Details

sample40.0ms

Algorithm

intervals

Results

28.0ms

269×

body

valid

simplify30.0ms

Calls

1 calls:

Slowest

30.0ms

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

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.6b

localize50.0ms

Local error

Found 2 expressions with local error:

27.6b	(/ (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`

Calls

2 calls:

Slowest

9.0ms	(/ (fma a c (* b d)) (fma d d (* c c)))
0.0ms	(fma a c (* b d))

series202.0ms

Calls

2 calls:

Slowest

148.0ms	(/ (fma a c (* b d)) (fma d d (* c c)))
53.0ms	(fma a c (* b d))

simplify1.2s

Calls

31 calls:

Slowest

483.0ms	(/ (* (* (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))))
77.0ms	(/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (* (cbrt (fma d d (* c c))) (cbrt (fma d d (* c c)))))
52.0ms	(/ (sqrt (fma a c (* b d))) (* (cbrt (fma d d (* c c))) (cbrt (fma d d (* c c)))))
45.0ms	(/ (sqrt (fma a c (* b d))) (sqrt (fma d d (* c c))))
45.0ms	(/ (sqrt (fma a c (* b d))) (sqrt (fma d d (* c c))))

prune588.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 27.1b

localize38.0ms

Local error

Found 4 expressions with local error:

30.8b	(sqrt (fma d d (* c c)))
30.8b	(sqrt (fma d d (* c c)))
17.7b	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
0.3b	(fma a c (* b d))

rewrite16.0ms

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

9.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
3.0ms	(sqrt (fma d d (* c c)))
2.0ms	(sqrt (fma d d (* c c)))
0.0ms	(fma a c (* b d))

series331.0ms

Calls

4 calls:

Slowest

142.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
68.0ms	(fma a c (* b d))
62.0ms	(sqrt (fma d d (* c c)))
58.0ms	(sqrt (fma d d (* c c)))

simplify1.9s

Calls

68 calls:

Slowest

298.0ms	(/ (* (* (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)))))
92.0ms	(/ (* (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))))))
60.0ms	(/ (* (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))))))
57.0ms	(/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (sqrt 1))
55.0ms	(/ (sqrt (fma a c (* b d))) (sqrt (* (cbrt (fma d d (* c c))) (cbrt (fma d d (* c c))))))

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 25.0b

localize37.0ms

Local error

Found 4 expressions with local error:

30.8b	(sqrt (fma d d (* c c)))
17.7b	(/ (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))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

150×	`times-frac`
93×	`add-sqr-sqrt`
92×	`*-un-lft-identity` `add-cube-cbrt`
45×	`sqrt-prod`
19×	`associate-/l*`
12×	`associate-/r*`
11×	`add-cbrt-cube` `add-exp-log`
9×	`div-inv` `associate-/l/`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg`
2×	`fma-udef`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `hypot-def`

Calls

4 calls:

Slowest

9.0ms	(/ (/ (fma a c (* b d)) (hypot d c)) (sqrt (fma d d (* c c))))
4.0ms	(/ (fma a c (* b d)) (hypot d c))
1.0ms	(sqrt (fma d d (* c c)))
0.0ms	(fma a c (* b d))

series512.0ms

Calls

4 calls:

Slowest

227.0ms	(/ (/ (fma a c (* b d)) (hypot d c)) (sqrt (fma d d (* c c))))
175.0ms	(/ (fma a c (* b d)) (hypot d c))
56.0ms	(fma a c (* b d))
54.0ms	(sqrt (fma d d (* c c)))

simplify10.5s

Calls

227 calls:

Slowest

340.0ms	(/ (/ (* (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))))))
308.0ms	(/ (* (* (fma a c (* b d)) (fma a c (* b d))) (fma a c (* b d))) (* (* (hypot d c) (hypot d c)) (hypot d c)))
204.0ms	(/ (/ (* (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))))))
189.0ms	(/ (/ (* (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))))))
189.0ms	(/ (/ (* (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)))))

prune2.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 15.9b

localize31.0ms

Local error

Found 3 expressions with local error:

17.7b	(/ (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))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

3 calls:

Slowest

8.0ms	(/ (/ (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))

series413.0ms

Calls

3 calls:

Slowest

191.0ms	(/ (fma a c (* b d)) (hypot d c))
172.0ms	(/ (/ (fma a c (* b d)) (hypot d c)) (hypot d c))
49.0ms	(fma a c (* b d))

simplify5.8s

Calls

138 calls:

Slowest

443.0ms	(/ (* (* (/ (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)))
300.0ms	(/ (* (* (fma a c (* b d)) (fma a c (* b d))) (fma a c (* b d))) (* (* (hypot d c) (hypot d c)) (hypot d c)))
202.0ms	(/ (/ (* (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))))
179.0ms	(/ (/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (* (cbrt (hypot d c)) (cbrt (hypot d c)))) (sqrt (hypot d c)))
169.0ms	(/ (/ (* (* (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)))

prune1.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.1b

regimes431.0ms

Accuracy

35.5% (7.0b remaining)

Error of 12.7b against oracle of 5.7b and baseline of 16.5b

bsearch163.0ms

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.2s

8413×

body

valid