Details

sample32.0ms

Algorithm

intervals

Results

23.0ms

274×

body

valid

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: 27.0b

localize16.0ms

Local error

Found 2 expressions with local error:

27.0b	(/ (fma a c (* b d)) (fma d d (* c c)))
0.5b	(fma a c (* b d))

rewrite13.0ms

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`

Calls

2 calls:

Slowest

13.0ms	(/ (fma a c (* b d)) (fma d d (* c c)))
0.0ms	(fma a c (* b d))

series86.0ms

Calls

2 calls:

Slowest

55.0ms	(/ (fma a c (* b d)) (fma d d (* c c)))
31.0ms	(fma a c (* b d))

simplify1.0s

Calls

31 calls:

Slowest

339.0ms	(/ (* (* (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))))
62.0ms	(/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (* (cbrt (fma d d (* c c))) (cbrt (fma d d (* c c)))))
41.0ms	(/ (sqrt (fma a c (* b d))) (* (cbrt (fma d d (* c c))) (cbrt (fma d d (* c c)))))
35.0ms	(/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) 1)
34.0ms	(/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (sqrt (fma d d (* c c))))

prune495.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 26.5b

localize10.0ms

Local error

Found 4 expressions with local error:

28.3b	(sqrt (fma d d (* c c)))
28.3b	(sqrt (fma d d (* c c)))
18.5b	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
0.5b	(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×	`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))))
2.0ms	(sqrt (fma d d (* c c)))
1.0ms	(sqrt (fma d d (* c c)))
0.0ms	(fma a c (* b d))

series186.0ms

Calls

4 calls:

Slowest

91.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
39.0ms	(fma a c (* b d))
29.0ms	(sqrt (fma d d (* c c)))
27.0ms	(sqrt (fma d d (* c c)))

simplify1.7s

Calls

66 calls:

Slowest

261.0ms	(/ (* (* (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)))))
55.0ms	(/ (* (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))))))
45.0ms	(/ (* (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))))))
39.0ms	(/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (sqrt 1))
38.0ms	(/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (sqrt (sqrt (fma d d (* c c)))))

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 23.8b

localize6.0ms

Local error

Found 4 expressions with local error:

28.3b	(sqrt (fma d d (* c c)))
18.5b	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
0.5b	(fma a c (* b d))
0.1b	(/ (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))) (hypot d c))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
96×	`add-sqr-sqrt`
95×	`*-un-lft-identity` `add-cube-cbrt`
51×	`sqrt-prod`
25×	`associate-/l*`
11×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/r*`
6×	`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

8.0ms	(/ (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))) (hypot d c))
4.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
1.0ms	(sqrt (fma d d (* c c)))
0.0ms	(fma a c (* b d))

series235.0ms

Calls

4 calls:

Slowest

107.0ms	(/ (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))) (hypot d c))
73.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
32.0ms	(fma a c (* b d))
23.0ms	(sqrt (fma d d (* c c)))

simplify9.1s

Calls

223 calls:

Slowest

271.0ms	(/ (* (* (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)))))
177.0ms	(/ (/ (* (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 (hypot d c)) (cbrt (hypot d c))))
173.0ms	(/ (/ (* (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 (hypot d c)) (cbrt (hypot d c))))
165.0ms	(/ (/ (* (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 (hypot d c)))
149.0ms	(/ (/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (sqrt (sqrt (fma d d (* c c))))) (* (cbrt (hypot d c)) (cbrt (hypot d c))))

prune2.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.0b

localize13.0ms

Local error

Found 3 expressions with local error:

18.5b	(/ (fma b d (* a c)) (hypot d c))
0.1b	(/ (/ (fma b d (* a c)) (hypot d c)) (hypot d c))
0.0b	(fma b d (* a c))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
53×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
16×	`associate-/l*`
10×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r*` `div-inv`
4×	`cbrt-undiv` `div-exp`
3×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg`
1×	`fma-udef` `associate-/l/`

Calls

3 calls:

Slowest

7.0ms	(/ (/ (fma b d (* a c)) (hypot d c)) (hypot d c))
4.0ms	(/ (fma b d (* a c)) (hypot d c))
0.0ms	(fma b d (* a c))

series226.0ms

Calls

3 calls:

Slowest

100.0ms	(/ (/ (fma b d (* a c)) (hypot d c)) (hypot d c))
88.0ms	(/ (fma b d (* a c)) (hypot d c))
39.0ms	(fma b d (* a c))

simplify4.5s

Calls

132 calls:

Slowest

387.0ms	(/ (* (* (/ (fma b d (* a c)) (hypot d c)) (/ (fma b d (* a c)) (hypot d c))) (/ (fma b d (* a c)) (hypot d c))) (* (* (hypot d c) (hypot d c)) (hypot d c)))
243.0ms	(/ (* (* (fma b d (* a c)) (fma b d (* a c))) (fma b d (* a c))) (* (* (hypot d c) (hypot d c)) (hypot d c)))
155.0ms	(/ (/ (* (cbrt (fma b d (* a c))) (cbrt (fma b d (* a c)))) (sqrt (hypot d c))) (* (cbrt (hypot d c)) (cbrt (hypot d c))))
141.0ms	(/ (/ (* (cbrt (fma b d (* a c))) (cbrt (fma b d (* a c)))) (* (cbrt (hypot d c)) (cbrt (hypot d c)))) (* (cbrt (hypot d c)) (cbrt (hypot d c))))
127.0ms	(/ (/ (* (* (fma b d (* a c)) (fma b d (* a c))) (fma b d (* a c))) (* (* (hypot d c) (hypot d c)) (hypot d c))) (* (* (hypot d c) (hypot d c)) (hypot d c)))

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.5b

regimes260.0ms

Accuracy

20.5% (10.9b remaining)

Error of 13.7b against oracle of 2.8b and baseline of 16.5b

bsearch112.0ms

end0.0ms

sample1.3s

Algorithm

intervals

Results

1.1s

8482×

body

valid