Details

Time bar (total: 14.9s)

sample121.0ms

Algorithm
intervals
Results
31.0ms256×pre80true
25.0ms199×body80valid
21.0ms27×body2560valid
10.0ms15×body1280valid
4.0ms6×body640valid
3.0ms2×body5120valid
2.0ms5×body160valid
1.0ms2×body320valid

simplify81.0ms

Counts
1 → 1

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.3b

localize36.0ms

Local error

Found 4 expressions with local error:

13.3b
(sqrt (fma p (* 4 p) (* x x)))
1.1b
(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
0.2b
(/ x (sqrt (fma p (* 4 p) (* x x))))
0.0b
(fma p (* 4 p) (* x x))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
20×*-un-lft-identity add-cube-cbrt
18×times-frac
15×sqrt-prod
6×associate-/r* add-cbrt-cube add-exp-log
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/l*
2×fma-udef
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-exp div-inv
Counts
4 → 80
Calls
4 calls:
Slowest
4.0ms
(/ x (sqrt (fma p (* 4 p) (* x x))))
1.0ms
(sqrt (fma p (* 4 p) (* x x)))
0.0ms
(fma p (* 4 p) (* x x))
0.0ms
(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)

series304.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
93.0ms
(/ x (sqrt (fma p (* 4 p) (* x x))))
81.0ms
(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
72.0ms
(fma p (* 4 p) (* x x))
56.0ms
(sqrt (fma p (* 4 p) (* x x)))

simplify1.2s

Counts
92 → 92

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.1b

localize55.0ms

Local error

Found 4 expressions with local error:

13.3b
(sqrt (fma p (* 4 p) (* x x)))
2.8b
(fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)
0.2b
(* x (/ 1 (sqrt (fma p (* 4 p) (* x x)))))
0.2b
(/ 1 (sqrt (fma p (* 4 p) (* x x))))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt
40×times-frac
36×*-un-lft-identity
34×add-cube-cbrt
26×sqrt-prod
22×associate-*r*
17×add-exp-log
11×add-cbrt-cube
9×pow1
6×associate-/r*
5×unswap-sqr
4×expm1-log1p-u div-exp prod-exp insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l* pow-flip associate-/l*
2×cbrt-undiv rec-exp sqrt-pow1 pow1/2 1-exp cbrt-unprod div-inv
1×rem-sqrt-square clear-num frac-2neg pow-prod-down associate-*r/ un-div-inv *-commutative fma-udef inv-pow
Counts
4 → 125
Calls
4 calls:
Slowest
11.0ms
(* x (/ 1 (sqrt (fma p (* 4 p) (* x x)))))
5.0ms
(/ 1 (sqrt (fma p (* 4 p) (* x x))))
1.0ms
(sqrt (fma p (* 4 p) (* x x)))
0.0ms
(fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)

series335.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
100.0ms
(fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)
88.0ms
(/ 1 (sqrt (fma p (* 4 p) (* x x))))
82.0ms
(* x (/ 1 (sqrt (fma p (* 4 p) (* x x)))))
65.0ms
(sqrt (fma p (* 4 p) (* x x)))

simplify1.6s

Counts
137 → 137

prune1.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.1b

localize42.0ms

Local error

Found 4 expressions with local error:

13.6b
(pow (fma p (* 4 p) (* x x)) (- 1/2))
2.8b
(fma (* x (pow (fma p (* 4 p) (* x x)) (- 1/2))) 0.5 0.5)
0.2b
(* x (pow (fma p (* 4 p) (* x x)) (- 1/2)))
0.0b
(fma p (* 4 p) (* x x))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
11×*-un-lft-identity add-cube-cbrt
10×pow-unpow add-exp-log
7×unpow-prod-down associate-*r*
6×add-cbrt-cube
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×distribute-lft-neg-in pow-neg distribute-rgt-neg-in associate-*l* prod-exp unswap-sqr sqr-pow
2×neg-sub0 pow-to-exp pow-exp associate-*r/ fma-udef pow-sub
1×neg-mul-1 pow-pow un-div-inv *-commutative cbrt-unprod
Counts
4 → 82
Calls
4 calls:
Slowest
13.0ms
(* x (pow (fma p (* 4 p) (* x x)) (- 1/2)))
2.0ms
(pow (fma p (* 4 p) (* x x)) (- 1/2))
0.0ms
(fma p (* 4 p) (* x x))
0.0ms
(fma (* x (pow (fma p (* 4 p) (* x x)) (- 1/2))) 0.5 0.5)

series370.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
169.0ms
(pow (fma p (* 4 p) (* x x)) (- 1/2))
90.0ms
(fma (* x (pow (fma p (* 4 p) (* x x)) (- 1/2))) 0.5 0.5)
64.0ms
(* x (pow (fma p (* 4 p) (* x x)) (- 1/2)))
47.0ms
(fma p (* 4 p) (* x x))

simplify728.0ms

Counts
94 → 94

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 11.1b

localize47.0ms

Local error

Found 4 expressions with local error:

13.6b
(pow (fma p (* 4 p) (* x x)) (- 1/2))
2.8b
(fma (* x (pow (fma p (* 4 p) (* x x)) (- 1/2))) 0.5 0.5)
0.5b
(log (fma (* x (pow (fma p (* 4 p) (* x x)) (- 1/2))) 0.5 0.5))
0.2b
(* x (pow (fma p (* 4 p) (* x x)) (- 1/2)))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
12×*-un-lft-identity add-cube-cbrt
11×add-exp-log
10×pow-unpow
7×unpow-prod-down associate-*r*
6×pow1 add-cbrt-cube
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×distribute-lft-neg-in log-prod pow-neg distribute-rgt-neg-in associate-*l* prod-exp unswap-sqr sqr-pow
2×neg-sub0 pow-to-exp pow-exp associate-*r/ pow-sub
1×neg-mul-1 pow-pow rem-log-exp log-pow un-div-inv *-commutative cbrt-unprod fma-udef
Counts
4 → 86
Calls
4 calls:
Slowest
9.0ms
(* x (pow (fma p (* 4 p) (* x x)) (- 1/2)))
2.0ms
(pow (fma p (* 4 p) (* x x)) (- 1/2))
1.0ms
(log (fma (* x (pow (fma p (* 4 p) (* x x)) (- 1/2))) 0.5 0.5))
0.0ms
(fma (* x (pow (fma p (* 4 p) (* x x)) (- 1/2))) 0.5 0.5)

series578.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
237.0ms
(log (fma (* x (pow (fma p (* 4 p) (* x x)) (- 1/2))) 0.5 0.5))
148.0ms
(pow (fma p (* 4 p) (* x x)) (- 1/2))
113.0ms
(fma (* x (pow (fma p (* 4 p) (* x x)) (- 1/2))) 0.5 0.5)
80.0ms
(* x (pow (fma p (* 4 p) (* x x)) (- 1/2)))

simplify999.0ms

Counts
98 → 98

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.3b

regimes176.0ms

Accuracy

0% (3.5b remaining)

Error of 13.0b against oracle of 9.5b and baseline of 13.0b

bsearch5.0ms

end0.0ms

sample2.7s

Algorithm
intervals
Results
851.0ms743×body2560valid
702.0ms6047×body80valid
365.0ms595×body1280valid
328.0ms8000×pre80true
169.0ms309×body640valid
66.0ms159×body320valid
49.0ms62×body5120valid
19.0ms85×body160valid