Details

sample40.0ms

Algorithm

intervals

Results

31.0ms

271×

body

valid

simplify106.0ms

Calls

1 calls:

Slowest

106.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.6b

localize24.0ms

Local error

Found 2 expressions with local error:

28.6b	(/ (- (* b c) (* a d)) (fma d d (* c c)))
1.0b	(- (* b c) (* a d))

rewrite14.0ms

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` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`expm1-log1p-u` `pow1` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `div-inv`

Calls

2 calls:

Slowest

8.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))
4.0ms	(- (* b c) (* a d))

series153.0ms

Calls

2 calls:

Slowest

107.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))
46.0ms	(- (* b c) (* a d))

simplify2.1s

Calls

37 calls:

Slowest

430.0ms	(/ (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (fma d d (* c c)) (fma d d (* c c))) (fma d d (* c c))))
318.0ms	(- (pow (* b c) 3) (pow (* a d) 3))
213.0ms	(- (* (* b c) (* b c)) (* (* a d) (* a d)))
89.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
84.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))

prune591.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 28.1b

localize14.0ms

Local error

Found 4 expressions with local error:

32.2b	(sqrt (fma d d (* c c)))
32.2b	(sqrt (fma d d (* c c)))
18.4b	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
1.0b	(- (* b c) (* a d))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`associate-/r*` `add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
3×	`associate-/l*`
2×	`rem-sqrt-square` `flip3--` `pow1/2` `fma-udef` `hypot-def` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `div-inv`

Calls

4 calls:

Slowest

13.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
4.0ms	(- (* b c) (* a d))
2.0ms	(sqrt (fma d d (* c c)))
2.0ms	(sqrt (fma d d (* c c)))

series370.0ms

Calls

4 calls:

Slowest

175.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
71.0ms	(sqrt (fma d d (* c c)))
63.0ms	(sqrt (fma d d (* c c)))
62.0ms	(- (* b c) (* a d))

simplify2.9s

Calls

72 calls:

Slowest

436.0ms	(/ (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (sqrt (fma d d (* c c))) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c)))))
242.0ms	(- (pow (* b c) 3) (pow (* a d) 3))
157.0ms	(- (* (* b c) (* b c)) (* (* a d) (* a d)))
115.0ms	(/ (- (* b c) (* a d)) (sqrt (sqrt (fma d d (* c c)))))
102.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))

prune933.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 26.4b

localize6.0ms

Local error

Found 4 expressions with local error:

32.2b	(sqrt (fma d d (* c c)))
18.4b	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
1.0b	(- (* b c) (* a d))
0.1b	(/ (/ (- (* b c) (* a d)) (sqrt (fma d d (* c c)))) (hypot d c))

rewrite23.0ms

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` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`div-sub` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3--` `flip--`
1×	`rem-sqrt-square` `sub-neg` `pow1/2` `fma-neg` `diff-log` `prod-diff` `fma-udef` `hypot-def`

Calls

4 calls:

Slowest

10.0ms	(/ (/ (- (* b c) (* a d)) (sqrt (fma d d (* c c)))) (hypot d c))
7.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
2.0ms	(- (* b c) (* a d))
1.0ms	(sqrt (fma d d (* c c)))

series382.0ms

Calls

4 calls:

Slowest

167.0ms	(/ (/ (- (* b c) (* a d)) (sqrt (fma d d (* c c)))) (hypot d c))
118.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
49.0ms	(sqrt (fma d d (* c c)))
47.0ms	(- (* b c) (* a d))

simplify11.7s

Calls

230 calls:

Slowest

285.0ms	(/ (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (sqrt (fma d d (* c c))) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c)))))
237.0ms	(- (pow (* b c) 3) (pow (* a d) 3))
179.0ms	(/ (/ (- (* b c) (* a d)) (sqrt (sqrt (fma d d (* c c))))) (hypot d c))
176.0ms	(/ (/ (- (* b c) (* a d)) (sqrt (sqrt (fma d d (* c c))))) (hypot d c))
174.0ms	(/ (/ (- (* b c) (* a d)) (cbrt (sqrt (fma d d (* c c))))) (hypot d c))

prune1.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.4b

localize5.0ms

Local error

Found 3 expressions with local error:

18.4b	(/ (- (* b c) (* a d)) (hypot d c))
1.0b	(- (* b c) (* a d))
0.1b	(/ (/ (- (* b c) (* a d)) (hypot d c)) (hypot d c))

rewrite19.0ms

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`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`expm1-log1p-u` `pow1` `div-sub` `insert-posit16` `log1p-expm1-u` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3--` `flip--`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff`

Calls

3 calls:

Slowest

8.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (hypot d c))
7.0ms	(/ (- (* b c) (* a d)) (hypot d c))
2.0ms	(- (* b c) (* a d))

series277.0ms

Calls

3 calls:

Slowest

120.0ms	(/ (- (* b c) (* a d)) (hypot d c))
115.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (hypot d c))
43.0ms	(- (* b c) (* a d))

simplify6.5s

Calls

139 calls:

Slowest

361.0ms	(/ (- (* b c) (* a d)) (* (cbrt (hypot d c)) (cbrt (hypot d c))))
231.0ms	(/ (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (hypot d c) (hypot d c)) (hypot d c)))
229.0ms	(- (pow (* b c) 3) (pow (* a d) 3))
153.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (sqrt (hypot d c)))
151.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (cbrt (hypot d c)))

prune876.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.4b

regimes217.0ms

Accuracy

18.6% (8.6b remaining)

Error of 14.2b against oracle of 5.6b and baseline of 16.2b

bsearch41.0ms

end0.0ms

sample915.0ms

Algorithm

intervals

Results

733.0ms

8474×

body

valid