Details

sample47.0ms

Algorithm

intervals

Results

36.0ms

271×

body

valid

simplify117.0ms

Calls

1 calls:

Slowest

117.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.6b

localize29.0ms

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))

rewrite41.0ms

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

33.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))
8.0ms	(- (* b c) (* a d))

series202.0ms

Calls

2 calls:

Slowest

129.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))
73.0ms	(- (* b c) (* a d))

simplify2.4s

Calls

37 calls:

Slowest

512.0ms	(/ (* (* (- (* 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))))
384.0ms	(- (pow (* b c) 3) (pow (* a d) 3))
231.0ms	(- (* (* b c) (* b c)) (* (* a d) (* a d)))
177.0ms	(/ (exp (* b c)) (exp (* a d)))
120.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))

prune591.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 28.1b

localize47.0ms

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))

rewrite52.0ms

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` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `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

33.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
13.0ms	(- (* b c) (* a d))
3.0ms	(sqrt (fma d d (* c c)))
2.0ms	(sqrt (fma d d (* c c)))

series362.0ms

Calls

4 calls:

Slowest

151.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
79.0ms	(sqrt (fma d d (* c c)))
67.0ms	(- (* b c) (* a d))
65.0ms	(sqrt (fma d d (* c c)))

simplify3.6s

Calls

74 calls:

Slowest

410.0ms	(/ (* (* (- (* 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)))))
353.0ms	(- (pow (* b c) 3) (pow (* a d) 3))
221.0ms	(- (* (* b c) (* b c)) (* (* a d) (* a d)))
193.0ms	(/ (exp (* b c)) (exp (* a d)))
121.0ms	(/ (- (* b c) (* a d)) (sqrt (sqrt (fma d d (* c c)))))

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 26.4b

localize51.0ms

Local error

Found 4 expressions with local error:

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

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

150×	`times-frac`
91×	`add-sqr-sqrt`
90×	`*-un-lft-identity` `add-cube-cbrt`
45×	`sqrt-prod`
16×	`associate-/l*`
11×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/r*` `div-inv`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `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` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `fma-udef` `hypot-def`

Calls

4 calls:

Slowest

35.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (sqrt (fma d d (* c c))))
32.0ms	(/ (- (* b c) (* a d)) (hypot d c))
15.0ms	(- (* b c) (* a d))
3.0ms	(sqrt (fma d d (* c c)))

series486.0ms

Calls

4 calls:

Slowest

213.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (sqrt (fma d d (* c c))))
140.0ms	(/ (- (* b c) (* a d)) (hypot d c))
79.0ms	(sqrt (fma d d (* c c)))
54.0ms	(- (* b c) (* a d))

simplify19.9s

Calls

228 calls:

Slowest

520.0ms	(/ (/ (* (cbrt (- (* b c) (* a d))) (cbrt (- (* b c) (* a d)))) (* (cbrt (hypot d c)) (cbrt (hypot d c)))) (sqrt (sqrt (fma d d (* c c)))))
389.0ms	(/ (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (hypot d c) (hypot d c)) (hypot d c)))
375.0ms	(- (pow (* b c) 3) (pow (* a d) 3))
361.0ms	(/ (/ (* (cbrt (- (* b c) (* a d))) (cbrt (- (* b c) (* a d)))) (* (cbrt (hypot d c)) (cbrt (hypot d c)))) (* (cbrt (sqrt (fma d d (* c c)))) (cbrt (sqrt (fma d d (* c c))))))
305.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (cbrt (sqrt (fma d d (* c c)))))

prune2.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 17.1b

localize16.0ms

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))

rewrite51.0ms

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

22.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (hypot d c))
19.0ms	(/ (- (* b c) (* a d)) (hypot d c))
8.0ms	(- (* b c) (* a d))

series339.0ms

Calls

3 calls:

Slowest

154.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (hypot d c))
135.0ms	(/ (- (* b c) (* a d)) (hypot d c))
50.0ms	(- (* b c) (* a d))

simplify7.8s

Calls

139 calls:

Slowest

311.0ms	(- (pow (* b c) 3) (pow (* a d) 3))
302.0ms	(/ (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (hypot d c) (hypot d c)) (hypot d c)))
185.0ms	(- (* (* b c) (* b c)) (* (* a d) (* a d)))
176.0ms	(/ (/ (* (cbrt (- (* b c) (* a d))) (cbrt (- (* b c) (* a d)))) (* (cbrt (hypot d c)) (cbrt (hypot d c)))) (* (cbrt (hypot d c)) (cbrt (hypot d c))))
164.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (sqrt (hypot d c)))

prune956.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.4b

regimes232.0ms

Accuracy

18.6% (8.6b remaining)

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

bsearch45.0ms

end0.0ms

sample1.2s

Algorithm

intervals

Results

1.1s

8474×

body

valid