Details

sample60.0ms

Algorithm

intervals

Results

44.0ms

273×

body

valid

simplify128.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

128.0ms

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

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.8b

localize20.0ms

Local error

Found 3 expressions with local error:

23.8b	(/ (- (* b c) (* a d)) (fma d d (* c c)))
0.4b	(- (* b c) (* a d))
0.0b	(fma d d (* c c))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`expm1-log1p-u` `pow1` `associate-/r` `insert-posit16` `log1p-expm1-u` `associate-/l`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `fma-udef` `div-inv`

Counts

3 → 61

Calls

3 calls:

Slowest

17.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))
15.0ms	(- (* b c) (* a d))
0.0ms	(fma d d (* c c))

series228.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

143.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))
44.0ms	(- (* b c) (* a d))
40.0ms	(fma d d (* c c))

simplify2.6s

Counts

40 → 70

Calls

40 calls:

Slowest

506.0ms	(/ (* (* (- (* 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))))
367.0ms	(- (pow (* b c) 3) (pow (* a d) 3))
249.0ms	(- (* (* b c) (* b c)) (* (* a d) (* a d)))
159.0ms	(/ (exp (* b c)) (exp (* a d)))
146.0ms	(/ (- (* b c) (* a d)) (cbrt (fma d d (* c c))))

prune816.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 23.3b

localize28.0ms

Local error

Found 4 expressions with local error:

27.9b	(sqrt (fma d d (* c c)))
27.9b	(sqrt (fma d d (* c c)))
15.0b	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
0.4b	(- (* b c) (* a d))

rewrite45.0ms

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

26.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
15.0ms	(- (* b c) (* a d))
1.0ms	(sqrt (fma d d (* c c)))
1.0ms	(sqrt (fma d d (* c c)))

series365.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

169.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
74.0ms	(sqrt (fma d d (* c c)))
66.0ms	(sqrt (fma d d (* c c)))
56.0ms	(- (* b c) (* a d))

simplify3.6s

Counts

74 → 108

Calls

74 calls:

Slowest

396.0ms	(/ (* (* (- (* 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)))))
343.0ms	(- (pow (* b c) 3) (pow (* a d) 3))
248.0ms	(- (* (* b c) (* b c)) (* (* a d) (* a d)))
151.0ms	(/ (- (* b c) (* a d)) (sqrt (cbrt (fma d d (* c c)))))
133.0ms	(/ (exp (* b c)) (exp (* a d)))

prune1.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 21.7b

localize45.0ms

Local error

Found 4 expressions with local error:

27.9b	(sqrt (fma d d (* c c)))
15.0b	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
0.4b	(- (* b c) (* a d))
0.1b	(/ (/ (- (* b c) (* a d)) (sqrt (fma d d (* c c)))) (hypot d c))

rewrite58.0ms

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`
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 → 189

Calls

4 calls:

Slowest

26.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
19.0ms	(/ (/ (- (* b c) (* a d)) (sqrt (fma d d (* c c)))) (hypot d c))
8.0ms	(- (* b c) (* a d))
2.0ms	(sqrt (fma d d (* c c)))

series466.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

177.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
169.0ms	(/ (/ (- (* b c) (* a d)) (sqrt (fma d d (* c c)))) (hypot d c))
62.0ms	(sqrt (fma d d (* c c)))
57.0ms	(- (* b c) (* a d))

simplify18.9s

Counts

231 → 201

Calls

231 calls:

Slowest

430.0ms	(/ (* (* (- (* 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)))))
374.0ms	(- (pow (* b c) 3) (pow (* a d) 3))
323.0ms	(/ (/ (- (* b c) (* a d)) (sqrt (fma d d (* c c)))) (cbrt (hypot d c)))
317.0ms	(- (* (* b c) (* b c)) (* (* a d) (* a d)))
305.0ms	(/ (/ (- (* b c) (* a d)) (sqrt (cbrt (fma d d (* c c))))) (cbrt (hypot d c)))

prune2.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.7b

localize18.0ms

Local error

Found 4 expressions with local error:

15.0b	(/ (- (* b c) (* a d)) (hypot d c))
0.4b	(- (* b c) (* a d))
0.1b	(/ (/ (- (* b c) (* a d)) (hypot d c)) (hypot d c))
0.0b	(hypot d c)

rewrite411.0ms

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

368.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (hypot d c))
25.0ms	(/ (- (* b c) (* a d)) (hypot d c))
15.0ms	(- (* b c) (* a d))
0.0ms	(hypot d c)

series450.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

176.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (hypot d c))
135.0ms	(/ (- (* b c) (* a d)) (hypot d c))
72.0ms	(- (* b c) (* a d))
67.0ms	(hypot d c)

simplify10.2s

Counts

142 → 147

Calls

142 calls:

Slowest

439.0ms	(/ (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (hypot d c) (hypot d c)) (hypot d c)))
349.0ms	(- (pow (* b c) 3) (pow (* a d) 3))
250.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (cbrt (hypot d c)))
250.0ms	(/ (/ (- (* b c) (* a d)) (cbrt (hypot d c))) (sqrt (hypot d c)))
243.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (sqrt (hypot d c)))

prune1.6s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.7b

regimes359.0ms

Accuracy

20.4% (8.2b remaining)

Error of 14.0b against oracle of 5.8b and baseline of 16.2b

bsearch39.0ms

end0.0ms

sample1.3s

Algorithm

intervals

Results

1.0s

8474×

body

valid