Details

Time bar (total: 23.0s)

sample37.0ms

Algorithm
intervals
Results
27.0ms269×body80valid

simplify15.0ms

Calls
1 calls:
Slowest
15.0ms
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.2b

localize16.0ms

Local error

Found 3 expressions with local error:

25.2b
(/ (fma a c (* b d)) (fma d d (* c c)))
0.3b
(fma a c (* b d))
0.0b
(fma d d (* c c))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
5×add-cbrt-cube add-exp-log
3×expm1-log1p-u pow1 associate-/r* insert-posit16 log1p-expm1-u associate-/l* add-log-exp
2×fma-udef
1×cbrt-undiv clear-num frac-2neg div-exp div-inv
Calls
3 calls:
Slowest
4.0ms
(/ (fma a c (* b d)) (fma d d (* c c)))
0.0ms
(fma a c (* b d))
0.0ms
(fma d d (* c c))

series130.0ms

Calls
3 calls:
Slowest
72.0ms
(/ (fma a c (* b d)) (fma d d (* c c)))
34.0ms
(fma a c (* b d))
24.0ms
(fma d d (* c c))

simplify1.3s

Calls
34 calls:
Slowest
338.0ms
(/ (* (* (fma a c (* b d)) (fma a c (* b d))) (fma a c (* b d))) (* (* (fma d d (* c c)) (fma d d (* c c))) (fma d d (* c c))))
311.0ms
(cbrt (fma d d (* c c)))
64.0ms
(/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (* (cbrt (fma d d (* c c))) (cbrt (fma d d (* c c)))))
37.0ms
(/ (sqrt (fma a c (* b d))) (* (cbrt (fma d d (* c c))) (cbrt (fma d d (* c c)))))
34.0ms
(- (log (fma a c (* b d))) (log (fma d d (* c c))))

prune637.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 24.8b

localize8.0ms

Local error

Found 4 expressions with local error:

29.5b
(sqrt (fma d d (* c c)))
29.5b
(sqrt (fma d d (* c c)))
15.9b
(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
0.3b
(fma a c (* b d))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
18×times-frac sqrt-prod
6×associate-/r* add-cbrt-cube add-exp-log
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
3×fma-udef associate-/l*
2×rem-sqrt-square pow1/2 hypot-def
1×cbrt-undiv clear-num frac-2neg div-exp div-inv
Calls
4 calls:
Slowest
5.0ms
(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
1.0ms
(sqrt (fma d d (* c c)))
1.0ms
(sqrt (fma d d (* c c)))
0.0ms
(fma a c (* b d))

series149.0ms

Calls
4 calls:
Slowest
74.0ms
(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
27.0ms
(fma a c (* b d))
25.0ms
(sqrt (fma d d (* c c)))
23.0ms
(sqrt (fma d d (* c c)))

simplify1.4s

Calls
66 calls:
Slowest
203.0ms
(/ (* (* (fma a c (* b d)) (fma a c (* b d))) (fma a c (* b d))) (* (* (sqrt (fma d d (* c c))) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c)))))
72.0ms
(/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (* (cbrt (sqrt (fma d d (* c c)))) (cbrt (sqrt (fma d d (* c c))))))
53.0ms
(/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (sqrt (* (cbrt (fma d d (* c c))) (cbrt (fma d d (* c c))))))
42.0ms
(/ (cbrt (fma a c (* b d))) (cbrt (sqrt (fma d d (* c c)))))
37.0ms
(/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (sqrt (sqrt (fma d d (* c c)))))

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 22.0b

localize12.0ms

Local error

Found 4 expressions with local error:

29.5b
(sqrt (fma d d (* c c)))
15.9b
(/ (fma a c (* b d)) (hypot d c))
0.3b
(fma a c (* b d))
0.1b
(/ (/ (fma a c (* b d)) (hypot d c)) (sqrt (fma d d (* c c))))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
150×times-frac
91×add-sqr-sqrt
90×*-un-lft-identity add-cube-cbrt
45×sqrt-prod
16×associate-/l*
11×add-cbrt-cube add-exp-log
9×associate-/r* div-inv
4×expm1-log1p-u pow1 cbrt-undiv div-exp insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg fma-udef
1×rem-sqrt-square pow1/2 hypot-def associate-/l/
Calls
4 calls:
Slowest
11.0ms
(/ (/ (fma a c (* b d)) (hypot d c)) (sqrt (fma d d (* c c))))
6.0ms
(/ (fma a c (* b d)) (hypot d c))
1.0ms
(sqrt (fma d d (* c c)))
0.0ms
(fma a c (* b d))

