Details

sample31.0ms

Algorithm

intervals

Results

22.0ms

275×

body

valid

simplify98.0ms

Calls

1 calls:

Slowest

97.0ms

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.4b

localize32.0ms

Local error

Found 2 expressions with local error:

23.4b	(/ (- (* b c) (* a d)) (fma d d (* c c)))
0.5b	(- (* b c) (* a d))

rewrite12.0ms

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)))
3.0ms	(- (* b c) (* a d))

series177.0ms

Calls

2 calls:

Slowest

120.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))
57.0ms	(- (* b c) (* a d))

simplify2.1s

Calls

37 calls:

Slowest

477.0ms	(/ (* (* (- (* 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))))
341.0ms	(- (pow (* b c) 3) (pow (* a d) 3))
207.0ms	(- (* (* b c) (* b c)) (* (* a d) (* a d)))
92.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))
89.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))

prune636.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 23.1b

localize13.0ms

Local error

Found 4 expressions with local error:

27.8b	(sqrt (fma d d (* c c)))
27.8b	(sqrt (fma d d (* c c)))
13.8b	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
0.5b	(- (* b c) (* a 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×	`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

8.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
3.0ms	(- (* b c) (* a d))
1.0ms	(sqrt (fma d d (* c c)))
1.0ms	(sqrt (fma d d (* c c)))

series301.0ms

Calls

4 calls:

Slowest

145.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
57.0ms	(- (* b c) (* a d))
50.0ms	(sqrt (fma d d (* c c)))
49.0ms	(sqrt (fma d d (* c c)))

simplify2.3s

Calls

72 calls:

Slowest

334.0ms	(/ (* (* (- (* 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))
153.0ms	(- (* (* b c) (* b c)) (* (* a d) (* a d)))
73.0ms	(/ (- (* b c) (* a d)) (sqrt (cbrt (fma d d (* c c)))))
73.0ms	(/ (- (* b c) (* a d)) (cbrt (sqrt (fma d d (* c c)))))

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 22.1b

localize13.0ms

Local error

Found 4 expressions with local error:

27.8b	(sqrt (fma d d (* c c)))
27.8b	(sqrt (fma d d (* c c)))
13.8b	(/ (fma b c (- (* a d))) (sqrt (fma d d (* c c))))
0.3b	(fma b c (- (* a 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×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`fma-udef` `associate-/l*`
2×	`rem-sqrt-square` `pow1/2` `hypot-def`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Calls

4 calls:

Slowest

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

series268.0ms

Calls

4 calls:

Slowest

121.0ms	(/ (fma b c (- (* a d))) (sqrt (fma d d (* c c))))
51.0ms	(fma b c (- (* a d)))
50.0ms	(sqrt (fma d d (* c c)))
46.0ms	(sqrt (fma d d (* c c)))

simplify1.6s

Calls

66 calls:

Slowest

276.0ms	(/ (* (* (fma b c (- (* a d))) (fma b c (- (* a d)))) (fma b c (- (* a d)))) (* (* (sqrt (fma d d (* c c))) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c)))))
53.0ms	(/ (fma b c (- (* a d))) (sqrt (cbrt (fma d d (* c c)))))
53.0ms	(/ (* (cbrt (fma b c (- (* a d)))) (cbrt (fma b c (- (* a d))))) (* (cbrt (sqrt (fma d d (* c c)))) (cbrt (sqrt (fma d d (* c c))))))
52.0ms	(/ (fma b c (- (* a d))) (cbrt (sqrt (fma d d (* c c)))))
52.0ms	(/ (fma b c (- (* a d))) (sqrt (sqrt (fma d d (* c c)))))

prune1.0s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 22.1b

localize9.0ms

Local error

Found 3 expressions with local error:

16.8b	(/ (* b c) (fma d d (* c c)))
14.4b	(/ (* a d) (fma d d (* c c)))
0.0b	(- (/ (* b c) (fma d d (* c c))) (/ (* a d) (fma d d (* c c))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

51×	`times-frac`
49×	`prod-diff`
39×	`add-sqr-sqrt` `*-un-lft-identity`
37×	`add-cube-cbrt`
19×	`div-inv`
7×	`add-cbrt-cube` `fma-neg` `add-exp-log`
6×	`associate-/r*`
5×	`add-log-exp`
3×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `associate-/l*`
1×	`sub-neg` `flip3--` `distribute-rgt-out--` `diff-log` `frac-sub` `flip--` `distribute-lft-out--` `sub-div` `difference-of-squares`

Calls

3 calls:

Slowest

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

series234.0ms

Calls

3 calls:

Slowest

133.0ms	(- (/ (* b c) (fma d d (* c c))) (/ (* a d) (fma d d (* c c))))
52.0ms	(/ (* b c) (fma d d (* c c)))
49.0ms	(/ (* a d) (fma d d (* c c)))

simplify14.0s

Calls

145 calls:

Slowest

394.0ms	(fma (- (/ (* a d) (fma d d (* c c)))) 1 (* (/ (* a d) (fma d d (* c c))) 1))
320.0ms	(fma (* b c) (/ 1 (fma d d (* c c))) (- (* (/ d (cbrt (fma d d (* c c)))) (/ a (* (cbrt (fma d d (* c c))) (cbrt (fma d d (* c c))))))))
266.0ms	(fma (/ b (* (cbrt (fma d d (* c c))) (cbrt (fma d d (* c c))))) (/ c (cbrt (fma d d (* c c)))) (- (* (/ 1 (fma d d (* c c))) (* a d))))
245.0ms	(fma 1 (/ (* b c) (fma d d (* c c))) (- (* (/ 1 (fma d d (* c c))) (* a d))))
233.0ms	(fma (sqrt (/ (* b c) (fma d d (* c c)))) (sqrt (/ (* b c) (fma d d (* c c)))) (- (* (/ 1 (fma d d (* c c))) (* a d))))

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 21.3b

regimes379.0ms

Accuracy

-79.5% (2.1b remaining)

Error of 24.1b against oracle of 22.0b and baseline of 23.1b

bsearch67.0ms

end0.0ms

sample1.2s

Algorithm

intervals

Results

942.0ms

8454×

body

valid