Details

sample88.0ms

Algorithm

intervals

Results

44.0ms	276×	body	80	valid
21.0ms	92×	body	80	nan

simplify260.0ms

Calls

1 calls:

Slowest

260.0ms

(if (>= b 0) (/ (- (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a)) (/ (* 2 c) (+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.5b

localize160.0ms

Local error

Found 4 expressions with local error:

21.3b	(sqrt (fma (* -4 a) c (* b b)))
21.3b	(sqrt (fma (* -4 a) c (* b b)))
1.1b	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
1.1b	(- (sqrt (fma (* -4 a) c (* b b))) b)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

78×	`prod-diff`
71×	`add-sqr-sqrt`
67×	`*-un-lft-identity`
61×	`add-cube-cbrt`
50×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
16×	`fma-neg`
10×	`add-log-exp`
7×	`neg-mul-1`
6×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
3×	`diff-log` `distribute-lft-out--`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `flip--`
1×	`associate--l-` `neg-sub0` `neg-log`

Calls

4 calls:

Slowest

20.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
11.0ms	(- (sqrt (fma (* -4 a) c (* b b))) b)
2.0ms	(sqrt (fma (* -4 a) c (* b b)))
2.0ms	(sqrt (fma (* -4 a) c (* b b)))

series454.0ms

Calls

4 calls:

Slowest

119.0ms	(sqrt (fma (* -4 a) c (* b b)))
118.0ms	(- (sqrt (fma (* -4 a) c (* b b))) b)
116.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
100.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify16.1s

Calls

204 calls:

Slowest

296.0ms	(fma (sqrt (- b)) (sqrt (- b)) (- (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (cbrt (sqrt (fma (* -4 a) c (* b b))))))))
252.0ms	(fma (* (cbrt b) (cbrt b)) (- (cbrt b)) (- (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (cbrt (sqrt (fma (* -4 a) c (* b b))))))))
251.0ms	(fma (- (sqrt b)) (sqrt b) (- (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (cbrt (sqrt (fma (* -4 a) c (* b b))))))))
245.0ms	(fma (sqrt b) (- (sqrt b)) (- (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (cbrt (sqrt (fma (* -4 a) c (* b b))))))))
244.0ms	(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (- (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (cbrt (sqrt (fma (* -4 a) c (* b b))))))))

prune2.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 10.8b

localize147.0ms

Local error

Found 4 expressions with local error:

21.3b	(sqrt (fma (* -4 a) c (* b b)))
21.3b	(sqrt (fma (* -4 a) c (* b b)))
21.3b	(sqrt (fma (* -4 a) c (* b b)))
1.1b	(- (- b) (sqrt (fma (* -4 a) c (* b b))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

60×	`prod-diff`
55×	`add-sqr-sqrt`
52×	`*-un-lft-identity`
48×	`add-cube-cbrt`
40×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
10×	`fma-neg`
8×	`add-log-exp`
7×	`pow1` `neg-mul-1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`diff-log` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `sub-neg` `flip3--` `neg-log` `flip--`

Calls

4 calls:

Slowest

27.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
3.0ms	(sqrt (fma (* -4 a) c (* b b)))
2.0ms	(sqrt (fma (* -4 a) c (* b b)))
2.0ms	(sqrt (fma (* -4 a) c (* b b)))

series431.0ms

Calls

4 calls:

Slowest

118.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
116.0ms	(sqrt (fma (* -4 a) c (* b b)))
103.0ms	(sqrt (fma (* -4 a) c (* b b)))
94.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify13.2s

Calls

162 calls:

Slowest

255.0ms	(fma (- 1) b (- (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (cbrt (sqrt (fma (* -4 a) c (* b b))))))))
249.0ms	(fma (sqrt (- b)) (sqrt (- b)) (- (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (cbrt (sqrt (fma (* -4 a) c (* b b))))))))
240.0ms	(fma (- (* (cbrt b) (cbrt b))) (cbrt b) (- (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (cbrt (sqrt (fma (* -4 a) c (* b b))))))))
239.0ms	(fma 1 (- b) (- (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (cbrt (sqrt (fma (* -4 a) c (* b b))))))))
239.0ms	(fma (* (cbrt b) (cbrt b)) (- (cbrt b)) (- (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (cbrt (sqrt (fma (* -4 a) c (* b b))))))))

prune2.4s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 10.8b

localize185.0ms

Local error

Found 4 expressions with local error:

22.0b	(cbrt (fma (* -4 a) c (* b b)))
22.0b	(cbrt (fma (* -4 a) c (* b b)))
22.0b	(cbrt (fma (* -4 a) c (* b b)))
21.3b	(sqrt (fma (* -4 a) c (* b b)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Calls

4 calls:

Slowest

2.0ms	(sqrt (fma (* -4 a) c (* b b)))
1.0ms	(cbrt (fma (* -4 a) c (* b b)))
1.0ms	(cbrt (fma (* -4 a) c (* b b)))
1.0ms	(cbrt (fma (* -4 a) c (* b b)))

series802.0ms

Calls

4 calls:

Slowest

245.0ms	(cbrt (fma (* -4 a) c (* b b)))
235.0ms	(cbrt (fma (* -4 a) c (* b b)))
200.0ms	(cbrt (fma (* -4 a) c (* b b)))
121.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify3.1s

Calls

26 calls:

Slowest

395.0ms	(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
360.0ms	(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
314.0ms	(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))
309.0ms	(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))
297.0ms	(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))

prune2.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 10.8b

localize218.0ms

Local error

Found 4 expressions with local error:

22.0b	(cbrt (fma (* -4 a) c (* b b)))
22.0b	(cbrt (fma (* -4 a) c (* b b)))
22.0b	(cbrt (fma (* -4 a) c (* b b)))
22.0b	(cbrt (fma (* -4 a) c (* b b)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `pow1/3` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Calls

4 calls:

Slowest

2.0ms	(cbrt (fma (* -4 a) c (* b b)))
1.0ms	(cbrt (fma (* -4 a) c (* b b)))
1.0ms	(cbrt (fma (* -4 a) c (* b b)))
1.0ms	(cbrt (fma (* -4 a) c (* b b)))

series948.0ms

Calls

4 calls:

Slowest

264.0ms	(cbrt (fma (* -4 a) c (* b b)))
242.0ms	(cbrt (fma (* -4 a) c (* b b)))
229.0ms	(cbrt (fma (* -4 a) c (* b b)))
213.0ms	(cbrt (fma (* -4 a) c (* b b)))

simplify3.8s

Calls

24 calls:

Slowest

358.0ms	(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
341.0ms	(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
337.0ms	(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
322.0ms	(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
313.0ms	(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))

prune1.7s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 10.8b

regimes322.0ms

Accuracy

84.6% (1.1b remaining)

Error of 13.8b against oracle of 12.8b and baseline of 19.7b

bsearch186.0ms

end0.0ms

sample3.1s

Algorithm

intervals

Results

2.2s	8721×	body	80	valid
577.0ms	2866×	body	80	nan