Details

sample134.0ms

Algorithm

intervals

Results

71.0ms	279×	body	80	valid
37.0ms	108×	body	80	nan

simplify253.0ms

Calls

1 calls:

Slowest

252.0ms

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

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.3b

localize124.0ms

Local error

Found 4 expressions with local error:

23.7b	(sqrt (fma -4 (* c a) (* b b)))
23.7b	(sqrt (fma -4 (* c a) (* b b)))
0.8b	(- (sqrt (fma -4 (* c a) (* b b))) b)
0.4b	(- (- b) (sqrt (fma -4 (* c a) (* b b))))

rewrite42.0ms

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

19.0ms	(- (- b) (sqrt (fma -4 (* c a) (* b b))))
7.0ms	(- (sqrt (fma -4 (* c a) (* b b))) b)
3.0ms	(sqrt (fma -4 (* c a) (* b b)))
1.0ms	(sqrt (fma -4 (* c a) (* b b)))

series396.0ms

Calls

4 calls:

Slowest

106.0ms	(sqrt (fma -4 (* c a) (* b b)))
98.0ms	(sqrt (fma -4 (* c a) (* b b)))
97.0ms	(- (- b) (sqrt (fma -4 (* c a) (* b b))))
95.0ms	(- (sqrt (fma -4 (* c a) (* b b))) b)

simplify15.0s

Calls

204 calls:

Slowest

264.0ms	(fma (* (cbrt b) (cbrt b)) (- (cbrt b)) (- (* (cbrt (sqrt (fma -4 (* c a) (* b b)))) (* (cbrt (sqrt (fma -4 (* c a) (* b b)))) (cbrt (sqrt (fma -4 (* c a) (* b b))))))))
262.0ms	(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (- (* (cbrt (sqrt (fma -4 (* c a) (* b b)))) (* (cbrt (sqrt (fma -4 (* c a) (* b b)))) (cbrt (sqrt (fma -4 (* c a) (* b b))))))))
250.0ms	(fma 1 (- b) (- (* (cbrt (sqrt (fma -4 (* c a) (* b b)))) (* (cbrt (sqrt (fma -4 (* c a) (* b b)))) (cbrt (sqrt (fma -4 (* c a) (* b b))))))))
240.0ms	(fma (sqrt (- b)) (sqrt (- b)) (- (* (cbrt (sqrt (fma -4 (* c a) (* b b)))) (* (cbrt (sqrt (fma -4 (* c a) (* b b)))) (cbrt (sqrt (fma -4 (* c a) (* b b))))))))
219.0ms	(fma -1 b (- (* (cbrt (sqrt (fma -4 (* c a) (* b b)))) (* (cbrt (sqrt (fma -4 (* c a) (* b b)))) (cbrt (sqrt (fma -4 (* c a) (* b b))))))))

prune3.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.2b

localize144.0ms

Local error

Found 4 expressions with local error:

23.7b	(sqrt (fma (* -4 c) a (* b b)))
23.7b	(sqrt (fma -4 (* c a) (* b b)))
0.8b	(- (sqrt (fma (* -4 c) a (* b b))) b)
0.4b	(- (- b) (sqrt (fma -4 (* c a) (* b b))))

rewrite45.0ms

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

21.0ms	(- (- b) (sqrt (fma -4 (* c a) (* b b))))
15.0ms	(- (sqrt (fma (* -4 c) a (* b b))) b)
2.0ms	(sqrt (fma (* -4 c) a (* b b)))
2.0ms	(sqrt (fma -4 (* c a) (* b b)))

series459.0ms

Calls

4 calls:

Slowest

126.0ms	(sqrt (fma -4 (* c a) (* b b)))
120.0ms	(sqrt (fma (* -4 c) a (* b b)))
119.0ms	(- (sqrt (fma (* -4 c) a (* b b))) b)
94.0ms	(- (- b) (sqrt (fma -4 (* c a) (* b b))))

simplify14.9s

Calls

204 calls:

