Details

Time bar (total: 27.2s)

sample40.0ms

Algorithm
intervals
Results
27.0ms269×body80valid

simplify24.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
24.0ms
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.9b

localize17.0ms

Local error

Found 2 expressions with local error:

24.9b
(/ (fma a c (* b d)) (fma d d (* c c)))
0.3b
(fma a c (* b d))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
4×add-cbrt-cube add-exp-log
3×associate-/r* associate-/l*
2×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
1×cbrt-undiv clear-num frac-2neg div-exp fma-udef div-inv
Counts
2 → 41
Calls
2 calls:
Slowest
8.0ms
(/ (fma a c (* b d)) (fma d d (* c c)))
0.0ms
(fma a c (* b d))

series169.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
124.0ms
(/ (fma a c (* b d)) (fma d d (* c c)))
45.0ms
(fma a c (* b d))

simplify1.1s

Counts
31 → 47
Calls
31 calls:
Slowest
359.0ms
(/ (* (* (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))))
60.0ms
(/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (* (cbrt (fma d d (* c c))) (cbrt (fma d d (* c c)))))
50.0ms
(/ (sqrt (fma a c (* b d))) (* (cbrt (fma d d (* c c))) (cbrt (fma d d (* c c)))))
44.0ms
(/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (sqrt (fma d d (* c c))))
42.0ms
(/ (cbrt (fma a c (* b d))) (sqrt (fma d d (* c c))))

prune668.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 24.5b

localize45.0ms

Local error

Found 4 expressions with local error:

30.8b
(sqrt (fma d d (* c c)))
30.8b
(sqrt (fma d d (* c c)))
16.4b
(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
0.3b
(fma a c (* b d))

rewrite9.0ms

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×fma-udef associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 hypot-def
1×cbrt-undiv clear-num frac-2neg div-exp div-inv
Counts
4 → 87
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))

series346.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
148.0ms
(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
70.0ms
(sqrt (fma d d (* c c)))
68.0ms
(sqrt (fma d d (* c c)))
59.0ms
(fma a c (* b d))

simplify2.0s

Counts
68 → 99
Calls
68 calls:
Slowest
258.0ms
(/ (* (* (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)))))
64.0ms
(/ (* (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))))))
59.0ms
(/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (sqrt (sqrt (fma d d (* c c)))))
52.0ms
(/ (sqrt (fma a c (* b d))) (sqrt (* (cbrt (fma d d (* c c))) (cbrt (fma d d (* c c))))))
52.0ms
(/ (sqrt (fma a c (* b d))) (* (cbrt (sqrt (fma d d (* c c)))) (cbrt (sqrt (fma d d (* c c))))))

prune1.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 22.5b

localize42.0ms

Local error

Found 4 expressions with local error:

30.8b
(sqrt (fma d d (* c c)))
16.4b
(/ (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))))

rewrite43.0ms

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
5×pow1
4×expm1-log1p-u cbrt-undiv div-exp insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg fma-udef
1×rem-sqrt-square sqrt-pow1 pow1/2 hypot-def associate-/l/
Counts
4 → 173
Calls
4 calls:
Slowest
18.0ms
(/ (/ (fma a c (* b d)) (hypot d c)) (sqrt (fma d d (* c c))))
18.0ms
(/ (fma a c (* b d)) (hypot d c))
3.0ms
(sqrt (fma d d (* c c)))
0.0ms
(fma a c (* b d))

series481.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
206.0ms
(/ (/ (fma a c (* b d)) (hypot d c)) (sqrt (fma d d (* c c))))
157.0ms
(/ (fma a c (* b d)) (hypot d c))
61.0ms
(sqrt (fma d d (* c c)))
57.0ms
(fma a c (* b d))

simplify9.5s

Counts
221 → 185
Calls
221 calls:
Slowest
317.0ms
(/ (/ (* (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))))))
307.0ms
(/ (* (* (fma a c (* b d)) (fma a c (* b d))) (fma a c (* b d))) (* (* (hypot d c) (hypot d c)) (hypot d c)))
192.0ms
(/ (/ (* (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))))))
191.0ms
(/ (* (* (/ (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)))))
177.0ms
(/ (/ (* (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))))))

prune2.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.6b

localize22.0ms

Local error

Found 4 expressions with local error:

16.4b
(/ (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)

rewrite27.0ms

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/
Counts
4 → 125
Calls
4 calls:
Slowest
15.0ms
(/ (/ (fma a c (* b d)) (hypot d c)) (hypot d c))
8.0ms
(/ (fma a c (* b d)) (hypot d c))
0.0ms
(fma a c (* b d))
0.0ms
(hypot d c)

series496.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
192.0ms
(/ (/ (fma a c (* b d)) (hypot d c)) (hypot d c))
149.0ms
(/ (fma a c (* b d)) (hypot d c))
84.0ms
(hypot d c)
71.0ms
(fma a c (* b d))

simplify4.8s

Counts
135 → 137
Calls
135 calls:
Slowest
400.0ms
(/ (* (* (/ (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)))
257.0ms
(/ (* (* (fma a c (* b d)) (fma a c (* b d))) (fma a c (* b d))) (* (* (hypot d c) (hypot d c)) (hypot d c)))
196.0ms
(/ (/ (* (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))))
157.0ms
(/ (/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) 1) (* (cbrt (hypot d c)) (cbrt (hypot d c))))
147.0ms
(/ (/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (sqrt (hypot d c))) (* (cbrt (hypot d c)) (cbrt (hypot d c))))

prune1.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.9b

regimes324.0ms

Accuracy

33.5% (7.1b remaining)

Error of 13.1b against oracle of 6.0b and baseline of 16.7b

bsearch130.0ms

end0.0ms

sample1.8s

Algorithm
intervals
Results
1.5s8453×body80valid