Details

Time bar (total: 19.3s)

sample140.0ms

Algorithm
intervals
Results
110.0ms412×body80valid

simplify1.7s

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

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize61.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* (fabs x) (fabs x)) (fabs x))
0.1b
(* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
0.1b
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
1.0b
(sqrt PI)

rewrite753.0ms

Algorithm
rewrite-expression-head
Rules
115×add-exp-log
75×add-cbrt-cube prod-exp
53×pow1
45×cbrt-unprod
27×associate-*l*
24×pow-prod-down
22×add-sqr-sqrt
20×*-un-lft-identity add-cube-cbrt
18×times-frac
13×div-exp
8×cbrt-undiv
6×pow-plus pow-prod-up
5×rec-exp 1-exp associate-*r*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative sqrt-prod
2×pow2 associate-*l/ pow-sqr div-inv
1×rem-sqrt-square sqrt-pow1 pow1/2 pow3 unswap-sqr
Counts
4 → 149
Calls
4 calls:
15.0ms
(* (* (fabs x) (fabs x)) (fabs x))
635.0ms
(* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
97.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
2.0ms
(sqrt PI)

series148.0ms

Counts
4 → 10
Calls
4 calls:
36.0ms
(* (* (fabs x) (fabs x)) (fabs x))
68.0ms
(* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
43.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify1.1s

Counts
159 → 159
Iterations
IterNodes
done2000
22000
1644
0234

prune860.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (fabs x) (* (fabs x) (fabs x)))
0.2b
(* 1/21 (* (fabs x) (fabs x)))
0.3b
(/ (fma 2/3 (* (fabs x) (* (fabs x) (fabs x))) (fma (* (* (fabs x) (fabs x)) (* (fabs x) (* (fabs x) (fabs x)))) (+ (* 1/21 (* (fabs x) (fabs x))) 1/5) (* (fabs x) 2))) (sqrt PI))
1.0b
(sqrt PI)

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
24×pow1
22×*-un-lft-identity add-cube-cbrt
18×times-frac
16×add-cbrt-cube add-exp-log
15×sqrt-prod
6×associate-/r* associate-*l* pow-prod-down prod-exp cbrt-unprod
5×pow-prod-up
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/l*
2×associate-*r* *-commutative unswap-sqr
1×pow2 cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow-plus pow1/2 cube-unmult div-exp pow-sqr div-inv
Counts
4 → 107
Calls
4 calls:
27.0ms
(* (fabs x) (* (fabs x) (fabs x)))
19.0ms
(* 1/21 (* (fabs x) (fabs x)))
5.0ms
(/ (fma 2/3 (* (fabs x) (* (fabs x) (fabs x))) (fma (* (* (fabs x) (fabs x)) (* (fabs x) (* (fabs x) (fabs x)))) (+ (* 1/21 (* (fabs x) (fabs x))) 1/5) (* (fabs x) 2))) (sqrt PI))
1.0ms
(sqrt PI)

series407.0ms

Counts
4 → 10
Calls
4 calls:
34.0ms
(* (fabs x) (* (fabs x) (fabs x)))
41.0ms
(* 1/21 (* (fabs x) (fabs x)))
331.0ms
(/ (fma 2/3 (* (fabs x) (* (fabs x) (fabs x))) (fma (* (* (fabs x) (fabs x)) (* (fabs x) (* (fabs x) (fabs x)))) (+ (* 1/21 (* (fabs x) (fabs x))) 1/5) (* (fabs x) 2))) (sqrt PI))
0.0ms
(sqrt PI)

simplify1.6s

Counts
117 → 117
Iterations
IterNodes
done2002
42002
31989
2800
1313
0160

prune609.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize61.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (fma 2/3 (* (fabs x) (* (fabs x) (fabs x))) (fma (* (* (fabs x) (fabs x)) (* (fabs x) (* (fabs x) (fabs x)))) (+ (* 1/21 (* (fabs x) (fabs x))) 1/5) (* (fabs x) 2))) (sqrt PI))
0.5b
(* (sqrt (/ (fma 2/3 (* (fabs x) (* (fabs x) (fabs x))) (fma (* (* (fabs x) (fabs x)) (* (fabs x) (* (fabs x) (fabs x)))) (+ (* 1/21 (* (fabs x) (fabs x))) 1/5) (* (fabs x) 2))) (sqrt PI))) (sqrt (/ (fma 2/3 (* (fabs x) (* (fabs x) (fabs x))) (fma (* (* (fabs x) (fabs x)) (* (fabs x) (* (fabs x) (fabs x)))) (+ (* 1/21 (* (fabs x) (fabs x))) 1/5) (* (fabs x) 2))) (sqrt PI))))
1.0b
(sqrt PI)
1.0b
(sqrt PI)

