Details

Time bar (total: 31.6s)

sample82.0ms

Algorithm
intervals
Results
24.0ms202×body80valid
12.0ms16×body2560valid
12.0ms17×body1280valid
11.0ms256×pre80true
6.0ms13×body640valid
1.0ms5×body160valid
1.0ms1×body5120valid
1.0ms2×body320valid

simplify122.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
122.0ms
(sqrt (* 0.5 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))))

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.1b

localize48.0ms

Local error

Found 4 expressions with local error:

14.7b
(sqrt (fma p (* 4 p) (* x x)))
1.1b
(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
0.0b
(/ 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
5.0ms
(/ 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)

series320.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
115.0ms
(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
81.0ms
(/ x (sqrt (fma p (* 4 p) (* x x))))
73.0ms
(sqrt (fma p (* 4 p) (* x x)))
52.0ms
(fma p (* 4 p) (* x x))

simplify1.8s

Counts
63 → 92
Calls
63 calls:
Slowest
249.0ms
(/ (* (* x x) x) (* (* (sqrt (fma p (* 4 p) (* x x))) (sqrt (fma p (* 4 p) (* x x)))) (sqrt (fma p (* 4 p) (* x x)))))
57.0ms
(/ (* (cbrt x) (cbrt x)) (* (cbrt (sqrt (fma p (* 4 p) (* x x)))) (cbrt (sqrt (fma p (* 4 p) (* x x))))))
55.0ms
(/ 1 (* (cbrt (sqrt (fma p (* 4 p) (* x x)))) (cbrt (sqrt (fma p (* 4 p) (* x x))))))
52.0ms
(/ 1 (sqrt (* (cbrt (fma p (* 4 p) (* x x))) (cbrt (fma p (* 4 p) (* x x))))))
46.0ms
(/ (sqrt x) (sqrt (* (cbrt (fma p (* 4 p) (* x x))) (cbrt (fma p (* 4 p) (* x x))))))

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 10.8b

localize28.0ms

Local error

Found 4 expressions with local error:

14.7b
(sqrt (fma p (* 4 p) (* x x)))
1.1b
(fma (/ 1 (/ (sqrt (fma p (* 4 p) (* x x))) x)) 0.5 0.5)
0.3b
(/ 1 (/ (sqrt (fma p (* 4 p) (* x x))) x))
0.0b
(/ (sqrt (fma p (* 4 p) (* x x))) x)

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
156×times-frac
96×add-sqr-sqrt
95×*-un-lft-identity add-cube-cbrt
51×sqrt-prod
25×associate-/r*
17×add-exp-log
11×add-cbrt-cube
9×associate-/l*
8×div-exp
6×pow1 div-inv
4×expm1-log1p-u cbrt-undiv insert-posit16 log1p-expm1-u add-log-exp
2×rec-exp clear-num frac-2neg 1-exp
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/ fma-udef pow-flip inv-pow
Counts
4 → 184
Calls
4 calls:
Slowest
7.0ms
(sqrt (fma p (* 4 p) (* x x)))
7.0ms
(/ 1 (/ (sqrt (fma p (* 4 p) (* x x))) x))
5.0ms
(/ (sqrt (fma p (* 4 p) (* x x))) x)
0.0ms
(fma (/ 1 (/ (sqrt (fma p (* 4 p) (* x x))) x)) 0.5 0.5)

series404.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
122.0ms
(/ (sqrt (fma p (* 4 p) (* x x))) x)
106.0ms
(fma (/ 1 (/ (sqrt (fma p (* 4 p) (* x x))) x)) 0.5 0.5)
106.0ms
(/ 1 (/ (sqrt (fma p (* 4 p) (* x x))) x))
69.0ms
(sqrt (fma p (* 4 p) (* x x)))

simplify11.7s

Counts
225 → 196
Calls
225 calls:
Slowest
400.0ms
(/ (* (* 1 1) 1) (* (* (/ (sqrt (fma p (* 4 p) (* x x))) x) (/ (sqrt (fma p (* 4 p) (* x x))) x)) (/ (sqrt (fma p (* 4 p) (* x x))) x)))
339.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (sqrt (fma p (* 4 p) (* x x)))) (cbrt (sqrt (fma p (* 4 p) (* x x))))) (* (cbrt x) (cbrt x))))
327.0ms
(/ (sqrt 1) (/ (* (cbrt (sqrt (fma p (* 4 p) (* x x)))) (cbrt (sqrt (fma p (* 4 p) (* x x))))) (* (cbrt x) (cbrt x))))
254.0ms
(/ (* (* 1 1) 1) (/ (* (* (sqrt (fma p (* 4 p) (* x x))) (sqrt (fma p (* 4 p) (* x x)))) (sqrt (fma p (* 4 p) (* x x)))) (* (* x x) x)))
250.0ms
(/ (* (* (sqrt (fma p (* 4 p) (* x x))) (sqrt (fma p (* 4 p) (* x x)))) (sqrt (fma p (* 4 p) (* x x)))) (* (* x x) x))

prune2.5s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.8b

localize32.0ms

Local error

Found 4 expressions with local error:

