* (fabs x) (* (fabs x) (fabs x))) 2/3 (/ (* (* (fabs x) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) 5)))) (sqrt (sqrt PI))))
2.0ms
(sqrt PI)
2.0ms
(sqrt PI)

series947.0ms

Counts
4 → 8
Calls
4 calls:
590.0ms
(/ (fma 1/21 (* (* (fabs x) (* (fabs x) (fabs x))) (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x)))) (fma 2 (fabs x) (fma (* (fabs x) (* (fabs x) (fabs x))) 2/3 (/ (* (* (fabs x) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) 5)))) (sqrt (sqrt PI)))
357.0ms
(* (/ 1 (sqrt (sqrt PI))) (/ (fma 1/21 (* (* (fabs x) (* (fabs x) (fabs x))) (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x)))) (fma 2 (fabs x) (fma (* (fabs x) (* (fabs x) (fabs x))) 2/3 (/ (* (* (fabs x) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) 5)))) (sqrt (sqrt PI))))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify1.9s

Counts
211 → 211
Iterations
IterNodes
done2002
32002
21882
1606
0229

prune4.0s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize88.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
28×pow1
22×*-un-lft-identity add-cube-cbrt
19×cbrt-prod pow1/3
18×sqrt-pow1
12×times-frac
11×pow-flip
10×add-exp-log
6×add-cbrt-cube swap-sqr associate-*r* associate-*l* pow-prod-down pow-sqr pow-prod-up
5×sqrt-prod
4×expm1-log1p-u associate-/r* insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×pow2 pow-plus associate-/l*
2×pow1/2 div-exp
1×cbrt-undiv rem-sqrt-square rec-exp clear-num frac-2neg 1-exp prod-exp *-commutative cbrt-unprod div-inv inv-pow
Counts
4 → 127
Calls
4 calls:
1.0ms
(cbrt PI)
17.0ms
(/ 1 (sqrt (* (cbrt PI) (cbrt PI))))
5.0ms
(sqrt (* (cbrt PI) (cbrt PI)))
8.0ms
(* (cbrt PI) (cbrt PI))

series0.0ms

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

simplify1.6s

Counts
131 → 131
Iterations
IterNodes
done2014
42014
31118
2478
1253
0137

prune2.2s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes251.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify22.0ms

Iterations
IterNodes
done53
153
032

end0.0ms

sample4.8s

Algorithm
intervals
Results
4.6s14037×body80valid