Details

sample86.0ms

Algorithm

intervals

Results

49.0ms	276×	body	80	valid
18.0ms	99×	body	80	nan

simplify223.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

223.0ms

(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: 18.5b

localize143.0ms

Local error

Found 4 expressions with local error:

21.7b	(sqrt (fma (* -4 a) c (* b b)))
21.7b	(sqrt (fma (* -4 a) c (* b b)))
0.9b	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
0.4b	(- (sqrt (fma (* -4 a) c (* b b))) b)

rewrite24.0ms

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)))

series486.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

135.0ms	(- (sqrt (fma (* -4 a) c (* b b))) b)
132.0ms	(sqrt (fma (* -4 a) c (* b b)))
131.0ms	(sqrt (fma (* -4 a) c (* b b)))
88.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))

simplify21.6s

Counts

265 → 177

Calls

265 calls:

Slowest

696.0ms	(- (* (sqrt (fma (* -4 a) c (* b b))) (sqrt (fma (* -4 a) c (* b b)))) (* b b))
593.0ms	(fma (- (cbrt (sqrt (fma (* -4 a) c (* b 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)))) (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (cbrt (sqrt (fma (* -4 a) c (* b b)))))))
360.0ms	(- (pow (sqrt (fma (* -4 a) c (* b b))) 3) (pow b 3))
344.0ms	(- (* (- b) (- b)) (* (sqrt (fma (* -4 a) c (* b b))) (sqrt (fma (* -4 a) c (* b b)))))
327.0ms	(* (* (- (sqrt (fma (* -4 a) c (* b b))) b) (- (sqrt (fma (* -4 a) c (* b b))) b)) (- (sqrt (fma (* -4 a) c (* b b))) b))

prune2.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 11.1b

localize167.0ms

Local error

Found 4 expressions with local error:

21.7b	(sqrt (fma (* -4 a) c (* b b)))
21.7b	(sqrt (fma (* -4 a) c (* b b)))
21.7b	(sqrt (fma (* -4 a) c (* b b)))
15.5b	(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))

series693.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

389.0ms	(fma (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b)))) (- b))
110.0ms	(sqrt (fma (* -4 a) c (* b b)))
103.0ms	(sqrt (fma (* -4 a) c (* b b)))
91.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify3.8s

Counts

74 → 71

Calls

74 calls:

Slowest

516.0ms	(* (* (fma (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b)))) (- b)) (fma (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b)))) (- b))) (fma (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b)))) (- b)))
332.0ms	(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
221.0ms	(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)
175.0ms	(* (* (sqrt (fma (* -4 a) c (* b b))) (sqrt (fma (* -4 a) c (* b b)))) (sqrt (fma (* -4 a) c (* b b))))
159.0ms	(* (* (sqrt (fma (* -4 a) c (* b b))) (sqrt (fma (* -4 a) c (* b b)))) (sqrt (fma (* -4 a) c (* b b))))

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 10.9b

localize191.0ms

Local error

Found 4 expressions with local error:

21.7b	(sqrt (fma (* -4 a) c (* b b)))
21.7b	(sqrt (fma (* -4 a) c (* b b)))
21.7b	(sqrt (fma (* -4 a) c (* b b)))
21.7b	(sqrt (fma (* -4 a) c (* b b)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `add-cbrt-cube` `pow1/2` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 64

Calls

4 calls:

Slowest

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

series434.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

132.0ms	(sqrt (fma (* -4 a) c (* b b)))
108.0ms	(sqrt (fma (* -4 a) c (* b b)))
99.0ms	(sqrt (fma (* -4 a) c (* b b)))
95.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify3.0s

Counts

80 → 76

Calls

80 calls:

Slowest

182.0ms	(* (* (sqrt (fma (* -4 a) c (* b b))) (sqrt (fma (* -4 a) c (* b b)))) (sqrt (fma (* -4 a) c (* b b))))
169.0ms	(* (* (sqrt (fma (* -4 a) c (* b b))) (sqrt (fma (* -4 a) c (* b b)))) (sqrt (fma (* -4 a) c (* b b))))
159.0ms	(* (* (sqrt (fma (* -4 a) c (* b b))) (sqrt (fma (* -4 a) c (* b b)))) (sqrt (fma (* -4 a) c (* b b))))
137.0ms	(* (* (sqrt (fma (* -4 a) c (* b b))) (sqrt (fma (* -4 a) c (* b b)))) (sqrt (fma (* -4 a) c (* b b))))
62.0ms	(sqrt (* (cbrt (fma (* -4 a) c (* b b))) (cbrt (fma (* -4 a) c (* b b)))))

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 10.9b

localize154.0ms

Local error

Found 4 expressions with local error:

21.7b	(sqrt (fma (* -4 a) c (* b b)))
21.7b	(sqrt (fma (* -4 a) c (* b b)))
21.7b	(sqrt (fma (* -4 a) c (* b b)))
21.7b	(sqrt (fma (* -4 a) c (* b b)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `add-cbrt-cube` `pow1/2` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 64

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

series432.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

118.0ms	(sqrt (fma (* -4 a) c (* b b)))
115.0ms	(sqrt (fma (* -4 a) c (* b b)))
102.0ms	(sqrt (fma (* -4 a) c (* b b)))
97.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify3.0s

Counts

80 → 76

Calls

80 calls:

Slowest

174.0ms	(* (* (sqrt (fma (* -4 a) c (* b b))) (sqrt (fma (* -4 a) c (* b b)))) (sqrt (fma (* -4 a) c (* b b))))
164.0ms	(* (* (sqrt (fma (* -4 a) c (* b b))) (sqrt (fma (* -4 a) c (* b b)))) (sqrt (fma (* -4 a) c (* b b))))
161.0ms	(* (* (sqrt (fma (* -4 a) c (* b b))) (sqrt (fma (* -4 a) c (* b b)))) (sqrt (fma (* -4 a) c (* b b))))
127.0ms	(* (* (sqrt (fma (* -4 a) c (* b b))) (sqrt (fma (* -4 a) c (* b b)))) (sqrt (fma (* -4 a) c (* b b))))
63.0ms	(sqrt (sqrt (fma (* -4 a) c (* b b))))

prune1.5s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 10.9b

regimes295.0ms

Accuracy

86.4% (1.0b remaining)

Error of 12.8b against oracle of 11.8b and baseline of 19.0b

bsearch160.0ms

end0.0ms

sample3.0s

Algorithm

intervals

Results

2.1s	8723×	body	80	valid
523.0ms	2927×	body	80	nan