Details

sample103.0ms

Algorithm

intervals

Results

63.0ms	284×	body	80	valid
19.0ms	98×	body	80	nan

simplify276.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

276.0ms

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.7b

localize164.0ms

Local error

Found 4 expressions with local error:

22.3b	(sqrt (fma (* -4 a) c (* b b)))
22.3b	(sqrt (fma (* -4 a) c (* b b)))
1.8b	(- (sqrt (fma (* -4 a) c (* b b))) b)
1.6b	(- (- b) (sqrt (fma (* -4 a) c (* b b))))

rewrite23.0ms

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`

Counts

4 → 165

Calls

4 calls:

Slowest

11.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
8.0ms	(- (sqrt (fma (* -4 a) c (* b b))) b)
1.0ms	(sqrt (fma (* -4 a) c (* b b)))
1.0ms	(sqrt (fma (* -4 a) c (* b b)))

series498.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

131.0ms	(sqrt (fma (* -4 a) c (* b b)))
129.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
119.0ms	(- (sqrt (fma (* -4 a) c (* b b))) b)
118.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify14.7s

Counts

204 → 177

Calls

204 calls:

Slowest

251.0ms	(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 (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))))))))
232.0ms	(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))))))))
230.0ms	(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))))))))
230.0ms	(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))))))))

prune2.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.1b

localize170.0ms

Local error

Found 4 expressions with local error:

22.3b	(sqrt (fma (* -4 a) c (* b b)))
22.3b	(sqrt (fma (* -4 a) c (* b b)))
22.3b	(sqrt (fma (* -4 a) c (* b b)))
17.0b	(fma (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b)))) (- b))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

Slowest

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)))
0.0ms	(fma (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b)))) (- b))

series787.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

392.0ms	(fma (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b)))) (- b))
138.0ms	(sqrt (fma (* -4 a) c (* b b)))
133.0ms	(sqrt (fma (* -4 a) c (* b b)))
124.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify861.0ms

Counts

27 → 71

Calls

27 calls:

Slowest

289.0ms	(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
174.0ms	(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)
54.0ms	(sqrt (sqrt (fma (* -4 a) c (* b b))))
42.0ms	(sqrt (fma (* -4 a) c (* b b)))
41.0ms	(sqrt (* (cbrt (fma (* -4 a) c (* b b))) (cbrt (fma (* -4 a) c (* b b)))))

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.7b

localize186.0ms

Local error

Found 4 expressions with local error:

24.2b	(fma (- (* (cbrt b) (cbrt b))) (cbrt b) (- (* (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b)))))))
22.3b	(sqrt (fma (* -4 a) c (* b b)))
22.3b	(sqrt (fma (* -4 a) c (* b b)))
22.3b	(sqrt (fma (* -4 a) c (* b b)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

Slowest

2.0ms	(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)))
0.0ms	(fma (- (* (cbrt b) (cbrt b))) (cbrt b) (- (* (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b)))))))

series953.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

559.0ms	(fma (- (* (cbrt b) (cbrt b))) (cbrt b) (- (* (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b)))))))
136.0ms	(sqrt (fma (* -4 a) c (* b b)))
129.0ms	(sqrt (fma (* -4 a) c (* b b)))
129.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify769.0ms

Counts

27 → 71

Calls

27 calls:

Slowest

208.0ms	(- (* 2 (/ (* a c) b)))
120.0ms	(- (* 2 (/ (* a c) b)) (* 2 b))
61.0ms	(sqrt (* (cbrt (fma (* -4 a) c (* b b))) (cbrt (fma (* -4 a) c (* b b)))))
55.0ms	(sqrt (sqrt (fma (* -4 a) c (* b b))))
46.0ms	(sqrt (* (cbrt (fma (* -4 a) c (* b b))) (cbrt (fma (* -4 a) c (* b b)))))

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.7b

localize259.0ms

Local error

Found 4 expressions with local error:

24.2b	(fma (- (* (cbrt b) (cbrt b))) (cbrt b) (- (* (sqrt (* (sqrt (* (cbrt (fma (* -4 a) c (* b b))) (cbrt (fma (* -4 a) c (* b b))))) (sqrt (cbrt (fma (* -4 a) c (* b b)))))) (sqrt (sqrt (fma (* -4 a) c (* b b)))))))
23.1b	(cbrt (fma (* -4 a) c (* b b)))
23.1b	(cbrt (fma (* -4 a) c (* b b)))
23.1b	(cbrt (fma (* -4 a) c (* b b)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 53

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

series927.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

245.0ms	(cbrt (fma (* -4 a) c (* b b)))
240.0ms	(cbrt (fma (* -4 a) c (* b b)))
224.0ms	(cbrt (fma (* -4 a) c (* b b)))
217.0ms	(fma (- (* (cbrt b) (cbrt b))) (cbrt b) (- (* (sqrt (* (sqrt (* (cbrt (fma (* -4 a) c (* b b))) (cbrt (fma (* -4 a) c (* b b))))) (sqrt (cbrt (fma (* -4 a) c (* b b)))))) (sqrt (sqrt (fma (* -4 a) c (* b b)))))))

simplify3.2s

Counts

21 → 65

Calls

21 calls:

Slowest

349.0ms	(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
349.0ms	(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
312.0ms	(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
310.0ms	(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))
300.0ms	(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))

prune1.7s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 12.7b

regimes350.0ms

Accuracy

86% (1.0b remaining)

Error of 13.1b against oracle of 12.1b and baseline of 19.5b

bsearch180.0ms

end0.0ms

sample3.1s

Algorithm

intervals

Results

2.3s	8717×	body	80	valid
535.0ms	2866×	body	80	nan