Details

Time bar (total: 28.2s)

sample177.0ms

Algorithm
intervals
Results
145.0ms431×body80valid

simplify2.8s

Counts
1 → 1
Iterations
IterNodes
done5001
31447
2271
175
028

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize67.0ms

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)

rewrite2.5s

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:
1.8s
(* (/ 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)))))
640.0ms
(* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
61.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
2.0ms
(sqrt PI)

series538.0ms

Counts
4 → 10
Calls
4 calls:
400.0ms
(* (/ 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)))
59.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify3.5s

Counts
191 → 191
Iterations
IterNodes
done5000
24636
11232
0362

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize37.0ms

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)

rewrite84.0ms

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))
16.0ms
(* (* (fabs x) (fabs x)) (fabs x))
14.0ms
(* (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)))
52.0ms
(* (* (* (fabs x) (fabs x)) (fabs x)) 2/3)

series575.0ms

Counts
4 → 12
Calls
4 calls:
149.0ms
(fma 1/21 (pow (fabs x) 7) (* (* (* (fabs x) (fabs x)) (fabs x)) 2/3))
45.0ms
(* (* (fabs x) (fabs x)) (fabs x))
325.0ms
(* (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)))
56.0ms
(* (* (* (fabs x) (fabs x)) (fabs x)) 2/3)

simplify2.5s

Counts
116 → 116
Iterations
IterNodes
done5008
33500
2885
1334
0165

prune720.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize58.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma 1/5 (pow (fabs x) 5) (* 2 (fabs x)))
0.3b
(/ (fma (* (fabs x) 2/3) (* (fabs x) (fabs x)) (fma 1/21 (pow (fabs x) 7) (fma 1/5 (pow (fabs x) 5) (* 2 (fabs x))))) (sqrt PI))
0.4b
(* (fabs x) 2/3)
1.0b
(sqrt PI)

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
22×*-un-lft-identity add-cube-cbrt
18×times-frac
15×sqrt-prod
8×add-cbrt-cube add-exp-log
7×pow1
6×associate-/r*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r* associate-*l* associate-/l*
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-exp pow-prod-down prod-exp *-commutative cbrt-unprod fma-udef div-inv unswap-sqr
Counts
4 → 90
Calls
4 calls:
0.0ms
(fma 1/5 (pow (fabs x) 5) (* 2 (fabs x)))
5.0ms
(/ (fma (* (fabs x) 2/3) (* (fabs x) (fabs x)) (fma 1/21 (pow (fabs x) 7) (fma 1/5 (pow (fabs x) 5) (* 2 (fabs x))))) (sqrt PI))
5.0ms
(* (fabs x) 2/3)
1.0ms
(sqrt PI)

series501.0ms

Counts
4 → 10
Calls
4 calls:
107.0ms
(fma 1/5 (pow (fabs x) 5) (* 2 (fabs x)))
367.0ms
(/ (fma (* (fabs x) 2/3) (* (fabs x) (fabs x)) (fma 1/21 (pow (fabs x) 7) (fma 1/5 (pow (fabs x) 5) (* 2 (fabs x))))) (sqrt PI))
26.0ms
(* (fabs x) 2/3)
0.0ms
(sqrt PI)

simplify2.6s

Counts
100 → 100
Iterations
IterNodes
done5038
32947
2730
1257
0141

prune813.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize80.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (fma (* (fabs x) 2/3) (* (fabs x) (fabs x)) (fma 1/21 (pow (fabs x) 7) (fma 1/5 (pow (fabs x) 5) (* 2 (fabs x))))) (* (sqrt (sqrt PI)) (sqrt (sqrt PI))))
0.4b
(* (fabs x) 2/3)
1.0b
(sqrt PI)
1.0b
(sqrt PI)

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
11×add-cbrt-cube add-exp-log
10×*-un-lft-identity add-cube-cbrt
8×pow1
6×sqrt-prod
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×times-frac associate-*r* associate-*l* associate-/l*
2×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 div-exp prod-exp cbrt-unprod
1×clear-num associate-/r* frac-2neg pow-prod-down *-commutative div-inv unswap-sqr
Counts
4 → 77
Calls
4 calls:
11.0ms
(/ (fma (* (fabs x) 2/3) (* (fabs x) (fabs x)) (fma 1/21 (pow (fabs x) 7) (fma 1/5 (pow (fabs x) 5) (* 2 (fabs x))))) (* (sqrt (sqrt PI)) (sqrt (sqrt PI))))
5.0ms
(* (fabs x) 2/3)
1.0ms
(sqrt PI)
1.0ms
(sqrt PI)

series384.0ms

Counts
4 → 8
Calls
4 calls:
354.0ms
(/ (fma (* (fabs x) 2/3) (* (fabs x) (fabs x)) (fma 1/21 (pow (fabs x) 7) (fma 1/5 (pow (fabs x) 5) (* 2 (fabs x))))) (* (sqrt (sqrt PI)) (sqrt (sqrt PI))))
29.0ms
(* (fabs x) 2/3)
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify2.5s

Counts
85 → 85
Iterations
IterNodes
done5006
32255
2663
1236
0115

prune716.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes104.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
done27
127
022

end0.0ms

sample5.6s

Algorithm
intervals
Results
5.4s14004×body80valid