Details

sample60.0ms

Algorithm

intervals

Results

40.0ms

271×

body

valid

simplify29.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

29.0ms

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

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.3b

localize17.0ms

Local error

Found 2 expressions with local error:

24.3b	(/ (fma a c (* b d)) (fma d d (* c c)))
0.3b	(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

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

series160.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

112.0ms	(/ (fma a c (* b d)) (fma d d (* c c)))
47.0ms	(fma a c (* b d))

simplify1.2s

Counts

31 → 47

Calls

31 calls:

Slowest

425.0ms	(/ (* (* (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)))))
52.0ms	(/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (sqrt (fma d d (* c c))))
49.0ms	(- (log (fma a c (* b d))) (log (fma d d (* c c))))
44.0ms	(/ (sqrt (fma a c (* b d))) (sqrt (fma d d (* c c))))

prune683.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 23.9b

localize39.0ms

Local error

Found 4 expressions with local error:

28.3b	(sqrt (fma d d (* c c)))
28.3b	(sqrt (fma d d (* c c)))
14.9b	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
0.3b	(fma a c (* b d))

rewrite8.0ms

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

5.0ms	(/ (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))

series340.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

153.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
77.0ms	(sqrt (fma d d (* c c)))
56.0ms	(sqrt (fma d d (* c c)))
54.0ms	(fma a c (* b d))

simplify1.8s

Counts

68 → 99

Calls

68 calls:

Slowest

232.0ms	(/ (* (* (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)))))
70.0ms	(/ (* (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)))))
49.0ms	(/ (sqrt (fma a c (* b d))) (sqrt (sqrt (fma d d (* c c)))))
47.0ms	(/ (sqrt (fma a c (* b d))) (sqrt (cbrt (fma d d (* c c)))))

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 20.8b

localize25.0ms

Local error

Found 4 expressions with local error:

28.3b	(sqrt (fma d d (* c c)))
28.3b	(sqrt (fma d d (* c c)))
14.9b	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
0.3b	(fma a c (* b d))

rewrite15.0ms

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

series335.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

167.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
73.0ms	(sqrt (fma d d (* c c)))
54.0ms	(sqrt (fma d d (* c c)))
42.0ms	(fma a c (* b d))

simplify1.9s

Counts

68 → 99

Calls

68 calls:

Slowest

321.0ms	(/ (* (* (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)))))
80.0ms	(/ (* (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))))))
63.0ms	(/ (* (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))))))
56.0ms	(/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (sqrt (sqrt (fma d d (* c c)))))
54.0ms	(/ (sqrt (fma a c (* b d))) (* (cbrt (sqrt (fma d d (* c c)))) (cbrt (sqrt (fma d d (* c c))))))

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 20.8b

localize33.0ms

Local error

Found 2 expressions with local error:

24.3b	(/ (fma a c (* b d)) (fma d d (* c c)))
0.3b	(fma a c (* b d))

rewrite9.0ms

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

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

series180.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

131.0ms	(/ (fma a c (* b d)) (fma d d (* c c)))
49.0ms	(fma a c (* b d))

simplify1.1s

Counts

31 → 47

Calls

31 calls:

Slowest

369.0ms	(/ (* (* (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))))
63.0ms	(/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (* (cbrt (fma d d (* c c))) (cbrt (fma d d (* c c)))))
53.0ms	(/ (sqrt (fma a c (* b d))) (* (cbrt (fma d d (* c c))) (cbrt (fma d d (* c c)))))
41.0ms	(/ (cbrt (fma a c (* b d))) (fma d d (* c c)))
41.0ms	(/ (sqrt (fma a c (* b d))) (fma d d (* c c)))

prune569.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 20.8b

regimes437.0ms

Accuracy

0% (2.4b remaining)

Error of 25.9b against oracle of 23.5b and baseline of 25.9b

bsearch3.0ms

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.6s

8456×

body

valid