Details

Time bar (total: 26.5s)

sample58.0ms

Algorithm
intervals
Results
41.0ms431×body80valid

simplify2.3s

Counts
1 → 1
Iterations
IterNodes
done5000
31250
2261
175
028

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize73.0ms

Local error

Found 4 expressions with local error:

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

rewrite2.1s

Algorithm
rewrite-expression-head
Rules
119×add-exp-log
76×prod-exp
75×add-cbrt-cube
48×associate-*l*
46×add-sqr-sqrt
44×cbrt-unprod
40×times-frac
36×pow1
35×*-un-lft-identity
33×add-cube-cbrt
22×pow-prod-down
15×div-exp associate-*l/
14×sqrt-prod
12×frac-add
9×cbrt-undiv
6×frac-times rec-exp flip3-+ 1-exp associate-*r/ flip-+
5×associate-*r* unswap-sqr
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative div-inv
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2
Counts
4 → 181
Calls
4 calls:
1.5s
(* (/ 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)))))
490.0ms
(* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
59.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms
(sqrt PI)

series478.0ms

Counts
4 → 10
Calls
4 calls:
345.0ms
(* (/ 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)))))
78.0ms
(* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
55.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify3.4s

Counts
191 → 191
Iterations
IterNodes
done5000
24521
11232
0362

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize66.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma 1/21 (pow (fabs x) 7) (* (* (* (fabs x) (fabs x)) (fabs x)) 2/3))
0.1b
(* (* (fabs x) (fabs x)) (fabs x))
0.1b
(* (fma 1/5 (pow (fabs x) 5) (fma (fabs x) 2 (fma 1/21 (pow (fabs x) 7) (* (* (* (fabs x) (fabs x)) (fabs x)) 2/3)))) (sqrt (/ 1 PI)))
0.2b
(* (* (* (fabs x) (fabs x)) (fabs x)) 2/3)

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
34×pow1
25×add-sqr-sqrt
22×associate-*r*
20×add-cbrt-cube add-exp-log
16×*-un-lft-identity sqrt-prod
15×add-cube-cbrt
11×times-frac
10×pow-prod-down prod-exp cbrt-unprod
6×pow-plus pow-prod-up
5×associate-*l* unswap-sqr
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative
2×pow2 pow-sqr
1×sqrt-div pow3 associate-*r/ fma-udef div-inv
Counts
4 → 104
Calls
4 calls:
0.0ms
(fma 1/21 (pow (fabs x) 7) (* (* (* (fabs x) (fabs x)) (fabs x)) 2/3))
27.0ms
(* (* (fabs x) (fabs x)) (fabs x))
10.0ms
(* (fma 1/5 (pow (fabs x) 5) (fma (fabs x) 2 (fma 1/21 (pow (fabs x) 7) (* (* (* (fabs x) (fabs x)) (fabs x)) 2/3)))) (sqrt (/ 1 PI)))
53.0ms
(* (* (* (fabs x) (fabs x)) (fabs x)) 2/3)

series641.0ms

Counts
4 → 12
Calls
4 calls:
180.0ms
(fma 1/21 (pow (fabs x) 7) (* (* (* (fabs x) (fabs x)) (fabs x)) 2/3))
30.0ms
(* (* (fabs x) (fabs x)) (fabs x))
382.0ms
(* (fma 1/5 (pow (fabs x) 5) (fma (fabs x) 2 (fma 1/21 (pow (fabs x) 7) (* (* (* (fabs x) (fabs x)) (fabs x)) 2/3)))) (sqrt (/ 1 PI)))
49.0ms
(* (* (* (fabs x) (fabs x)) (fabs x)) 2/3)

simplify2.6s

Counts
116 → 116
Iterations
IterNodes
done5010
33367
2830
1334
0165

prune767.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (pow (fabs x) 5) 1/5 (* 2 (fabs x)))
0.1b
(* (fabs x) (* (fabs x) (fabs x)))
0.3b
(/ (fma 2/3 (* (fabs x) (* (fabs x) (fabs x))) (fma (pow (fabs x) 7) 1/21 (fma (pow (fabs x) 5) 1/5 (* 2 (fabs x))))) (sqrt PI))
1.0b
(sqrt PI)

