Details

sample48.0ms

Algorithm

intervals

Results

36.0ms

268×

body

valid

simplify15.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

15.0ms

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

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.3b

localize26.0ms

Local error

Found 2 expressions with local error:

23.3b	(/ (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`

Counts

2 → 41

Calls

2 calls:

Slowest

5.0ms	(/ (fma a c (* b d)) (fma d d (* c c)))
0.0ms	(fma a c (* b d))

series211.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

143.0ms	(/ (fma a c (* b d)) (fma d d (* c c)))
68.0ms	(fma a c (* b d))

simplify1.6s

Counts

31 → 47

Calls

31 calls:

Slowest

752.0ms	(/ (* (* (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))))
60.0ms	(/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (* (cbrt (fma d d (* c c))) (cbrt (fma d d (* c c)))))
50.0ms	(- (log (fma a c (* b d))) (log (fma d d (* c c))))
49.0ms	(/ (sqrt (fma a c (* b d))) (* (cbrt (fma d d (* c c))) (cbrt (fma d d (* c c)))))
48.0ms	(/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (sqrt (fma d d (* c c))))

prune612.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 22.9b

localize27.0ms

Local error

Found 4 expressions with local error:

29.6b	(sqrt (fma d d (* c c)))
29.6b	(sqrt (fma d d (* c c)))
14.4b	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
0.5b	(fma a c (* b d))

rewrite17.0ms

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

10.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
2.0ms	(sqrt (fma d d (* c c)))
2.0ms	(sqrt (fma d d (* c c)))
0.0ms	(fma a c (* b d))

series324.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

132.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
77.0ms	(sqrt (fma d d (* c c)))
69.0ms	(sqrt (fma d d (* c c)))
45.0ms	(fma a c (* b d))

simplify1.9s

Counts

68 → 99

Calls

68 calls:

Slowest

241.0ms	(/ (* (* (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)))))
88.0ms	(/ (* (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))))))
55.0ms	(/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (sqrt (sqrt (fma d d (* c c)))))
54.0ms	(/ (* (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))))))
53.0ms	(/ (sqrt (fma a c (* b d))) (sqrt (* (cbrt (fma d d (* c c))) (cbrt (fma d d (* c c))))))

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 21.4b

localize40.0ms

Local error

Found 4 expressions with local error:

29.6b	(sqrt (fma d d (* c c)))
14.4b	(/ (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))

rewrite25.0ms

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

14.0ms	(/ (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))) (hypot d c))
5.0ms	(/ (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))

series479.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

205.0ms	(/ (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))) (hypot d c))
154.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
71.0ms	(sqrt (fma d d (* c c)))
49.0ms	(fma a c (* b d))

simplify10.7s

Counts

224 → 191

Calls

224 calls:

Slowest

303.0ms	(/ (* (* (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)))))
253.0ms	(/ (/ (* (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))))
203.0ms	(/ (/ (* (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))))
191.0ms	(/ (/ (* (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))))
180.0ms	(/ (/ (* (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)))

prune2.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.6b

localize23.0ms

Local error

Found 4 expressions with local error:

14.4b	(/ (fma a c (* b d)) (hypot d c))
0.5b	(fma a c (* b d))
0.1b	(/ (/ (fma a c (* b d)) (hypot d c)) (hypot d c))
0.0b	(hypot d c)

rewrite15.0ms

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×	`clear-num` `frac-2neg`
1×	`hypot-udef` `fma-udef` `associate-/l/`

Counts

4 → 125

Calls

4 calls:

Slowest

8.0ms	(/ (/ (fma a c (* b d)) (hypot d c)) (hypot d c))
5.0ms	(/ (fma a c (* b d)) (hypot d c))
0.0ms	(fma a c (* b d))
0.0ms	(hypot d c)

series390.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

146.0ms	(/ (fma a c (* b d)) (hypot d c))
128.0ms	(/ (/ (fma a c (* b d)) (hypot d c)) (hypot d c))
70.0ms	(hypot d c)
47.0ms	(fma a c (* b d))

simplify4.4s

Counts

135 → 137

Calls

135 calls:

Slowest

378.0ms	(/ (* (* (/ (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)))
229.0ms	(/ (* (* (fma a c (* b d)) (fma a c (* b d))) (fma a c (* b d))) (* (* (hypot d c) (hypot d c)) (hypot d c)))
177.0ms	(/ (/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (sqrt (hypot d c))) (* (cbrt (hypot d c)) (cbrt (hypot d c))))
177.0ms	(/ (/ (* (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))))
115.0ms	(/ (/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (* (cbrt (hypot d c)) (cbrt (hypot d c)))) (sqrt (hypot d c)))

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.6b

regimes403.0ms

Accuracy

36.4% (6.6b remaining)

Error of 12.6b against oracle of 6.0b and baseline of 16.4b

bsearch107.0ms

end0.0ms

sample1.2s

Algorithm

intervals

Results

1000.0ms

8460×

body

valid