Details

Time bar (total: 32.4s)

sample67.0ms

Algorithm
intervals
Results
48.0ms445×body80valid

simplify3.3s

Counts
1 → 1
Iterations
IterNodes
done5000
43921
3997
2247
170
028

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize86.0ms

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)))) (* (/ 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)

rewrite2.2s

Algorithm
rewrite-expression-head
Rules
75×add-cbrt-cube add-exp-log
48×associate-*l*
44×prod-exp cbrt-unprod
42×add-sqr-sqrt
38×times-frac
36×pow1
33×*-un-lft-identity add-cube-cbrt
22×pow-prod-down
15×associate-*l/
13×sqrt-prod
12×frac-add
9×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 → 163
Calls
4 calls:
739.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
1.4s
(* (/ 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)))))
58.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms
(sqrt PI)

series625.0ms

Counts
4 → 10
Calls
4 calls:
81.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
465.0ms
(* (/ 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)))))
79.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify2.5s

Counts
173 → 173
Iterations
IterNodes
done5001
11200
0350

prune1.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize63.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sqrt (/ 1.0 (sqrt PI))) (fma (* (* (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0) (fma (fabs x) 2.0 (fma (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)) (* (* (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (/ 1.0 5.0))))))
0.3b
(* (sqrt (/ 1.0 (sqrt PI))) (* (sqrt (/ 1.0 (sqrt PI))) (fma (* (* (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0) (fma (fabs x) 2.0 (fma (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)) (* (* (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (/ 1.0 5.0)))))))
1.0b
(sqrt PI)
1.0b
(sqrt PI)

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
72×sqrt-prod
50×associate-*l*
47×add-sqr-sqrt
38×times-frac
35×*-un-lft-identity add-cube-cbrt
13×pow1
11×add-cbrt-cube add-exp-log
6×fma-udef
5×distribute-rgt-in distribute-lft-in sqrt-div
4×expm1-log1p-u associate-*r* pow-prod-down associate-*l/ prod-exp cbrt-unprod log1p-expm1-u add-log-exp unswap-sqr
2×rem-sqrt-square sqrt-pow1 pow1/2 *-commutative div-inv
1×frac-times associate-*r/
Counts
4 → 127
Calls
4 calls:
35.0ms
(* (sqrt (/ 1.0 (sqrt PI))) (fma (* (* (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0) (fma (fabs x) 2.0 (fma (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)) (* (* (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (/ 1.0 5.0))))))
62.0ms
(* (sqrt (/ 1.0 (sqrt PI))) (* (sqrt (/ 1.0 (sqrt PI))) (fma (* (* (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0) (fma (fabs x) 2.0 (fma (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)) (* (* (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (/ 1.0 5.0)))))))
2.0ms
(sqrt PI)
2.0ms
(sqrt PI)

series1.3s

Counts
4 → 8
Calls
4 calls:
748.0ms
(* (sqrt (/ 1.0 (sqrt PI))) (fma (* (* (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0) (fma (fabs x) 2.0 (fma (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)) (* (* (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (/ 1.0 5.0))))))
592.0ms
(* (sqrt (/ 1.0 (sqrt PI))) (* (sqrt (/ 1.0 (sqrt PI))) (fma (* (* (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0) (fma (fabs x) 2.0 (fma (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)) (* (* (* (fabs x) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (/ 1.0 5.0)))))))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify2.8s

Counts
135 → 135
Iterations
IterNodes
done5001
21481
1427
0183

prune1.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize92.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 0.6666666666666666 (* (fabs x) (fabs x)))
0.2b
(* (fma 0.2 (pow (fabs x) 5) (fma 0.047619047619047616 (pow (fabs x) 7) (* (fabs x) (+ 2.0 (* 0.6666666666666666 (* (fabs x) (fabs x))))))) (pow (/ 1 PI) 1/4))
0.3b
(* (sqrt (/ 1.0 (sqrt PI))) (* (sqrt 1.0) (* (fma 0.2 (pow (fabs x) 5) (fma 0.047619047619047616 (pow (fabs x) 7) (* (fabs x) (+ 2.0 (* 0.6666666666666666 (* (fabs x) (fabs x))))))) (pow (/ 1 PI) 1/4))))
1.0b
(sqrt PI)

