Details

sample39.0ms

Algorithm

intervals

Results

21.0ms

272×

body

valid

simplify83.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

83.0ms

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.3b

localize19.0ms

Local error

Found 2 expressions with local error:

25.3b	(/ (- (* b c) (* a d)) (fma d d (* c c)))
0.7b	(- (* b c) (* a d))

rewrite25.0ms

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`

Counts

2 → 50

Calls

2 calls:

Slowest

16.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))
8.0ms	(- (* b c) (* a d))

series191.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

129.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))
62.0ms	(- (* b c) (* a d))

simplify2.7s

Counts

37 → 56

Calls

37 calls:

Slowest

588.0ms	(/ (* (* (- (* 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))))
418.0ms	(- (pow (* b c) 3) (pow (* a d) 3))
292.0ms	(- (* (* b c) (* b c)) (* (* a d) (* a d)))
165.0ms	(/ (exp (* b c)) (exp (* a d)))
139.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))

prune670.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 24.9b

localize51.0ms

Local error

Found 4 expressions with local error:

29.2b	(sqrt (fma d d (* c c)))
29.2b	(sqrt (fma d d (* c c)))
15.2b	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
0.7b	(- (* b c) (* a d))

rewrite54.0ms

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`

Counts

4 → 96

Calls

4 calls:

Slowest

33.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
15.0ms	(- (* b c) (* a d))
2.0ms	(sqrt (fma d d (* c c)))
2.0ms	(sqrt (fma d d (* c c)))

series359.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

161.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
80.0ms	(sqrt (fma d d (* c c)))
62.0ms	(sqrt (fma d d (* c c)))
56.0ms	(- (* b c) (* a d))

simplify3.7s

Counts

74 → 108

Calls

74 calls:

Slowest

441.0ms	(/ (* (* (- (* 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)))))
430.0ms	(- (pow (* b c) 3) (pow (* a d) 3))
272.0ms	(- (* (* b c) (* b c)) (* (* a d) (* a d)))
212.0ms	(/ (exp (* b c)) (exp (* a d)))
137.0ms	(/ (- (* b c) (* a d)) (sqrt (sqrt (fma d d (* c c)))))

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 22.2b

localize39.0ms

Local error

Found 4 expressions with local error:

29.2b	(sqrt (fma d d (* c c)))
15.2b	(/ (- (* b c) (* a d)) (hypot d c))
0.7b	(- (* b c) (* a d))
0.0b	(/ (/ (- (* b c) (* a d)) (hypot d c)) (sqrt (fma d d (* c c))))

rewrite59.0ms

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`

Counts

4 → 183

Calls

4 calls:

Slowest

30.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (sqrt (fma d d (* c c))))
16.0ms	(/ (- (* b c) (* a d)) (hypot d c))
9.0ms	(- (* b c) (* a d))
1.0ms	(sqrt (fma d d (* c c)))

series496.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

215.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (sqrt (fma d d (* c c))))
176.0ms	(/ (- (* b c) (* a d)) (hypot d c))
57.0ms	(- (* b c) (* a d))
47.0ms	(sqrt (fma d d (* c c)))

simplify19.7s

Counts

228 → 195

Calls

228 calls:

Slowest

422.0ms	(/ (/ (* (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))))))
395.0ms	(/ (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (hypot d c) (hypot d c)) (hypot d c)))
384.0ms	(- (pow (* b c) 3) (pow (* a d) 3))
305.0ms	(/ (/ (- (* b c) (* a d)) (cbrt (hypot d c))) (cbrt (sqrt (fma d d (* c c)))))
284.0ms	(/ (/ (- (* b c) (* a d)) (sqrt (hypot d c))) (cbrt (sqrt (fma d d (* c c)))))

prune2.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.8b

localize26.0ms

Local error

Found 4 expressions with local error:

15.2b	(/ (- (* b c) (* a d)) (hypot d c))
0.7b	(- (* b c) (* a d))
0.0b	(/ (/ (- (* b c) (* a d)) (hypot d c)) (hypot d c))
0.0b	(hypot d c)

rewrite59.0ms

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` `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×	`hypot-udef` `sub-neg` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 135

Calls

4 calls:

Slowest

33.0ms	(/ (- (* b c) (* a d)) (hypot d c))
13.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (hypot d c))
11.0ms	(- (* b c) (* a d))
0.0ms	(hypot d c)

series441.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

179.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (hypot d c))
142.0ms	(/ (- (* b c) (* a d)) (hypot d c))
61.0ms	(hypot d c)
58.0ms	(- (* b c) (* a d))

simplify9.1s

Counts

142 → 147

Calls

142 calls:

Slowest

399.0ms	(/ (cbrt (- (* b c) (* a d))) (hypot d c))
345.0ms	(/ (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (hypot d c) (hypot d c)) (hypot d c)))
321.0ms	(- (pow (* b c) 3) (pow (* a d) 3))
224.0ms	(/ (/ (- (* b c) (* a d)) (sqrt (hypot d c))) (cbrt (hypot d c)))
218.0ms	(- (* (* b c) (* b c)) (* (* a d) (* a d)))

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.6b

regimes259.0ms

Accuracy

32% (7.2b remaining)

Error of 13.2b against oracle of 6.0b and baseline of 16.6b

bsearch140.0ms

end0.0ms

sample1.3s

Algorithm

intervals

Results

999.0ms

8458×

body

valid