Details

sample148.0ms

Algorithm

intervals

Results

49.0ms	37×	body	2560	valid
29.0ms	186×	body	80	valid
21.0ms	27×	body	1280	valid
15.0ms	92×	body	80	nan
9.0ms	14×	body	640	valid
4.0ms	9×	body	320	valid
3.0ms	2×	body	5120	valid
1.0ms	4×	body	160	valid

simplify176.0ms

Calls

1 calls:

Slowest

176.0ms

(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize45.0ms

Local error

Found 3 expressions with local error:

21.1b	(sqrt (fma c (* -4 a) (* b b)))
1.1b	(- (sqrt (fma c (* -4 a) (* b b))) b)
0.1b	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
134×	`add-sqr-sqrt`
107×	`*-un-lft-identity`
81×	`add-cube-cbrt`
28×	`sqrt-prod`
26×	`difference-of-squares`
22×	`associate-/l*`
18×	`prod-diff`
13×	`distribute-lft-out--`
8×	`add-cbrt-cube` `add-exp-log`
6×	`fma-neg`
5×	`div-inv` `add-log-exp`
4×	`pow1`
3×	`expm1-log1p-u` `cbrt-undiv` `associate-/r*` `div-exp` `insert-posit16` `log1p-expm1-u`
2×	`div-sub`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `flip--` `associate-/l/`

Calls

3 calls:

Slowest

29.0ms	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
15.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
3.0ms	(sqrt (fma c (* -4 a) (* b b)))

series391.0ms

Calls

3 calls:

Slowest

149.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
134.0ms	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
107.0ms	(sqrt (fma c (* -4 a) (* b b)))

simplify15.3s

Calls

222 calls:

Slowest

524.0ms	(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (* (cbrt 2) (cbrt 2))) (* (cbrt a) (cbrt a)))
522.0ms	(/ (/ (+ (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt b)) (sqrt 2)) (* (cbrt a) (cbrt a)))
205.0ms	(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (* (cbrt 2) (cbrt 2))) (sqrt a))
196.0ms	(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (* (cbrt 2) (cbrt 2))) 1)
194.0ms	(/ (* (* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (* (* a a) a))

prune2.6s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 27.0b

localize26.0ms

Local error

Found 3 expressions with local error:

21.1b	(sqrt (fma c (* -4 a) (* b b)))
1.1b	(- (sqrt (fma c (* -4 a) (* b b))) b)
0.2b	(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

69×	`add-sqr-sqrt`
45×	`*-un-lft-identity`
35×	`add-cube-cbrt`
34×	`times-frac`
25×	`add-exp-log`
22×	`associate-l`
19×	`sqrt-prod`
18×	`prod-diff`
15×	`add-cbrt-cube`
13×	`associate-r`
8×	`div-exp` `prod-exp` `difference-of-squares`
6×	`pow1` `fma-neg` `unswap-sqr`
5×	`add-log-exp`
4×	`cbrt-undiv` `cbrt-unprod` `distribute-lft-out--`
3×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
2×	`rec-exp` `1-exp` `div-inv`
1×	`frac-times` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `pow-prod-down` `associate-l/` `associate-r/` `un-div-inv` `*-commutative` `flip--`

Calls

3 calls:

Slowest

49.0ms	(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))
15.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
2.0ms	(sqrt (fma c (* -4 a) (* b b)))

series370.0ms

Calls

3 calls:

Slowest

138.0ms	(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))
117.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
114.0ms	(sqrt (fma c (* -4 a) (* b b)))

simplify7.8s

Calls

123 calls:

Slowest

319.0ms	(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))
299.0ms	(+ (log (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (- 0 (log a)))
295.0ms	(* (/ (* (* (- (sqrt (fma c (* -4 a) (* b b))) b) (- (sqrt (fma c (* -4 a) (* b b))) b)) (- (sqrt (fma c (* -4 a) (* b b))) b)) (* (* 2 2) 2)) (/ (* (* 1 1) 1) (* (* a a) a)))
274.0ms	(+ (- (log (- (sqrt (fma c (* -4 a) (* b b))) b)) (log 2)) (- 0 (log a)))
260.0ms	(+ (log (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (- (log 1) (log a)))

prune1.9s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 27.0b

localize38.0ms

Local error

Found 4 expressions with local error:

