Details

sample78.0ms

Algorithm

intervals

Results

47.0ms	284×	body	80	valid
13.0ms	87×	body	80	nan

simplify227.0ms

Calls

1 calls:

Slowest

227.0ms

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

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.9b

localize162.0ms

Local error

Found 4 expressions with local error:

20.3b	(sqrt (fma (* -4 a) c (* b b)))
20.3b	(sqrt (fma (* -4 a) c (* b b)))
1.1b	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
0.5b	(- (sqrt (fma (* -4 a) c (* b b))) b)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
24×	`prod-diff`
23×	`add-cube-cbrt`
22×	`sqrt-prod`
10×	`fma-neg`
7×	`neg-mul-1`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
2×	`rem-sqrt-square` `sub-neg` `flip3--` `pow1/2` `flip--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `diff-log` `distribute-lft-out--`

Calls

4 calls:

Slowest

13.0ms	(- (sqrt (fma (* -4 a) c (* b b))) b)
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)))

series243.0ms

Calls

4 calls:

Slowest

70.0ms	(sqrt (fma (* -4 a) c (* b b)))
61.0ms	(- (sqrt (fma (* -4 a) c (* b b))) b)
57.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
54.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify5.3s

Calls

81 calls:

Slowest

173.0ms	(- (* 2 (/ (* a c) b)) (* 2 b))
132.0ms	(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))))))))
130.0ms	(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (- (* (sqrt (cbrt (fma (* -4 a) c (* b b)))) (sqrt (* (cbrt (fma (* -4 a) c (* b b))) (cbrt (fma (* -4 a) c (* b b))))))))
125.0ms	(fma 1 (- b) (- (* (sqrt (cbrt (fma (* -4 a) c (* b b)))) (sqrt (* (cbrt (fma (* -4 a) c (* b b))) (cbrt (fma (* -4 a) c (* b b))))))))
119.0ms	(fma (sqrt (- b)) (sqrt (- b)) (- (* (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b)))))))

prune1.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.8b

localize142.0ms

Local error

Found 4 expressions with local error:

20.3b	(sqrt (fma (* -4 a) c (* b b)))
20.3b	(sqrt (fma (* -4 a) c (* b b)))
20.3b	(sqrt (fma (* -4 a) c (* b b)))
12.4b	(fma (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b)))) (- b))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`*-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×	`rem-sqrt-square` `pow1/2`
1×	`fma-udef`

Calls

4 calls:

Slowest

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

series395.0ms

Calls

4 calls:

Slowest

247.0ms	(fma (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b)))) (- b))
59.0ms	(sqrt (fma (* -4 a) c (* b b)))
45.0ms	(sqrt (fma (* -4 a) c (* b b)))
44.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify988.0ms

Calls

24 calls:

Slowest

346.0ms	(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)
278.0ms	(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
55.0ms	(sqrt (sqrt (fma (* -4 a) c (* b b))))
48.0ms	(sqrt (sqrt (fma (* -4 a) c (* b b))))
42.0ms	(sqrt (sqrt (fma (* -4 a) c (* b b))))

prune1.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 11.5b

localize121.0ms

Local error

Found 4 expressions with local error:

20.3b	(sqrt (fma (* -4 a) c (* b b)))
20.3b	(sqrt (fma (* -4 a) c (* b b)))
20.3b	(sqrt (fma (* -4 a) c (* b b)))
15.9b	(- (- b) (* (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b))))))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

5.0ms	(- (- b) (* (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b))))))
1.0ms	(sqrt (fma (* -4 a) c (* b b)))
1.0ms	(sqrt (fma (* -4 a) c (* b b)))
1.0ms	(sqrt (fma (* -4 a) c (* b b)))

series195.0ms

Calls

4 calls:

Slowest

54.0ms	(- (- b) (* (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b))))))
51.0ms	(sqrt (fma (* -4 a) c (* b b)))
47.0ms	(sqrt (fma (* -4 a) c (* b b)))
43.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify1.4s

Calls

37 calls:

Slowest

121.0ms	(fma (sqrt (- b)) (sqrt (- b)) (- (* (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b)))))))
113.0ms	(- (* 2 (/ (* a c) b)) (* 2 b))
95.0ms	(* -2 (/ (* a c) b))
94.0ms	(/ (exp (- b)) (exp (* (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b)))))))
91.0ms	(fma 1 (- b) (- (* (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b)))))))

prune1.5s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 11.5b

localize118.0ms

Local error

Found 4 expressions with local error:

21.0b	(cbrt (fma (* -4 a) c (* b b)))
21.0b	(cbrt (fma (* -4 a) c (* b b)))
21.0b	(cbrt (fma (* -4 a) c (* b b)))
20.3b	(sqrt (fma (* -4 a) c (* b b)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`*-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` `sqrt-prod`
1×	`rem-sqrt-square` `pow1/2`

Calls

4 calls:

Slowest

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

series613.0ms

Calls

4 calls:

Slowest

207.0ms	(cbrt (fma (* -4 a) c (* b b)))
173.0ms	(cbrt (fma (* -4 a) c (* b b)))
164.0ms	(cbrt (fma (* -4 a) c (* b b)))
69.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify2.8s

Calls

25 calls:

Slowest

373.0ms	(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))
333.0ms	(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))
308.0ms	(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))
284.0ms	(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
266.0ms	(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))

prune1.4s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 11.5b

regimes313.0ms

Accuracy

86.6% (1.0b remaining)

Error of 12.9b against oracle of 11.9b and baseline of 19.2b

bsearch149.0ms

end0.0ms

sample2.7s

Algorithm

intervals

Results

2.0s	8688×	body	80	valid
482.0ms	3016×	body	80	nan