Details

sample35.0ms

Algorithm

intervals

Results

25.0ms

274×

body

valid

simplify28.0ms

Calls

1 calls:

Slowest

28.0ms

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.7b

localize16.0ms

Local error

Found 2 expressions with local error:

25.7b	(/ (fma a c (* b d)) (fma d d (* c c)))
0.0b	(fma d d (* c c))

rewrite8.0ms

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

7.0ms	(/ (fma a c (* b d)) (fma d d (* c c)))
0.0ms	(fma d d (* c c))

series175.0ms

Calls

2 calls:

Slowest

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

simplify1.1s

Calls

31 calls:

Slowest

407.0ms	(/ (* (* (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))))
59.0ms	(/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (* (cbrt (fma d d (* c c))) (cbrt (fma d d (* c c)))))
45.0ms	(/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) 1)
43.0ms	(/ (cbrt (fma a c (* b d))) (sqrt (fma d d (* c c))))
40.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))

prune561.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 25.3b

localize44.0ms

Local error

Found 4 expressions with local error:

27.5b	(sqrt (fma d d (* c c)))
27.5b	(sqrt (fma d d (* c c)))
16.1b	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
0.0b	(/ (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

9.0ms	(/ (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c))))
6.0ms	(/ (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)))

series449.0ms

Calls

4 calls:

Slowest

170.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
159.0ms	(/ (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c))))
65.0ms	(sqrt (fma d d (* c c)))
55.0ms	(sqrt (fma d d (* c c)))

simplify17.4s

Calls

364 calls:

Slowest

497.0ms	(/ (* (* (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))) (/ (fma a c (* b d)) (sqrt (fma d d (* c c))))) (/ (fma a c (* b d)) (sqrt (fma d d (* c c))))) (* (* (sqrt (fma d d (* c c))) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c)))))
245.0ms	(/ (* (* (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)))))
239.0ms	(/ (/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (sqrt (sqrt (fma d d (* c c))))) (* (cbrt (sqrt (fma d d (* c c)))) (cbrt (sqrt (fma d d (* c c))))))
213.0ms	(/ (/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (sqrt (sqrt (fma d d (* c c))))) (* (cbrt (sqrt (fma d d (* c c)))) (cbrt (sqrt (fma d d (* c c))))))
206.0ms	(/ (/ (* (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 (sqrt (fma d d (* c c)))))

prune3.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 14.8b

localize18.0ms

Local error

Found 4 expressions with local error:

16.1b	(/ (fma a c (* b d)) (hypot d c))
0.0b	(/ (/ (fma a c (* b d)) (hypot d c)) (hypot d c))
0.0b	(hypot d c)
0.0b	(hypot d c)

rewrite20.0ms

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

Calls

4 calls:

Slowest

12.0ms	(/ (/ (fma a c (* b d)) (hypot d c)) (hypot d c))
4.0ms	(/ (fma a c (* b d)) (hypot d c))
0.0ms	(hypot d c)
0.0ms	(hypot d c)

series510.0ms

Calls

4 calls:

Slowest

202.0ms	(/ (fma a c (* b d)) (hypot d c))
156.0ms	(/ (/ (fma a c (* b d)) (hypot d c)) (hypot d c))
81.0ms	(hypot d c)
71.0ms	(hypot d c)

simplify5.7s

Calls

135 calls:

Slowest

561.0ms	(/ (* (* (/ (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)))
332.0ms	(/ (* (* (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))))
183.0ms	(/ (/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (* (cbrt (hypot d c)) (cbrt (hypot d c)))) (sqrt (hypot d c)))
147.0ms	(/ (/ (* (* (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)))

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.2b

localize24.0ms

Local error

Found 4 expressions with local error:

16.1b	(/ (fma a c (* b d)) (hypot d c))
0.0b	(/ (/ (/ (fma a c (* b d)) (hypot d c)) 1) (hypot d c))
0.0b	(hypot d c)
0.0b	(hypot d c)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

402×	`times-frac`
196×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
46×	`associate-/l*`
20×	`add-exp-log`
18×	`div-inv`
15×	`add-cbrt-cube`
12×	`div-exp`
7×	`cbrt-undiv`
6×	`associate-/r*`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`hypot-udef` `clear-num` `frac-2neg` `1-exp`
1×	`associate-/l/`

Calls

4 calls:

Slowest

19.0ms	(/ (/ (/ (fma a c (* b d)) (hypot d c)) 1) (hypot d c))
4.0ms	(/ (fma a c (* b d)) (hypot d c))
0.0ms	(hypot d c)
0.0ms	(hypot d c)

series466.0ms

Calls

4 calls:

Slowest

180.0ms	(/ (fma a c (* b d)) (hypot d c))
159.0ms	(/ (/ (/ (fma a c (* b d)) (hypot d c)) 1) (hypot d c))
69.0ms	(hypot d c)
58.0ms	(hypot d c)

simplify19.1s

Calls

349 calls:

Slowest

564.0ms	(/ (/ (* (* (/ (fma a c (* b d)) (hypot d c)) (/ (fma a c (* b d)) (hypot d c))) (/ (fma a c (* b d)) (hypot d c))) (* (* 1 1) 1)) (* (* (hypot d c) (hypot d c)) (hypot d c)))
350.0ms	(/ (/ (/ (cbrt (fma a c (* b d))) (cbrt (hypot d c))) 1) (hypot d c))
348.0ms	(/ (* (* (/ (/ (fma a c (* b d)) (hypot d c)) 1) (/ (/ (fma a c (* b d)) (hypot d c)) 1)) (/ (/ (fma a c (* b d)) (hypot d c)) 1)) (* (* (hypot d c) (hypot d c)) (hypot d c)))
345.0ms	(/ (/ (/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (sqrt (hypot d c))) 1) (* (cbrt (hypot d c)) (cbrt (hypot d c))))
310.0ms	(/ (* (* (fma a c (* b d)) (fma a c (* b d))) (fma a c (* b d))) (* (* (hypot d c) (hypot d c)) (hypot d c)))

prune2.6s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.2b

regimes295.0ms

Accuracy

36.5% (6.7b remaining)

Error of 12.5b against oracle of 5.8b and baseline of 16.4b

bsearch95.0ms

end0.0ms

sample1.2s

Algorithm

intervals

Results

1.0s

8446×

body

valid