Details

sample31.0ms

Algorithm

intervals

Results

22.0ms

278×

body

valid

simplify14.0ms

Calls

1 calls:

Slowest

14.0ms

(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.1b

localize26.0ms

Local error

Found 2 expressions with local error:

28.1b	(/ (fma a c (* b d)) (fma d d (* c c)))
0.5b	(fma a c (* b d))

rewrite5.0ms

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

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

series166.0ms

Calls

2 calls:

Slowest

116.0ms	(/ (fma a c (* b d)) (fma d d (* c c)))
50.0ms	(fma a c (* b d))

simplify1.2s

Calls

31 calls:

Slowest

469.0ms	(/ (* (* (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))))
58.0ms	(/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (* (cbrt (fma d d (* c c))) (cbrt (fma d d (* c c)))))
47.0ms	(- (log (fma a c (* b d))) (log (fma d d (* c c))))
43.0ms	(/ (sqrt (fma a c (* b d))) (cbrt (fma d d (* c c))))
43.0ms	(/ (cbrt (fma a c (* b d))) (cbrt (fma d d (* c c))))

prune559.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 27.6b

localize24.0ms

Local error

Found 4 expressions with local error:

32.0b	(sqrt (fma d d (* c c)))
32.0b	(sqrt (fma d d (* c c)))
15.0b	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
0.5b	(fma a c (* b d))

rewrite13.0ms

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`

Calls

4 calls:

Slowest

8.0ms	(/ (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))

series336.0ms

Calls

4 calls:

Slowest

160.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
62.0ms	(sqrt (fma d d (* c c)))
58.0ms	(fma a c (* b d))
55.0ms	(sqrt (fma d d (* c c)))

simplify1.8s

Calls

68 calls:

Slowest

299.0ms	(/ (* (* (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)))))
62.0ms	(/ (* (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))))))
52.0ms	(/ (* (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))))))
47.0ms	(/ (fma a c (* b d)) (sqrt (sqrt (fma d d (* c c)))))
46.0ms	(/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) 1)

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 26.2b

localize24.0ms

Local error

Found 4 expressions with local error:

32.0b	(sqrt (fma d d (* c c)))
15.0b	(/ (fma a c (* b d)) (hypot d c))
0.5b	(fma a c (* b d))
0.0b	(/ (/ (fma a c (* b d)) (hypot d c)) (sqrt (fma d d (* c c))))

rewrite29.0ms

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/`

Calls

4 calls:

Slowest

16.0ms	(/ (/ (fma a c (* b d)) (hypot d c)) (sqrt (fma d d (* c c))))
8.0ms	(/ (fma a c (* b d)) (hypot d c))
1.0ms	(sqrt (fma d d (* c c)))
1.0ms	(fma a c (* b d))

series481.0ms

Calls

4 calls:

Slowest

226.0ms	(/ (/ (fma a c (* b d)) (hypot d c)) (sqrt (fma d d (* c c))))
154.0ms	(/ (fma a c (* b d)) (hypot d c))
52.0ms	(sqrt (fma d d (* c c)))
50.0ms	(fma a c (* b d))

simplify10.2s

Calls

221 calls:

Slowest

277.0ms	(/ (/ (* (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))))))
272.0ms	(/ (* (* (fma a c (* b d)) (fma a c (* b d))) (fma a c (* b d))) (* (* (hypot d c) (hypot d c)) (hypot d c)))
214.0ms	(/ (/ (* (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))))))
184.0ms	(/ (/ (* (* (fma a c (* b d)) (fma a c (* b d))) (fma a c (* b d))) (* (* (hypot d c) (hypot d c)) (hypot d c))) (* (* (sqrt (fma d d (* c c))) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c)))))
182.0ms	(/ (/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (* (cbrt (hypot d c)) (cbrt (hypot d c)))) (sqrt (sqrt (fma d d (* c c)))))

prune2.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.7b

localize16.0ms

Local error

Found 3 expressions with local error:

15.0b	(/ (fma a c (* b d)) (hypot d c))
0.5b	(fma a c (* b d))
0.0b	(/ (/ (fma a c (* b d)) (hypot d c)) (hypot d c))

rewrite17.0ms

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

11.0ms	(/ (/ (fma a c (* b d)) (hypot d c)) (hypot d c))
4.0ms	(/ (fma a c (* b d)) (hypot d c))
0.0ms	(fma a c (* b d))

series358.0ms

Calls

3 calls:

Slowest

177.0ms	(/ (/ (fma a c (* b d)) (hypot d c)) (hypot d c))
133.0ms	(/ (fma a c (* b d)) (hypot d c))
47.0ms	(fma a c (* b d))

simplify5.5s

Calls

132 calls:

Slowest

476.0ms	(/ (* (* (/ (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)))
328.0ms	(/ (* (* (fma a c (* b d)) (fma a c (* b d))) (fma a c (* b d))) (* (* (hypot d c) (hypot d c)) (hypot d c)))
198.0ms	(/ (/ (* (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))))
137.0ms	(/ (/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (* (cbrt (hypot d c)) (cbrt (hypot d c)))) (sqrt (hypot d c)))
132.0ms	(/ (/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (* (cbrt (hypot d c)) (cbrt (hypot d c)))) 1)

prune1.5s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.3b

regimes312.0ms

Accuracy

17.3% (8.4b remaining)

Error of 14.2b against oracle of 5.8b and baseline of 15.9b

bsearch81.0ms

end0.0ms

sample1.3s

Algorithm

intervals

Results

1.1s

8476×

body

valid