Details

Time bar (total: 1.5m)

sample31.0ms

Algorithm
intervals
Results
21.0ms271×body80valid

simplify14.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
14.0ms
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.9b

localize27.0ms

Local error

Found 1 expressions with local error:

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

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt *-un-lft-identity times-frac add-cube-cbrt
3×associate-/r* add-cbrt-cube add-exp-log associate-/l*
1×expm1-log1p-u pow1 cbrt-undiv clear-num frac-2neg div-exp insert-posit16 log1p-expm1-u div-inv add-log-exp
Counts
1 → 30
Calls
1 calls:
Slowest
4.0ms
(/ (fma a c (* b d)) (fma d d (* c c)))

series130.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
130.0ms
(/ (fma a c (* b d)) (fma d d (* c c)))

simplify1.1s

Counts
28 → 33
Calls
28 calls:
Slowest
438.0ms
(/ (* (* (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))))
48.0ms
(/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (* (cbrt (fma d d (* c c))) (cbrt (fma d d (* c c)))))
39.0ms
(/ (cbrt (fma a c (* b d))) (fma d d (* c c)))
37.0ms
(/ (sqrt (fma a c (* b d))) (fma d d (* c c)))
36.0ms
(/ (fma a c (* b d)) (fma d d (* c c)))

prune426.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 24.5b

localize22.0ms

Local error

Found 4 expressions with local error:

30.1b
(sqrt (fma d d (* c c)))
30.1b
(sqrt (fma d d (* c c)))
15.9b
(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
0.1b
(/ (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c))))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
276×times-frac
160×add-sqr-sqrt
158×*-un-lft-identity add-cube-cbrt
150×sqrt-prod
25×associate-/l*
12×associate-/r*
11×add-cbrt-cube add-exp-log
9×div-inv
6×pow1
4×expm1-log1p-u cbrt-undiv div-exp insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 fma-udef hypot-def
1×associate-/l/
Counts
4 → 254
Calls
4 calls:
Slowest
14.0ms
(/ (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c))))
6.0ms
(/ (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)))

series390.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
140.0ms
(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
133.0ms
(/ (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c))))
61.0ms
(sqrt (fma d d (* c c)))
56.0ms
(sqrt (fma d d (* c c)))

simplify17.0s

Counts
364 → 266
Calls
364 calls:
Slowest
340.0ms
(/ (* (* (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))) (/ (fma a c (* b d)) (sqrt (fma d d (* c c))))) (/ (fma a c (* b d)) (sqrt (fma d d (* c c))))) (* (* (sqrt (fma d d (* c c))) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c)))))
320.0ms
(/ (* (* (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)))))
227.0ms
(/ (/ (* (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)))))) (* (cbrt (sqrt (fma d d (* c c)))) (cbrt (sqrt (fma d d (* c c))))))
216.0ms
(/ (/ (* (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)))))) (sqrt (* (cbrt (fma d d (* c c))) (cbrt (fma d d (* c c))))))
180.0ms
(/ (/ (* (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)))))) (* (cbrt (sqrt (fma d d (* c c)))) (cbrt (sqrt (fma d d (* c c))))))

prune3.8s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 14.5b

localize36.0ms

Local error

Found 4 expressions with local error:

15.9b
(/ (fma a c (* b d)) (hypot d c))
0.1b
(/ (/ (fma a c (* b d)) (hypot d c)) (hypot d c))
0.0b
(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×hypot-udef clear-num frac-2neg
1×associate-/l/
Counts
4 → 125
Calls
4 calls:
Slowest
15.0ms
(/ (/ (fma a c (* b d)) (hypot d c)) (hypot d c))
9.0ms
(/ (fma a c (* b d)) (hypot d c))
0.0ms
(hypot d c)
0.0ms
(hypot d c)

series511.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
183.0ms
(/ (/ (fma a c (* b d)) (hypot d c)) (hypot d c))
182.0ms
(/ (fma a c (* b d)) (hypot d c))
88.0ms
(hypot d c)
59.0ms
(hypot d c)

simplify5.6s

Counts
135 → 137
Calls
135 calls:
Slowest
804.0ms
(/ (* (* (/ (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)))
291.0ms
(/ (* (* (fma a c (* b d)) (fma a c (* b d))) (fma a c (* b d))) (* (* (hypot d c) (hypot d c)) (hypot d c)))
234.0ms
(/ (/ (* (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))))
194.0ms
(/ (/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (* (cbrt (hypot d c)) (cbrt (hypot d c)))) (sqrt (hypot d c)))
193.0ms
(/ (/ (* (* (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)))

prune1.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.7b

localize45.0ms

Local error

Found 4 expressions with local error:

16.0b
(/ (hypot d c) (fma a c (* b d)))
0.2b
(/ 1 (/ (hypot d c) (fma a c (* b d))))
0.1b
(/ (/ 1 (/ (hypot d c) (fma a c (* b d)))) (hypot d c))
0.0b
(hypot d c)

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
480×times-frac
239×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
50×associate-/l*
36×add-exp-log
23×div-inv
22×div-exp
20×add-cbrt-cube
19×associate-/r*
10×cbrt-undiv
5×pow1 associate-/r/
4×expm1-log1p-u rec-exp 1-exp insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg
1×hypot-udef pow-flip inv-pow associate-/l/
Counts
4 → 323
Calls
4 calls:
Slowest
18.0ms
(/ (/ 1 (/ (hypot d c) (fma a c (* b d)))) (hypot d c))
12.0ms
(/ 1 (/ (hypot d c) (fma a c (* b d))))
8.0ms
(/ (hypot d c) (fma a c (* b d)))
0.0ms
(hypot d c)

series711.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
260.0ms
(/ (/ 1 (/ (hypot d c) (fma a c (* b d)))) (hypot d c))
241.0ms
(/ 1 (/ (hypot d c) (fma a c (* b d))))
136.0ms
(/ (hypot d c) (fma a c (* b d)))
73.0ms
(hypot d c)

simplify52.9s

Counts
457 → 335
Calls
457 calls:
Slowest
783.0ms
(/ (/ (sqrt 1) (/ (sqrt (hypot d c)) (sqrt (fma a c (* b d))))) (* (cbrt (hypot d c)) (cbrt (hypot d c))))
677.0ms
(/ (/ (* (* 1 1) 1) (* (* (/ (hypot d c) (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)))
590.0ms
(/ (/ (sqrt 1) (/ (* (cbrt (hypot d c)) (cbrt (hypot d c))) (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))))) (sqrt (hypot d c)))
568.0ms
(/ (/ (* (cbrt 1) (cbrt 1)) (/ 1 (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))))) (* (cbrt (hypot d c)) (cbrt (hypot d c))))
544.0ms
(/ (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (hypot d c)) (cbrt (hypot d c))) (sqrt (fma a c (* b d))))) (* (cbrt (hypot d c)) (cbrt (hypot d c))))

prune3.6s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.5b

regimes294.0ms

Accuracy

29.5% (9.8b remaining)

Error of 12.0b against oracle of 2.2b and baseline of 16.0b

bsearch115.0ms

end0.0ms

sample1.7s

Algorithm
intervals
Results
1.4s8507×body80valid