Details

Time bar (total: 39.4s)

sample188.0ms

Algorithm
intervals
Results
155.0ms436×body80valid

simplify4.6s

Counts
1 → 1

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize75.0ms

Local error

Found 4 expressions with local error:

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

rewrite2.7s

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:
Slowest
1.7s
(* (/ 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)))))
956.0ms
(* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
51.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
2.0ms
(sqrt PI)

series520.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
353.0ms
(* (/ 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)))))
94.0ms
(* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
72.0ms
(* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify3.1s

Counts
191 → 191

prune3.2s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

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

rewrite48.0ms

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:
Slowest
32.0ms
(* (/ 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 2/3 (* (* (fabs x) (fabs x)) (fabs x)) (* (* (* 1/5 (* (fabs x) (fabs x))) (fabs x)) (* (fabs x) (fabs x)))))) (sqrt (sqrt PI))))
9.0ms
(/ (fma 1/21 (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (* (fabs x) (fabs x)) (fabs x))) (fma 2 (fabs x) (fma 2/3 (* (* (fabs x) (fabs x)) (fabs x)) (* (* (* 1/5 (* (fabs x) (fabs x))) (fabs x)) (* (fabs x) (fabs x)))))) (sqrt (sqrt PI)))
1.0ms
(sqrt PI)
1.0ms
(sqrt PI)

series1.0s

Counts
4 → 8
Calls
4 calls:
Slowest
644.0ms
(/ (fma 1/21 (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (* (fabs x) (fabs x)) (fabs x))) (fma 2 (fabs x) (fma 2/3 (* (* (fabs x) (fabs x)) (fabs x)) (* (* (* 1/5 (* (fabs x) (fabs x))) (fabs x)) (* (fabs x) (fabs x)))))) (sqrt (sqrt PI)))
371.0ms
(* (/ 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 2/3 (* (* (fabs x) (fabs x)) (fabs x)) (* (* (* 1/5 (* (fabs x) (fabs x))) (fabs x)) (* (fabs x) (fabs x)))))) (sqrt (sqrt PI))))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify1.9s

Counts
211 → 211

prune3.6s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize60.0ms

Local error

Found 4 expressions with local error:

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

rewrite191.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
134×pow1
85×add-sqr-sqrt
83×*-un-lft-identity add-cube-cbrt
39×add-cbrt-cube add-exp-log sqrt-prod
36×pow-prod-down pow-prod-up
24×associate-/r*
22×pow-sqr
21×prod-exp cbrt-unprod
18×pow-plus
13×pow2
9×associate-/r/
5×div-inv
4×expm1-log1p-u flip3-+ associate-*r* flip-+ insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv div-exp associate-/l*
2×associate-*l* *-commutative fma-udef unswap-sqr
1×distribute-rgt-in rem-sqrt-square clear-num frac-2neg distribute-lft-in sqrt-pow1 pow1/2 swap-sqr
Counts
4 → 232
Calls
4 calls:
Slowest
121.0ms
(* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (fma 1/21 (* (fabs x) (fabs x)) 1/5))
32.0ms
(* (* (fabs x) (fabs x)) (* (fabs x) (fabs x)))
20.0ms
(/ (fabs x) (/ (sqrt PI) (+ (fma 2/3 (* (fabs x) (fabs x)) 2) (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (fma 1/21 (* (fabs x) (fabs x)) 1/5)))))
9.0ms
(sqrt PI)

series427.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
302.0ms
(/ (fabs x) (/ (sqrt PI) (+ (fma 2/3 (* (fabs x) (fabs x)) 2) (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (fma 1/21 (* (fabs x) (fabs x)) 1/5)))))
96.0ms
(* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (fma 1/21 (* (fabs x) (fabs x)) 1/5))
29.0ms
(* (* (fabs x) (fabs x)) (* (fabs x) (fabs x)))
0.0ms
(sqrt PI)

simplify2.1s

Counts
242 → 242

prune3.6s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize107.0ms

Local error

Found 4 expressions with local error:

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

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
67×sqrt-prod
34×associate-*r*
30×add-sqr-sqrt
27×*-un-lft-identity times-frac add-cube-cbrt
19×add-exp-log
13×add-cbrt-cube
12×pow1
9×prod-exp
8×sqrt-div
5×frac-times associate-*l/ cbrt-unprod
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down associate-*r/
2×div-exp
1×cbrt-undiv rec-exp 1-exp associate-*l* *-commutative div-inv
Counts
4 → 111
Calls
4 calls:
Slowest
91.0ms
(* (* (/ 1 (sqrt (sqrt PI))) (sqrt (/ (fma 1/21 (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (* (fabs x) (fabs x)) (fabs x))) (fma 2 (fabs x) (fma 2/3 (* (* (fabs x) (fabs x)) (fabs x)) (* (* (* 1/5 (* (fabs x) (fabs x))) (fabs x)) (* (fabs x) (fabs x)))))) (sqrt (sqrt PI))))) (sqrt (/ (fma 1/21 (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (* (fabs x) (fabs x)) (fabs x))) (fma 2 (fabs x) (fma 2/3 (* (* (fabs x) (fabs x)) (fabs x)) (* (* (* 1/5 (* (fabs x) (fabs x))) (fabs x)) (* (fabs x) (fabs x)))))) (sqrt (sqrt PI)))))
1.0ms
(sqrt PI)
1.0ms
(sqrt PI)
1.0ms
(sqrt PI)

series397.0ms

Counts
4 → 6
Calls
4 calls:
Slowest
396.0ms
(* (* (/ 1 (sqrt (sqrt PI))) (sqrt (/ (fma 1/21 (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (* (fabs x) (fabs x)) (fabs x))) (fma 2 (fabs x) (fma 2/3 (* (* (fabs x) (fabs x)) (fabs x)) (* (* (* 1/5 (* (fabs x) (fabs x))) (fabs x)) (* (fabs x) (fabs x)))))) (sqrt (sqrt PI))))) (sqrt (/ (fma 1/21 (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (* (fabs x) (fabs x)) (fabs x))) (fma 2 (fabs x) (fma 2/3 (* (* (fabs x) (fabs x)) (fabs x)) (* (* (* 1/5 (* (fabs x) (fabs x))) (fabs x)) (* (fabs x) (fabs x)))))) (sqrt (sqrt PI)))))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify3.2s

Counts
117 → 117

prune2.4s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes262.0ms

Accuracy

0% (0.2b remaining)

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

bsearch18.0ms

end0.0ms

sample5.4s

Algorithm
intervals
Results
5.2s14090×body80valid