Details

Time bar (total: 15.7s)

sample139.0ms

Algorithm
intervals
Results
47.0ms193×body80valid
27.0ms25×body2560valid
14.0ms17×body1280valid
14.0ms256×pre80true
10.0ms14×body640valid
3.0ms6×body320valid
0.0ms1×body160valid

simplify102.0ms

Counts
1 → 1

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.7b

localize38.0ms

Local error

Found 4 expressions with local error:

15.7b
(sqrt (fma p (* 4 p) (* x x)))
0.3b
(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
0.0b
(sqrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
0.0b
(/ x (sqrt (fma p (* 4 p) (* x x))))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
18×times-frac sqrt-prod
6×pow1 associate-/r* add-cbrt-cube add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2
1×cbrt-undiv clear-num frac-2neg div-exp fma-udef div-inv
Counts
4 → 85
Calls
4 calls:
Slowest
8.0ms
(/ x (sqrt (fma p (* 4 p) (* x x))))
2.0ms
(sqrt (fma p (* 4 p) (* x x)))
2.0ms
(sqrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
0.0ms
(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)

series508.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
260.0ms
(sqrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
96.0ms
(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
81.0ms
(sqrt (fma p (* 4 p) (* x x)))
71.0ms
(/ x (sqrt (fma p (* 4 p) (* x x))))

simplify1.0s

Counts
97 → 97

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.5b

localize36.0ms

Local error

Found 4 expressions with local error:

15.7b
(sqrt (fma p (* 4 p) (* x x)))
2.2b
(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)))))
0.0b
(sqrt (fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
22×*-un-lft-identity times-frac associate-*r*
20×add-cube-cbrt
17×sqrt-prod
13×add-exp-log
9×add-cbrt-cube
8×pow1
5×unswap-sqr
4×expm1-log1p-u prod-exp insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l*
2×rem-sqrt-square sqrt-pow1 pow1/2 div-exp cbrt-unprod
1×cbrt-undiv rec-exp 1-exp pow-prod-down associate-*r/ un-div-inv *-commutative fma-udef div-inv
Counts
4 → 93
Calls
4 calls:
Slowest
16.0ms
(* x (/ 1 (sqrt (fma p (* 4 p) (* x x)))))
1.0ms
(sqrt (fma p (* 4 p) (* x x)))
1.0ms
(sqrt (fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5))
0.0ms
(fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)

series439.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
208.0ms
(sqrt (fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5))
104.0ms
(fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)
65.0ms
(* x (/ 1 (sqrt (fma p (* 4 p) (* x x)))))
61.0ms
(sqrt (fma p (* 4 p) (* x x)))

simplify1.3s

Counts
105 → 105

prune911.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.5b

localize46.0ms

Local error

Found 4 expressions with local error:

15.7b
(sqrt (fma p (* 4 p) (* x x)))
15.7b
(sqrt (fma p (* 4 p) (* x x)))
15.7b
(sqrt (fma p (* 4 p) (* x x)))
2.2b
(fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
1×fma-udef
Counts
4 → 59
Calls
4 calls:
Slowest
1.0ms
(sqrt (fma p (* 4 p) (* x x)))
1.0ms
(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)

series244.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
81.0ms
(fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)
57.0ms
(sqrt (fma p (* 4 p) (* x x)))
53.0ms
(sqrt (fma p (* 4 p) (* x x)))
52.0ms
(sqrt (fma p (* 4 p) (* x x)))

simplify2.6s

Counts
71 → 71

prune914.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 12.5b

localize29.0ms

Local error

Found 4 expressions with local error:

15.7b
(sqrt (fma p (* 4 p) (* x x)))
15.7b
(sqrt (fma p (* 4 p) (* x x)))
8.3b
(fma (/ (/ x (sqrt (sqrt (fma p (* 4 p) (* x x))))) (sqrt (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)
0.3b
(/ x (sqrt (sqrt (fma p (* 4 p) (* x x)))))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
42×sqrt-prod
30×add-sqr-sqrt
28×*-un-lft-identity add-cube-cbrt
27×times-frac
9×associate-/r*
6×pow1 add-cbrt-cube add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2
1×cbrt-undiv clear-num frac-2neg div-exp fma-udef div-inv
Counts
4 → 97
Calls
4 calls:
Slowest
6.0ms
(/ x (sqrt (sqrt (fma p (* 4 p) (* x x)))))
1.0ms
(sqrt (fma p (* 4 p) (* x x)))
1.0ms
(sqrt (fma p (* 4 p) (* x x)))
0.0ms
(fma (/ (/ x (sqrt (sqrt (fma p (* 4 p) (* x x))))) (sqrt (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)

series336.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
145.0ms
(/ x (sqrt (sqrt (fma p (* 4 p) (* x x)))))
83.0ms
(fma (/ (/ x (sqrt (sqrt (fma p (* 4 p) (* x x))))) (sqrt (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)
56.0ms
(sqrt (fma p (* 4 p) (* x x)))
52.0ms
(sqrt (fma p (* 4 p) (* x x)))

simplify2.3s

Counts
109 → 109

prune1000.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.5b

regimes135.0ms

Accuracy

0% (1.3b remaining)

Error of 14.1b against oracle of 12.8b and baseline of 14.1b

bsearch3.0ms

end0.0ms

sample2.4s

Algorithm
intervals
Results
690.0ms6057×body80valid
593.0ms615×body1280valid
486.0ms757×body2560valid
258.0ms8000×pre80true
128.0ms307×body640valid
55.0ms137×body320valid
35.0ms75×body160valid
33.0ms52×body5120valid