Details

sample35.0ms

Algorithm

intervals

Results

24.0ms

278×

body

valid

simplify101.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

101.0ms

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

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.1b

localize17.0ms

Local error

Found 2 expressions with local error:

25.1b	(/ (- (* b c) (* a d)) (fma d d (* c c)))
0.2b	(- (* b c) (* a d))

rewrite39.0ms

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

22.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))
16.0ms	(- (* b c) (* a d))

series197.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

145.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))
52.0ms	(- (* b c) (* a d))

simplify2.4s

Counts

37 → 56

Calls

37 calls:

Slowest

595.0ms	(/ (* (* (- (* 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))))
319.0ms	(- (pow (* b c) 3) (pow (* a d) 3))
205.0ms	(- (* (* b c) (* b c)) (* (* a d) (* a d)))
166.0ms	(/ (exp (* b c)) (exp (* a d)))
96.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))

prune495.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 24.6b

localize30.0ms

Local error

Found 4 expressions with local error:

30.4b	(sqrt (fma d d (* c c)))
30.4b	(sqrt (fma d d (* c c)))
15.4b	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
0.2b	(- (* b c) (* a d))

rewrite29.0ms

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

17.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
9.0ms	(- (* b c) (* a d))
2.0ms	(sqrt (fma d d (* c c)))
1.0ms	(sqrt (fma d d (* c c)))

series307.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

136.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
62.0ms	(sqrt (fma d d (* c c)))
61.0ms	(sqrt (fma d d (* c c)))
48.0ms	(- (* b c) (* a d))

simplify3.2s

Counts

74 → 108

Calls

74 calls:

Slowest

364.0ms	(/ (* (* (- (* 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)))))
311.0ms	(- (pow (* b c) 3) (pow (* a d) 3))
234.0ms	(- (* (* b c) (* b c)) (* (* a d) (* a d)))
157.0ms	(/ (exp (* b c)) (exp (* a d)))
120.0ms	(/ (- (* b c) (* a d)) (cbrt (sqrt (fma d d (* c c)))))

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 23.5b

localize25.0ms

Local error

Found 4 expressions with local error:

30.4b	(sqrt (fma d d (* c c)))
30.4b	(sqrt (fma d d (* c c)))
15.5b	(/ (sqrt (fma d d (* c c))) (- (* b c) (* a d)))
0.2b	(/ 1 (/ (sqrt (fma d d (* c c))) (- (* b c) (* a d))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
100×	`add-sqr-sqrt`
98×	`*-un-lft-identity` `add-cube-cbrt`
54×	`sqrt-prod`
27×	`associate-/r*`
17×	`add-exp-log`
11×	`add-cbrt-cube` `associate-/r/`
9×	`associate-/l*`
8×	`div-exp`
7×	`pow1`
6×	`div-inv`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `cbrt-undiv` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `rec-exp` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `fma-udef` `hypot-def`
1×	`pow-flip` `inv-pow`

Counts

4 → 201

Calls

4 calls:

Slowest

28.0ms	(/ 1 (/ (sqrt (fma d d (* c c))) (- (* b c) (* a d))))
12.0ms	(/ (sqrt (fma d d (* c c))) (- (* b c) (* a d)))
1.0ms	(sqrt (fma d d (* c c)))
1.0ms	(sqrt (fma d d (* c c)))

series384.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

186.0ms	(/ 1 (/ (sqrt (fma d d (* c c))) (- (* b c) (* a d))))
92.0ms	(/ (sqrt (fma d d (* c c))) (- (* b c) (* a d)))
58.0ms	(sqrt (fma d d (* c c)))
47.0ms	(sqrt (fma d d (* c c)))

simplify16.9s

Counts

248 → 213

Calls

248 calls:

Slowest

489.0ms	(+ (* (* b c) (* b c)) (+ (* (* a d) (* a d)) (* (* b c) (* a d))))
318.0ms	(/ (cbrt 1) (/ (sqrt (cbrt (fma d d (* c c)))) (- (* b c) (* a d))))
307.0ms	(/ (* (* (sqrt (fma d d (* c c))) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c)))) (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))))
290.0ms	(/ (sqrt 1) (/ (sqrt (fma d d (* c c))) (- (* (* b c) (* b c)) (* (* a d) (* a d)))))
271.0ms	(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (sqrt (fma d d (* c c)))) (cbrt (sqrt (fma d d (* c c))))) (* (cbrt (- (* b c) (* a d))) (cbrt (- (* b c) (* a d))))))

prune2.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 22.8b

localize26.0ms

Local error

Found 3 expressions with local error:

24.8b	(/ (fma d d (* c c)) (- (* b c) (* a d)))
0.4b	(/ 1 (/ (fma d d (* c c)) (- (* b c) (* a d))))
0.2b	(- (* b c) (* a d))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
55×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
18×	`associate-/r*`
16×	`add-exp-log`
11×	`associate-/r/`
10×	`add-cbrt-cube`
8×	`div-exp`
6×	`flip3--` `div-inv` `flip--` `associate-/l*`
5×	`add-log-exp`
4×	`pow1` `cbrt-undiv`
3×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff` `pow-flip` `inv-pow`

Counts

3 → 136

Calls

3 calls:

Slowest

15.0ms	(/ 1 (/ (fma d d (* c c)) (- (* b c) (* a d))))
12.0ms	(/ (fma d d (* c c)) (- (* b c) (* a d)))
8.0ms	(- (* b c) (* a d))

series270.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

145.0ms	(/ 1 (/ (fma d d (* c c)) (- (* b c) (* a d))))
77.0ms	(/ (fma d d (* c c)) (- (* b c) (* a d)))
49.0ms	(- (* b c) (* a d))

simplify10.7s

Counts

154 → 145

Calls

154 calls:

Slowest

348.0ms	(/ (* (* (fma d d (* c c)) (fma d d (* c c))) (fma d d (* c c))) (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))))
294.0ms	(/ (sqrt 1) (/ (fma d d (* c c)) (- (* (* b c) (* b c)) (* (* a d) (* a d)))))
272.0ms	(/ (* (* 1 1) 1) (* (* (/ (fma d d (* c c)) (- (* b c) (* a d))) (/ (fma d d (* c c)) (- (* b c) (* a d)))) (/ (fma d d (* c c)) (- (* b c) (* a d)))))
264.0ms	(/ (* (cbrt 1) (cbrt 1)) (/ (fma d d (* c c)) (- (* (* b c) (* b c)) (* (* a d) (* a d)))))
246.0ms	(/ (cbrt 1) (+ (* (* b c) (* b c)) (+ (* (* a d) (* a d)) (* (* b c) (* a d)))))

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 13.7b

regimes250.0ms

Accuracy

0% (3.2b remaining)

Error of 16.2b against oracle of 13.1b and baseline of 16.2b

bsearch2.0ms

end0.0ms

sample1.0s

Algorithm

intervals

Results

822.0ms

8493×

body

valid