Details

sample80.0ms

Algorithm

intervals

Results

40.0ms	275×	body	80	valid
10.0ms	80×	body	80	nan

simplify263.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

263.0ms

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

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.5b

localize128.0ms

Local error

Found 4 expressions with local error:

20.8b	(sqrt (fma (* -4 a) c (* b b)))
20.8b	(sqrt (fma (* -4 a) c (* b b)))
1.1b	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
0.3b	(- (sqrt (fma (* -4 a) c (* b b))) b)

rewrite52.0ms

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

21.0ms	(- (sqrt (fma (* -4 a) c (* b b))) b)
21.0ms	(- (- 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)))

series483.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

140.0ms	(sqrt (fma (* -4 a) c (* b b)))
131.0ms	(- (sqrt (fma (* -4 a) c (* b b))) b)
113.0ms	(sqrt (fma (* -4 a) c (* b b)))
98.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))

simplify15.4s

Counts

204 → 177

Calls

204 calls:

Slowest

330.0ms	(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))))))))
243.0ms	(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))))))))
237.0ms	(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))))))))
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))))))))
228.0ms	(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: 11.0b

localize149.0ms

Local error

Found 4 expressions with local error:

20.8b	(sqrt (fma (* -4 a) c (* b b)))
20.8b	(sqrt (fma (* -4 a) c (* b b)))
20.8b	(sqrt (fma (* -4 a) c (* b b)))
11.8b	(- (- b) (* (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b))))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-cube-cbrt`
10×	`fma-neg` `prod-diff`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1`
6×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`neg-mul-1` `diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `flip3--` `neg-log` `flip--` `difference-of-squares`

Counts

4 → 86

Calls

4 calls:

Slowest

19.0ms	(- (- b) (* (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b))))))
3.0ms	(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)))

series435.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

116.0ms	(sqrt (fma (* -4 a) c (* b b)))
113.0ms	(sqrt (fma (* -4 a) c (* b b)))
103.0ms	(- (- b) (* (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b))))))
102.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify2.8s

Counts

58 → 98

Calls

58 calls:

Slowest

361.0ms	(/ (/ 1 (exp b)) (exp (* (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b)))))))
286.0ms	(/ (exp (- b)) (exp (* (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b)))))))
139.0ms	(- (* 2 (/ (* a c) b)) (* 2 b))
116.0ms	(fma (sqrt (- b)) (sqrt (- b)) (- (* (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b)))))))
112.0ms	(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (- (* (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b)))))))

prune1.7s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 11.0b

localize175.0ms

Local error

Found 4 expressions with local error:

20.8b	(sqrt (fma (* -4 a) c (* b b)))
20.8b	(sqrt (fma (* -4 a) c (* b b)))
20.8b	(sqrt (fma (* -4 a) c (* b b)))
1.1b	(- (- b) (sqrt (fma (* -4 a) c (* b b))))

rewrite21.0ms

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--`

Counts

4 → 139

Calls

4 calls:

Slowest

12.0ms	(- (- b) (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)))
2.0ms	(sqrt (fma (* -4 a) c (* b b)))

series467.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

122.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
120.0ms	(sqrt (fma (* -4 a) c (* b b)))
120.0ms	(sqrt (fma (* -4 a) c (* b b)))
105.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify13.7s

Counts

162 → 151

Calls

162 calls:

Slowest

353.0ms	(fma (- (sqrt (fma (* -4 a) c (* b b)))) (sqrt 1) (* (sqrt (fma (* -4 a) c (* b b))) (sqrt 1)))
291.0ms	(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))))))))
277.0ms	(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))))))))
255.0ms	(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))))))))
253.0ms	(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))))))))

prune2.8s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 11.0b

localize211.0ms

Local error

Found 4 expressions with local error:

23.0b	(fma (fabs (cbrt (fma (* -4 a) c (* b b)))) (sqrt (cbrt (fma (* -4 a) c (* b b)))) b)
21.6b	(cbrt (fma (* -4 a) c (* b b)))
21.6b	(cbrt (fma (* -4 a) c (* b b)))
20.8b	(sqrt (fma (* -4 a) c (* b b)))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

Slowest

1.0ms	(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)))
0.0ms	(fma (fabs (cbrt (fma (* -4 a) c (* b b)))) (sqrt (cbrt (fma (* -4 a) c (* b b)))) b)

series987.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

333.0ms	(fma (fabs (cbrt (fma (* -4 a) c (* b b)))) (sqrt (cbrt (fma (* -4 a) c (* b b)))) b)
284.0ms	(cbrt (fma (* -4 a) c (* b b)))
261.0ms	(cbrt (fma (* -4 a) c (* b b)))
109.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify2.9s

Counts

23 → 67

Calls

23 calls:

Slowest

389.0ms	(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
365.0ms	(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
365.0ms	(+ (* (fabs (pow (fma (* -4 a) c (pow b 2)) 1/3)) (exp (* 1/6 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a))))))) b)
285.0ms	(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))
261.0ms	(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))

prune1.2s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 11.0b

regimes433.0ms

Accuracy

93.8% (0.4b remaining)

Error of 12.5b against oracle of 12.1b and baseline of 19.0b

bsearch86.0ms

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.9s	8667×	body	80	valid
955.0ms	2853×	body	80	nan