21.1b	(sqrt (fma c (* -4 a) (* b b)))
21.1b	(sqrt (fma c (* -4 a) (* b b)))
1.1b	(- (sqrt (fma c (* -4 a) (* b b))) b)
1.1b	(- (sqrt (fma c (* -4 a) (* b b))) b)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
36×	`prod-diff`
34×	`add-cube-cbrt`
32×	`sqrt-prod`
12×	`fma-neg`
8×	`add-log-exp`
6×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `flip--` `distribute-lft-out--`

Calls

4 calls:

Slowest

12.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
7.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
1.0ms	(sqrt (fma c (* -4 a) (* b b)))
1.0ms	(sqrt (fma c (* -4 a) (* b b)))

series448.0ms

Calls

4 calls:

Slowest

119.0ms	(sqrt (fma c (* -4 a) (* b b)))
117.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
114.0ms	(sqrt (fma c (* -4 a) (* b b)))
97.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)

simplify3.5s

Calls

116 calls:

Slowest

123.0ms	(fma (* (cbrt (sqrt (fma c (* -4 a) (* b b)))) (cbrt (sqrt (fma c (* -4 a) (* b b))))) (cbrt (sqrt (fma c (* -4 a) (* b b)))) (- (* (cbrt b) (* (cbrt b) (cbrt b)))))
102.0ms	(fma (* (cbrt (sqrt (fma c (* -4 a) (* b b)))) (cbrt (sqrt (fma c (* -4 a) (* b b))))) (cbrt (sqrt (fma c (* -4 a) (* b b)))) (- (* (sqrt b) (sqrt b))))
95.0ms	(fma (* (cbrt (sqrt (fma c (* -4 a) (* b b)))) (cbrt (sqrt (fma c (* -4 a) (* b b))))) (cbrt (sqrt (fma c (* -4 a) (* b b)))) (- (* (sqrt b) (sqrt b))))
92.0ms	(fma (* (cbrt (sqrt (fma c (* -4 a) (* b b)))) (cbrt (sqrt (fma c (* -4 a) (* b b))))) (cbrt (sqrt (fma c (* -4 a) (* b b)))) (- (* (cbrt b) (* (cbrt b) (cbrt b)))))
86.0ms	(fma (* (cbrt (sqrt (fma c (* -4 a) (* b b)))) (cbrt (sqrt (fma c (* -4 a) (* b b))))) (cbrt (sqrt (fma c (* -4 a) (* b b)))) (- (* b 1)))

prune2.0s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 27.0b

localize35.0ms

Local error

Found 3 expressions with local error:

21.1b	(sqrt (fma c (* -4 a) (* b b)))
6.0b	(- (/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a) (/ (/ b 2) a))
0.1b	(/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a)

rewrite280.0ms

Algorithm

rewrite-expression-head

Rules

10113×	`times-frac`
5325×	`add-sqr-sqrt`
5299×	`*-un-lft-identity`
5273×	`add-cube-cbrt`
3010×	`prod-diff`
1230×	`sqrt-prod`
469×	`div-inv`
70×	`fma-neg`
22×	`associate-/l*`
13×	`distribute-lft-out--`
12×	`difference-of-squares`
8×	`add-cbrt-cube` `add-exp-log`
5×	`add-log-exp`
4×	`pow1` `distribute-rgt-out--`
3×	`expm1-log1p-u` `cbrt-undiv` `associate-/r*` `div-exp` `insert-posit16` `log1p-expm1-u`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `frac-sub` `flip--` `sub-div` `associate-/l/`

Calls

3 calls:

Slowest

47.0ms	(- (/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a) (/ (/ b 2) a))
9.0ms	(/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a)
1.0ms	(sqrt (fma c (* -4 a) (* b b)))

series384.0ms

Calls

3 calls:

Slowest

155.0ms	(/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a)
123.0ms	(- (/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a) (/ (/ b 2) a))
107.0ms	(sqrt (fma c (* -4 a) (* b b)))