Slowest

247.0ms	(fma 1 (- b) (- (* (cbrt (sqrt (fma -4 (* c a) (* b b)))) (* (cbrt (sqrt (fma -4 (* c a) (* b b)))) (cbrt (sqrt (fma -4 (* c a) (* b b))))))))
244.0ms	(fma (* (cbrt b) (cbrt b)) (- (cbrt b)) (- (* (cbrt (sqrt (fma -4 (* c a) (* b b)))) (* (cbrt (sqrt (fma -4 (* c a) (* b b)))) (cbrt (sqrt (fma -4 (* c a) (* b b))))))))
243.0ms	(fma (sqrt (- b)) (sqrt (- b)) (- (* (cbrt (sqrt (fma -4 (* c a) (* b b)))) (* (cbrt (sqrt (fma -4 (* c a) (* b b)))) (cbrt (sqrt (fma -4 (* c a) (* b b))))))))
241.0ms	(fma 1 (- b) (- (* (cbrt (sqrt (fma -4 (* c a) (* b b)))) (* (cbrt (sqrt (fma -4 (* c a) (* b b)))) (cbrt (sqrt (fma -4 (* c a) (* b b))))))))
231.0ms	(fma (- 1) b (- (* (cbrt (sqrt (fma -4 (* c a) (* b b)))) (* (cbrt (sqrt (fma -4 (* c a) (* b b)))) (cbrt (sqrt (fma -4 (* c a) (* b b))))))))

prune3.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.2b

localize90.0ms

Local error

Found 4 expressions with local error:

23.7b	(sqrt (fma (* -4 c) a (* b b)))
23.7b	(sqrt (fma (* -4 c) a (* b b)))
23.7b	(sqrt (fma -4 (* c a) (* b b)))
0.8b	(- (sqrt (fma (* -4 c) a (* b b))) b)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
22×	`sqrt-prod`
21×	`add-cube-cbrt`
18×	`prod-diff`
7×	`pow1`
6×	`fma-neg` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Calls

4 calls:

Slowest

15.0ms	(- (sqrt (fma (* -4 c) a (* b b))) b)
2.0ms	(sqrt (fma -4 (* c a) (* b b)))
2.0ms	(sqrt (fma (* -4 c) a (* b b)))
2.0ms	(sqrt (fma (* -4 c) a (* b b)))

series464.0ms

Calls

4 calls:

Slowest

123.0ms	(sqrt (fma -4 (* c a) (* b b)))
120.0ms	(sqrt (fma (* -4 c) a (* b b)))
118.0ms	(- (sqrt (fma (* -4 c) a (* b b))) b)
103.0ms	(sqrt (fma (* -4 c) a (* b b)))

simplify2.7s

Calls

74 calls:

Slowest

114.0ms	(fma (* (cbrt (sqrt (fma (* -4 c) a (* b b)))) (cbrt (sqrt (fma (* -4 c) a (* b b))))) (cbrt (sqrt (fma (* -4 c) a (* b b)))) (- (* (sqrt b) (sqrt b))))
111.0ms	(fma (sqrt (* (cbrt (fma (* -4 c) a (* b b))) (cbrt (fma (* -4 c) a (* b b))))) (sqrt (cbrt (fma (* -4 c) a (* b b)))) (- (* (cbrt b) (* (cbrt b) (cbrt b)))))
97.0ms	(fma (* (cbrt (sqrt (fma (* -4 c) a (* b b)))) (cbrt (sqrt (fma (* -4 c) a (* b b))))) (cbrt (sqrt (fma (* -4 c) a (* b b)))) (- (* (cbrt b) (* (cbrt b) (cbrt b)))))
94.0ms	(fma (sqrt 1) (sqrt (fma (* -4 c) a (* b b))) (- (* (cbrt b) (* (cbrt b) (cbrt b)))))
87.0ms	(fma (* (cbrt (sqrt (fma (* -4 c) a (* b b)))) (cbrt (sqrt (fma (* -4 c) a (* b b))))) (cbrt (sqrt (fma (* -4 c) a (* b b)))) (- (* b 1)))

prune2.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.2b

localize170.0ms

Local error

Found 4 expressions with local error:

24.5b	(cbrt (fma (* -4 c) a (* b b)))
24.5b	(cbrt (fma (* -4 c) a (* b b)))
24.5b	(cbrt (fma (* -4 c) a (* b b)))
23.7b	(sqrt (fma -4 (* c a) (* b b)))

rewrite8.0ms

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

series794.0ms

Calls

4 calls:

Slowest

232.0ms	(cbrt (fma (* -4 c) a (* b b)))
224.0ms	(cbrt (fma (* -4 c) a (* b b)))
218.0ms	(cbrt (fma (* -4 c) a (* b b)))
119.0ms	(sqrt (fma -4 (* c a) (* b b)))

simplify3.0s

Calls

26 calls:

Slowest

368.0ms	(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
342.0ms	(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
326.0ms	(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))
318.0ms	(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
269.0ms	(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))

prune1.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 14.2b

regimes297.0ms

Accuracy

91% (0.6b remaining)

Error of 12.7b against oracle of 12.1b and baseline of 19.3b

bsearch219.0ms

end0.0ms

sample3.2s

Algorithm

intervals

Results

2.3s	8731×	body	80	valid
583.0ms	2837×	body	80	nan