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
19×pow1
18×times-frac
15×sqrt-prod
11×add-cbrt-cube add-exp-log
6×associate-/r*
5×pow-prod-up
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l* pow-prod-down prod-exp cbrt-unprod associate-/l*
1×pow2 cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow-plus pow1/2 cube-unmult div-exp associate-*r* pow-sqr *-commutative fma-udef div-inv unswap-sqr
Counts
4 → 96
Calls
4 calls:
0.0ms
(fma (pow (fabs x) 5) 1/5 (* 2 (fabs x)))
13.0ms
(* (fabs x) (* (fabs x) (fabs x)))
5.0ms
(/ (fma 2/3 (* (fabs x) (* (fabs x) (fabs x))) (fma (pow (fabs x) 7) 1/21 (fma (pow (fabs x) 5) 1/5 (* 2 (fabs x))))) (sqrt PI))
1.0ms
(sqrt PI)

series519.0ms

Counts
4 → 10
Calls
4 calls:
116.0ms
(fma (pow (fabs x) 5) 1/5 (* 2 (fabs x)))
31.0ms
(* (fabs x) (* (fabs x) (fabs x)))
371.0ms
(/ (fma 2/3 (* (fabs x) (* (fabs x) (fabs x))) (fma (pow (fabs x) 7) 1/21 (fma (pow (fabs x) 5) 1/5 (* 2 (fabs x))))) (sqrt PI))
0.0ms
(sqrt PI)

simplify2.9s

Counts
106 → 106
Iterations
IterNodes
done5000
31684
2575
1246
0144

prune801.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize62.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (fabs x) (* (fabs x) (fabs x)))
0.3b
(/ (fma 2/3 (* (fabs x) (* (fabs x) (fabs x))) (fma (pow (fabs x) 7) 1/21 (fma (pow (fabs x) 5) 1/5 (* 2 (fabs x))))) (* (sqrt (sqrt PI)) (sqrt (sqrt PI))))
1.0b
(sqrt PI)
1.0b
(sqrt PI)

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
20×pow1
14×add-cbrt-cube add-exp-log
12×add-sqr-sqrt
9×*-un-lft-identity add-cube-cbrt
6×sqrt-prod
5×pow-prod-up
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×times-frac associate-*l* pow-prod-down associate-/l*
2×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 div-exp
1×pow2 clear-num associate-/r* frac-2neg pow-plus cube-unmult associate-*r* pow-sqr *-commutative div-inv unswap-sqr
Counts
4 → 83
Calls
4 calls:
35.0ms
(* (fabs x) (* (fabs x) (fabs x)))
22.0ms
(/ (fma 2/3 (* (fabs x) (* (fabs x) (fabs x))) (fma (pow (fabs x) 7) 1/21 (fma (pow (fabs x) 5) 1/5 (* 2 (fabs x))))) (* (sqrt (sqrt PI)) (sqrt (sqrt PI))))
2.0ms
(sqrt PI)
2.0ms
(sqrt PI)

series758.0ms

Counts
4 → 8
Calls
4 calls:
28.0ms
(* (fabs x) (* (fabs x) (fabs x)))
730.0ms
(/ (fma 2/3 (* (fabs x) (* (fabs x) (fabs x))) (fma (pow (fabs x) 7) 1/21 (fma (pow (fabs x) 5) 1/5 (* 2 (fabs x))))) (* (sqrt (sqrt PI)) (sqrt (sqrt PI))))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify3.6s

Counts
91 → 91
Iterations
IterNodes
done5000
31513
2575
1230
0117

prune747.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes122.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify9.0ms

Iterations
IterNodes
done27
127
022

end0.0ms

sample3.1s

Algorithm
intervals
Results
2.9s14004×body80valid