14.7b
(sqrt (fma p (* 4 p) (* x x)))
1.1b
(fma (/ 1 (/ (sqrt (fma p (* 4 p) (* x x))) x)) 0.5 0.5)
0.5b
(log (fma (/ 1 (/ (sqrt (fma p (* 4 p) (* x x))) x)) 0.5 0.5))
0.3b
(/ 1 (/ (sqrt (fma p (* 4 p) (* x x))) x))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
82×add-sqr-sqrt
81×*-un-lft-identity add-cube-cbrt
39×sqrt-prod
22×associate-/r*
16×add-exp-log
9×add-cbrt-cube
7×pow1 div-exp
5×div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv log-prod associate-/l*
2×rec-exp 1-exp
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 rem-log-exp associate-/r/ log-pow fma-udef pow-flip inv-pow
Counts
4 → 157
Calls
4 calls:
Slowest
8.0ms
(/ 1 (/ (sqrt (fma p (* 4 p) (* x x))) x))
1.0ms
(sqrt (fma p (* 4 p) (* x x)))
1.0ms
(log (fma (/ 1 (/ (sqrt (fma p (* 4 p) (* x x))) x)) 0.5 0.5))
0.0ms
(fma (/ 1 (/ (sqrt (fma p (* 4 p) (* x x))) x)) 0.5 0.5)

series363.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
154.0ms
(log (fma (/ 1 (/ (sqrt (fma p (* 4 p) (* x x))) x)) 0.5 0.5))
80.0ms
(fma (/ 1 (/ (sqrt (fma p (* 4 p) (* x x))) x)) 0.5 0.5)
71.0ms
(/ 1 (/ (sqrt (fma p (* 4 p) (* x x))) x))
57.0ms
(sqrt (fma p (* 4 p) (* x x)))

simplify7.2s

Counts
184 → 169
Calls
184 calls:
Slowest
314.0ms
(/ (* (* 1 1) 1) (* (* (/ (sqrt (fma p (* 4 p) (* x x))) x) (/ (sqrt (fma p (* 4 p) (* x x))) x)) (/ (sqrt (fma p (* 4 p) (* x x))) x)))
227.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (sqrt (fma p (* 4 p) (* x x)))) (cbrt (sqrt (fma p (* 4 p) (* x x))))) (* (cbrt x) (cbrt x))))
220.0ms
(/ (sqrt 1) (/ (* (cbrt (sqrt (fma p (* 4 p) (* x x)))) (cbrt (sqrt (fma p (* 4 p) (* x x))))) (* (cbrt x) (cbrt x))))
162.0ms
(/ (* (* 1 1) 1) (/ (* (* (sqrt (fma p (* 4 p) (* x x))) (sqrt (fma p (* 4 p) (* x x)))) (sqrt (fma p (* 4 p) (* x x)))) (* (* x x) x)))
125.0ms
(/ 1 (/ (* (cbrt (sqrt (fma p (* 4 p) (* x x)))) (cbrt (sqrt (fma p (* 4 p) (* x x))))) (* (cbrt x) (cbrt x))))

prune1.7s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 10.8b

localize46.0ms

Local error

Found 4 expressions with local error:

14.7b
(sqrt (fma p (* 4 p) (* x x)))
14.7b
(sqrt (fma p (* 4 p) (* x x)))
14.7b
(sqrt (fma p (* 4 p) (* x x)))
1.1b
(fma (/ 1 (/ (sqrt (fma p (* 4 p) (* x 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 (/ 1 (/ (sqrt (fma p (* 4 p) (* x x))) x)) 0.5 0.5)

series230.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
77.0ms
(fma (/ 1 (/ (sqrt (fma p (* 4 p) (* x x))) x)) 0.5 0.5)
54.0ms
(sqrt (fma p (* 4 p) (* x x)))
51.0ms
(sqrt (fma p (* 4 p) (* x x)))
48.0ms
(sqrt (fma p (* 4 p) (* x x)))

simplify226.0ms

Counts
27 → 71
Calls
27 calls:
Slowest
19.0ms
(sqrt (* (cbrt (fma p (* 4 p) (* x x))) (cbrt (fma p (* 4 p) (* x x)))))
19.0ms
(sqrt (* (cbrt (fma p (* 4 p) (* x x))) (cbrt (fma p (* 4 p) (* x x)))))
19.0ms
(sqrt (* (cbrt (fma p (* 4 p) (* x x))) (cbrt (fma p (* 4 p) (* x x)))))
18.0ms
(sqrt (sqrt (fma p (* 4 p) (* x x))))
18.0ms
(sqrt (sqrt (fma p (* 4 p) (* x x))))

prune942.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 10.8b

regimes173.0ms

Accuracy

0% (0.3b remaining)

Error of 13.3b against oracle of 13.0b and baseline of 13.3b

bsearch7.0ms

end0.0ms

sample2.5s

Algorithm
intervals
Results
744.0ms773×body2560valid
647.0ms6005×body80valid
352.0ms8000×pre80true
295.0ms607×body1280valid
176.0ms317×body640valid
54.0ms59×body5120valid
41.0ms156×body320valid
16.0ms83×body160valid