Details

sample112.0ms

Algorithm

intervals

Results

68.0ms	281×	body	80	valid
16.0ms	79×	body	80	nan

simplify317.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

316.0ms

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

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.5b

localize173.0ms

Local error

Found 4 expressions with local error:

22.3b	(sqrt (fma -4 (* c a) (* b b)))
22.3b	(sqrt (fma -4 (* c a) (* b b)))
1.3b	(- (- b) (sqrt (fma -4 (* c a) (* b b))))
1.0b	(- (sqrt (fma -4 (* c a) (* b b))) b)

rewrite27.0ms

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

10.0ms	(- (- b) (sqrt (fma -4 (* c a) (* b b))))
7.0ms	(- (sqrt (fma -4 (* c a) (* b b))) b)
5.0ms	(sqrt (fma -4 (* c a) (* b b)))
2.0ms	(sqrt (fma -4 (* c a) (* b b)))

series417.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

118.0ms	(- (sqrt (fma -4 (* c a) (* b b))) b)
114.0ms	(- (- b) (sqrt (fma -4 (* c a) (* b b))))
105.0ms	(sqrt (fma -4 (* c a) (* b b)))
80.0ms	(sqrt (fma -4 (* c a) (* b b)))

simplify14.9s

Counts

204 → 177

Calls

204 calls:

Slowest

306.0ms	(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))))))))
264.0ms	(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))))))))
235.0ms	(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))))))))
231.0ms	(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))))))))
227.0ms	(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))))))))

prune2.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.0b

localize177.0ms

Local error

Found 4 expressions with local error:

22.3b	(sqrt (fma (* -4 a) c (* b b)))
22.3b	(sqrt (fma -4 (* c a) (* b b)))
1.3b	(- (- b) (sqrt (fma -4 (* c a) (* b b))))
1.0b	(- (sqrt (fma (* -4 a) c (* b 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`

Counts

4 → 165

Calls

4 calls:

Slowest

21.0ms	(- (- b) (sqrt (fma -4 (* c a) (* b b))))
15.0ms	(- (sqrt (fma (* -4 a) c (* b b))) b)
3.0ms	(sqrt (fma (* -4 a) c (* b b)))
2.0ms	(sqrt (fma -4 (* c a) (* b b)))

series473.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

138.0ms	(sqrt (fma (* -4 a) c (* b b)))
118.0ms	(- (- b) (sqrt (fma -4 (* c a) (* b b))))
116.0ms	(- (sqrt (fma (* -4 a) c (* b b))) b)
100.0ms	(sqrt (fma -4 (* c a) (* b b)))

simplify16.0s

Counts

204 → 177

Calls

204 calls:

Slowest

458.0ms	(fma (- (sqrt (sqrt (fma -4 (* c a) (* b b))))) (sqrt (sqrt (fma -4 (* c a) (* b b)))) (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b))))))
255.0ms	(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))))))))
251.0ms	(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))))))))
234.0ms	(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))))))))
223.0ms	(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))))))))

prune3.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.0b

localize181.0ms

Local error

Found 4 expressions with local error:

22.3b	(sqrt (fma (* -4 a) c (* b b)))
22.3b	(sqrt (fma -4 (* c a) (* b b)))
22.3b	(sqrt (fma -4 (* c a) (* b b)))
8.1b	(- (- b) (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* 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

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

series486.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

136.0ms	(sqrt (fma (* -4 a) c (* b b)))
131.0ms	(sqrt (fma -4 (* c a) (* b b)))
115.0ms	(- (- b) (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b))))))
104.0ms	(sqrt (fma -4 (* c a) (* b b)))

simplify2.9s

Counts

58 → 98

Calls

58 calls:

Slowest

311.0ms	(/ (/ 1 (exp b)) (exp (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b)))))))
279.0ms	(/ (exp (- b)) (exp (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b)))))))
153.0ms	(- (* 2 (/ (* a c) b)) (* 2 b))
138.0ms	(fma (sqrt (- b)) (sqrt (- b)) (- (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b)))))))
117.0ms	(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (- (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b)))))))

prune2.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 12.0b

localize237.0ms

Local error

Found 4 expressions with local error:

23.0b	(cbrt (fma -4 (* c a) (* b b)))
23.0b	(cbrt (fma -4 (* c a) (* b b)))
23.0b	(cbrt (fma -4 (* c a) (* b b)))
22.3b	(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`
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`

Counts

4 → 58

Calls

4 calls:

Slowest

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

series786.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

251.0ms	(cbrt (fma -4 (* c a) (* b b)))
236.0ms	(cbrt (fma -4 (* c a) (* b b)))
213.0ms	(cbrt (fma -4 (* c a) (* b b)))
86.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify3.1s

Counts

26 → 70

Calls

26 calls:

Slowest

370.0ms	(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
364.0ms	(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
361.0ms	(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))
334.0ms	(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
307.0ms	(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))

prune1.9s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.0b

regimes472.0ms

Accuracy

90.7% (0.6b remaining)

Error of 13.0b against oracle of 12.4b and baseline of 19.3b

bsearch103.0ms

end0.0ms

sample3.4s

Algorithm

intervals

Results

2.3s	8745×	body	80	valid
614.0ms	2992×	body	80	nan