series323.0ms

Calls
4 calls:
Slowest
167.0ms
(/ (/ (fma a c (* b d)) (hypot d c)) (sqrt (fma d d (* c c))))
92.0ms
(/ (fma a c (* b d)) (hypot d c))
34.0ms
(fma a c (* b d))
30.0ms
(sqrt (fma d d (* c c)))

simplify8.3s

Calls
220 calls:
Slowest
373.0ms
(/ (* (* (/ (fma a c (* b d)) (hypot d c)) (/ (fma a c (* b d)) (hypot d c))) (/ (fma a c (* b d)) (hypot d c))) (* (* (sqrt (fma d d (* c c))) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c)))))
251.0ms
(/ (* (* (fma a c (* b d)) (fma a c (* b d))) (fma a c (* b d))) (* (* (hypot d c) (hypot d c)) (hypot d c)))
180.0ms
(/ (/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (sqrt (hypot d c))) (* (cbrt (sqrt (fma d d (* c c)))) (cbrt (sqrt (fma d d (* c c))))))
176.0ms
(/ (/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (* (cbrt (hypot d c)) (cbrt (hypot d c)))) (* (cbrt (sqrt (fma d d (* c c)))) (cbrt (sqrt (fma d d (* c c))))))
170.0ms
(/ (/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (* (cbrt (hypot d c)) (cbrt (hypot d c)))) (sqrt (* (cbrt (fma d d (* c c))) (cbrt (fma d d (* c c))))))

prune2.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 13.5b

localize3.0ms

Local error

Found 4 expressions with local error:

15.9b
(/ (fma a c (* b d)) (hypot d c))
0.3b
(fma a c (* b d))
0.1b
(/ (/ (fma a c (* b d)) (hypot d c)) (hypot d c))
0.0b
(hypot d c)

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
54×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
16×associate-/l*
11×add-cbrt-cube add-exp-log
6×associate-/r* div-inv
4×expm1-log1p-u pow1 cbrt-undiv div-exp insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg
1×hypot-udef fma-udef associate-/l/
Calls
4 calls:
Slowest
10.0ms
(/ (/ (fma a c (* b d)) (hypot d c)) (hypot d c))
4.0ms
(/ (fma a c (* b d)) (hypot d c))
0.0ms
(hypot d c)
0.0ms
(fma a c (* b d))

series261.0ms

Calls
4 calls:
Slowest
104.0ms
(/ (/ (fma a c (* b d)) (hypot d c)) (hypot d c))
93.0ms
(/ (fma a c (* b d)) (hypot d c))
40.0ms
(fma a c (* b d))
24.0ms
(hypot d c)

simplify4.2s

Calls
135 calls:
Slowest
363.0ms
(/ (* (* (/ (fma a c (* b d)) (hypot d c)) (/ (fma a c (* b d)) (hypot d c))) (/ (fma a c (* b d)) (hypot d c))) (* (* (hypot d c) (hypot d c)) (hypot d c)))
225.0ms
(/ (* (* (fma a c (* b d)) (fma a c (* b d))) (fma a c (* b d))) (* (* (hypot d c) (hypot d c)) (hypot d c)))
142.0ms
(/ (/ (* (* (fma a c (* b d)) (fma a c (* b d))) (fma a c (* b d))) (* (* (hypot d c) (hypot d c)) (hypot d c))) (* (* (hypot d c) (hypot d c)) (hypot d c)))
139.0ms
(/ (/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (sqrt (hypot d c))) (* (cbrt (hypot d c)) (cbrt (hypot d c))))
112.0ms
(/ (/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (* (cbrt (hypot d c)) (cbrt (hypot d c)))) (* (cbrt (hypot d c)) (cbrt (hypot d c))))

prune1.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.5b

regimes342.0ms

Accuracy

34.1% (7.0b remaining)

Error of 12.7b against oracle of 5.7b and baseline of 16.3b

bsearch105.0ms

end0.0ms

sample1.3s

Algorithm
intervals
Results
1.1s8484×body80valid