rewrite193.0ms

Algorithm
rewrite-expression-head
Rules
50×add-exp-log
41×add-sqr-sqrt
34×sqrt-prod
31×associate-*l*
30×*-un-lft-identity prod-exp
29×times-frac add-cube-cbrt
20×add-cbrt-cube
19×associate-*r*
16×unpow-prod-down
15×pow1
10×cbrt-unprod
8×pow-exp
6×pow-prod-down unswap-sqr
4×expm1-log1p-u div-exp log1p-expm1-u add-log-exp
3×*-commutative
2×pow-to-exp rec-exp 1-exp div-inv sqr-pow
1×rem-sqrt-square sqrt-pow1 pow1/2 sqrt-div associate-*l/
Counts
4 → 128
Calls
4 calls:
26.0ms
(* 0.6666666666666666 (* (fabs x) (fabs x)))
31.0ms
(* (fma 0.2 (pow (fabs x) 5) (fma 0.047619047619047616 (pow (fabs x) 7) (* (fabs x) (+ 2.0 (* 0.6666666666666666 (* (fabs x) (fabs x))))))) (pow (/ 1 PI) 1/4))
130.0ms
(* (sqrt (/ 1.0 (sqrt PI))) (* (sqrt 1.0) (* (fma 0.2 (pow (fabs x) 5) (fma 0.047619047619047616 (pow (fabs x) 7) (* (fabs x) (+ 2.0 (* 0.6666666666666666 (* (fabs x) (fabs x))))))) (pow (/ 1 PI) 1/4))))
1.0ms
(sqrt PI)

series1.2s

Counts
4 → 10
Calls
4 calls:
46.0ms
(* 0.6666666666666666 (* (fabs x) (fabs x)))
658.0ms
(* (fma 0.2 (pow (fabs x) 5) (fma 0.047619047619047616 (pow (fabs x) 7) (* (fabs x) (+ 2.0 (* 0.6666666666666666 (* (fabs x) (fabs x))))))) (pow (/ 1 PI) 1/4))
518.0ms
(* (sqrt (/ 1.0 (sqrt PI))) (* (sqrt 1.0) (* (fma 0.2 (pow (fabs x) 5) (fma 0.047619047619047616 (pow (fabs x) 7) (* (fabs x) (+ 2.0 (* 0.6666666666666666 (* (fabs x) (fabs x))))))) (pow (/ 1 PI) 1/4))))
0.0ms
(sqrt PI)

simplify3.0s

Counts
138 → 138
Iterations
IterNodes
done5000
21979
1593
0259

prune1.5s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b
(fma (/ 2.0 3.0) (* (fabs x) (fabs x)) (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (fma (* (fabs x) (fabs x)) (/ 1.0 21.0) (/ 1.0 5.0))))
0.2b
(/ (sqrt PI) (fabs x))
0.3b
(/ 1.0 (/ (/ (sqrt PI) (fabs x)) (+ (fma (/ 2.0 3.0) (* (fabs x) (fabs x)) (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (fma (* (fabs x) (fabs x)) (/ 1.0 21.0) (/ 1.0 5.0)))) 2.0)))
1.0b
(sqrt PI)

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
940×times-frac
591×*-un-lft-identity
416×add-sqr-sqrt
415×add-cube-cbrt
159×sqrt-prod
97×associate-/r*
88×distribute-lft-out
22×div-inv
15×add-cbrt-cube add-exp-log
9×associate-/r/ associate-/l*
7×cbrt-undiv div-exp
5×pow1
4×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u add-log-exp
2×clear-num frac-2neg
1×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef
Counts
4 → 464
Calls
4 calls:
0.0ms
(fma (/ 2.0 3.0) (* (fabs x) (fabs x)) (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (fma (* (fabs x) (fabs x)) (/ 1.0 21.0) (/ 1.0 5.0))))
6.0ms
(/ (sqrt PI) (fabs x))
46.0ms
(/ 1.0 (/ (/ (sqrt PI) (fabs x)) (+ (fma (/ 2.0 3.0) (* (fabs x) (fabs x)) (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (fma (* (fabs x) (fabs x)) (/ 1.0 21.0) (/ 1.0 5.0)))) 2.0)))
2.0ms
(sqrt PI)

series624.0ms

Counts
4 → 10
Calls
4 calls:
169.0ms
(fma (/ 2.0 3.0) (* (fabs x) (fabs x)) (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (fma (* (fabs x) (fabs x)) (/ 1.0 21.0) (/ 1.0 5.0))))
51.0ms
(/ (sqrt PI) (fabs x))
402.0ms
(/ 1.0 (/ (/ (sqrt PI) (fabs x)) (+ (fma (/ 2.0 3.0) (* (fabs x) (fabs x)) (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (fma (* (fabs x) (fabs x)) (/ 1.0 21.0) (/ 1.0 5.0)))) 2.0)))
0.0ms
(sqrt PI)

simplify3.0s

Counts
474 → 474
Iterations
IterNodes
done5000
11822
0668

prune3.3s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes499.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify11.0ms

Iterations
IterNodes
done41
141
028

end0.0ms

sample3.3s

Algorithm
intervals
Results
3.0s14080×body80valid