Details

sample41.0ms

Algorithm

intervals

Results

30.0ms

273×

body

valid

simplify29.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

29.0ms

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

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.1b

localize34.0ms

Local error

Found 3 expressions with local error:

24.1b	(/ (fma a c (* b d)) (fma d d (* c c)))
0.3b	(fma a c (* b d))
0.0b	(fma d d (* c c))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 52

Calls

3 calls:

Slowest

8.0ms	(/ (fma a c (* b d)) (fma d d (* c c)))
0.0ms	(fma a c (* b d))
0.0ms	(fma d d (* c c))

series228.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

124.0ms	(/ (fma a c (* b d)) (fma d d (* c c)))
53.0ms	(fma d d (* c c))
51.0ms	(fma a c (* b d))

simplify1.3s

Counts

34 → 61

Calls

34 calls:

Slowest

413.0ms	(/ (* (* (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))))
91.0ms	(/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (* (cbrt (fma d d (* c c))) (cbrt (fma d d (* c c)))))
51.0ms	(/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (sqrt (fma d d (* c c))))
46.0ms	(/ (sqrt (fma a c (* b d))) (* (cbrt (fma d d (* c c))) (cbrt (fma d d (* c c)))))
46.0ms	(- (log (fma a c (* b d))) (log (fma d d (* c c))))

prune707.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 23.7b

localize23.0ms

Local error

Found 4 expressions with local error:

29.3b	(sqrt (fma d d (* c c)))
29.3b	(sqrt (fma d d (* c c)))
13.3b	(/ (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`

Counts

4 → 87

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))

series356.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

176.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
65.0ms	(sqrt (fma d d (* c c)))
62.0ms	(sqrt (fma d d (* c c)))
53.0ms	(fma a c (* b d))

simplify1.8s

Counts

68 → 99

Calls

68 calls:

Slowest

331.0ms	(/ (* (* (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)))))
56.0ms	(/ (* (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	(/ (sqrt (fma a c (* b d))) (* (cbrt (sqrt (fma d d (* c c)))) (cbrt (sqrt (fma d d (* c c))))))
46.0ms	(/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (sqrt 1))
45.0ms	(/ (cbrt (fma a c (* b d))) (sqrt (fma d d (* c c))))

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 22.6b

localize50.0ms

Local error

Found 4 expressions with local error:

29.3b	(sqrt (fma d d (* c c)))
13.3b	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
0.3b	(fma a c (* b d))
0.1b	(/ (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))) (hypot d c))

rewrite31.0ms

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`
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 → 179

Calls

4 calls:

Slowest

16.0ms	(/ (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))) (hypot d c))
9.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
3.0ms	(sqrt (fma d d (* c c)))
0.0ms	(fma a c (* b d))

series525.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

238.0ms	(/ (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))) (hypot d c))
163.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
67.0ms	(sqrt (fma d d (* c c)))
57.0ms	(fma a c (* b d))

simplify10.3s

Counts

224 → 191

Calls

224 calls:

Slowest

297.0ms	(/ (/ (* (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))))
290.0ms	(/ (* (* (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)))))
231.0ms	(/ (/ (* (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))))
164.0ms	(/ (/ (* (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))))
160.0ms	(/ (/ (* (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))))

prune2.7s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.9b

localize33.0ms

Local error

Found 3 expressions with local error:

13.3b	(/ (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))

rewrite32.0ms

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/`

Counts

3 → 114

Calls

3 calls:

Slowest

15.0ms	(/ (/ (fma a c (* b d)) (hypot d c)) (hypot d c))
14.0ms	(/ (fma a c (* b d)) (hypot d c))
0.0ms	(fma a c (* b d))

series386.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

172.0ms	(/ (/ (fma a c (* b d)) (hypot d c)) (hypot d c))
163.0ms	(/ (fma a c (* b d)) (hypot d c))
50.0ms	(fma a c (* b d))

simplify5.2s

Counts

132 → 123

Calls

132 calls:

Slowest

419.0ms	(/ (* (* (/ (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)))
303.0ms	(/ (* (* (fma a c (* b d)) (fma a c (* b d))) (fma a c (* b d))) (* (* (hypot d c) (hypot d c)) (hypot d c)))
222.0ms	(/ (/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (* (cbrt (hypot d c)) (cbrt (hypot d c)))) (sqrt (hypot d c)))
206.0ms	(/ (/ (* (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))))
138.0ms	(/ (/ (* (* (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)))

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.9b

regimes318.0ms

Accuracy

33.7% (6.9b remaining)

Error of 12.5b against oracle of 5.6b and baseline of 16.1b

bsearch115.0ms

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.3s

8470×

body

valid