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
194×sqrt-prod
147×add-sqr-sqrt
118×times-frac
81×*-un-lft-identity add-cube-cbrt
33×swap-sqr
25×associate-*r* associate-*l*
21×pow1
16×unswap-sqr
10×sqrt-pow1 pow1/2
8×add-cbrt-cube add-exp-log
6×associate-/r*
5×pow-prod-up div-inv
4×expm1-log1p-u sqrt-div insert-posit16 log1p-expm1-u add-log-exp
3×pow-prod-down pow-sqr associate-/l*
2×rem-sqrt-square
1×pow2 frac-times cbrt-undiv clear-num rem-square-sqrt frac-2neg pow-plus sqrt-unprod div-exp associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod
Counts
4 → 204
Calls
4 calls:
10.0ms
(/ (fma 2/3 (* (fabs x) (* (fabs x) (fabs x))) (fma (* (* (fabs x) (fabs x)) (* (fabs x) (* (fabs x) (fabs x)))) (+ (* 1/21 (* (fabs x) (fabs x))) 1/5) (* (fabs x) 2))) (sqrt PI))
37.0ms
(* (sqrt (/ (fma 2/3 (* (fabs x) (* (fabs x) (fabs x))) (fma (* (* (fabs x) (fabs x)) (* (fabs x) (* (fabs x) (fabs x)))) (+ (* 1/21 (* (fabs x) (fabs x))) 1/5) (* (fabs x) 2))) (sqrt PI))) (sqrt (/ (fma 2/3 (* (fabs x) (* (fabs x) (fabs x))) (fma (* (* (fabs x) (fabs x)) (* (fabs x) (* (fabs x) (fabs x)))) (+ (* 1/21 (* (fabs x) (fabs x))) 1/5) (* (fabs x) 2))) (sqrt PI))))
2.0ms
(sqrt PI)
2.0ms
(sqrt PI)

series705.0ms

Counts
4 → 8
Calls
4 calls:
369.0ms
(/ (fma 2/3 (* (fabs x) (* (fabs x) (fabs x))) (fma (* (* (fabs x) (fabs x)) (* (fabs x) (* (fabs x) (fabs x)))) (+ (* 1/21 (* (fabs x) (fabs x))) 1/5) (* (fabs x) 2))) (sqrt PI))
335.0ms
(* (sqrt (/ (fma 2/3 (* (fabs x) (* (fabs x) (fabs x))) (fma (* (* (fabs x) (fabs x)) (* (fabs x) (* (fabs x) (fabs x)))) (+ (* 1/21 (* (fabs x) (fabs x))) 1/5) (* (fabs x) 2))) (sqrt PI))) (sqrt (/ (fma 2/3 (* (fabs x) (* (fabs x) (fabs x))) (fma (* (* (fabs x) (fabs x)) (* (fabs x) (* (fabs x) (fabs x)))) (+ (* 1/21 (* (fabs x) (fabs x))) 1/5) (* (fabs x) 2))) (sqrt PI))))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify1.6s

Counts
212 → 212
Iterations
IterNodes
done2006
32006
2907
1401
0231

prune1.3s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize68.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
0.1b
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
1.0b
(expm1 (log1p (sqrt PI)))
1.0b
(sqrt PI)

rewrite848.0ms

Algorithm
rewrite-expression-head
Rules
110×add-exp-log
72×prod-exp
70×add-cbrt-cube
42×cbrt-unprod
34×pow1
26×associate-*l*
21×pow-prod-down
20×add-sqr-sqrt
19×*-un-lft-identity add-cube-cbrt
18×times-frac
13×div-exp
8×cbrt-undiv
5×rec-exp 1-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×sqrt-prod
2×associate-*r* associate-*l/ *-commutative div-inv
1×rem-sqrt-square expm1-log1p sqrt-pow1 pow1/2 expm1-udef
Counts
4 → 130
Calls
4 calls:
773.0ms
(* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
69.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(expm1 (log1p (sqrt PI)))
1.0ms
(sqrt PI)

series119.0ms

Counts
4 → 8
Calls
4 calls:
69.0ms
(* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
49.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(expm1 (log1p (sqrt PI)))
0.0ms
(sqrt PI)

simplify1.3s

Counts
138 → 138
Iterations
IterNodes
done2039
32039
21508
1535
0215

prune829.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes291.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify18.0ms

Iterations
IterNodes
done46
146
028

end0.0ms

sample4.5s

Algorithm
intervals
Results
4.3s13869×body80valid