Details

Time bar (total: 42.3s)

sample161.0ms

Algorithm
intervals
Results
51.0ms187×body80valid
34.0ms32×body2560valid
21.0ms25×body1280valid
12.0ms79×body80nan
10.0ms14×body640valid
5.0ms9×body320valid
4.0ms4×body5120valid
1.0ms4×body160valid

simplify235.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
235.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize45.0ms

Local error

Found 4 expressions with local error:

22.3b
(sqrt (fma (* a c) -4 (* b b)))
1.3b
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
0.8b
(fma (* a c) -4 (* b b))
0.1b
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
169×add-sqr-sqrt
168×*-un-lft-identity
159×times-frac
116×add-cube-cbrt
60×prod-diff
46×sqrt-prod
34×distribute-rgt-neg-in
26×distribute-lft-out-- difference-of-squares
25×associate-/l*
21×distribute-lft-neg-in
10×fma-neg
9×add-cbrt-cube add-exp-log
8×add-log-exp
7×neg-mul-1
5×pow1 div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×cbrt-undiv associate-/r* div-exp
2×diff-log div-sub
1×associate--l- neg-sub0 rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 neg-log fma-udef flip-- associate-/l/
Counts
4 → 240
Calls
4 calls:
Slowest
42.0ms
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)
21.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
3.0ms
(sqrt (fma (* a c) -4 (* b b)))
0.0ms
(fma (* a c) -4 (* b b))

series428.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
135.0ms
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)
112.0ms
(sqrt (fma (* a c) -4 (* b b)))
97.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
84.0ms
(fma (* a c) -4 (* b b))

simplify30.8s

Counts
334 → 252
Calls
334 calls:
Slowest
530.0ms
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) (sqrt a))
517.0ms
(/ (/ (* (cbrt (- (- b) (sqrt (fma (* a c) -4 (* b b))))) (cbrt (- (- b) (sqrt (fma (* a c) -4 (* b b)))))) (* (cbrt 2) (cbrt 2))) (* (cbrt a) (cbrt a)))
257.0ms
(fma (- (* (cbrt b) (cbrt b))) (cbrt b) (- (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b))))))))
256.0ms
(fma (- 1) b (- (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b))))))))
253.0ms
(/ (/ (* (cbrt (- (- b) (sqrt (fma (* a c) -4 (* b b))))) (cbrt (- (- b) (sqrt (fma (* a c) -4 (* b b)))))) (sqrt 2)) (* (cbrt a) (cbrt a)))

prune3.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.7b

localize26.0ms

Local error

Found 4 expressions with local error:

22.3b
(sqrt (fma a (* c -4) (* b b)))
1.3b
(+ b (sqrt (fma a (* c -4) (* b b))))
0.2b
(* (- (+ b (sqrt (fma a (* c -4) (* b b))))) (/ 1/2 a))
0.0b
(fma a (* c -4) (* b b))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt *-un-lft-identity
16×add-cube-cbrt
13×associate-*r*
12×associate-*l*
10×times-frac
9×add-cbrt-cube add-exp-log
7×pow1
6×add-log-exp
4×distribute-lft-neg-in expm1-log1p-u distribute-rgt-neg-in insert-posit16 log1p-expm1-u distribute-neg-frac
3×fma-def flip3-+ sqrt-prod flip-+ distribute-lft-out
2×frac-times associate-*l/ prod-exp cbrt-unprod unswap-sqr
1×distribute-lft-neg-out cbrt-undiv +-commutative rem-sqrt-square neg-mul-1 sum-log sqrt-pow1 pow1/2 div-exp pow-prod-down associate-*r/ *-commutative fma-udef div-inv
Counts
4 → 94
Calls
4 calls:
Slowest
59.0ms
(* (- (+ b (sqrt (fma a (* c -4) (* b b))))) (/ 1/2 a))
7.0ms
(+ b (sqrt (fma a (* c -4) (* b b))))
1.0ms
(sqrt (fma a (* c -4) (* b b)))
0.0ms
(fma a (* c -4) (* b b))

series427.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
119.0ms
(sqrt (fma a (* c -4) (* b b)))
110.0ms
(+ b (sqrt (fma a (* c -4) (* b b))))
107.0ms
(* (- (+ b (sqrt (fma a (* c -4) (* b b))))) (/ 1/2 a))
90.0ms
(fma a (* c -4) (* b b))

simplify4.1s

Counts
58 → 106
Calls
58 calls:
Slowest
343.0ms
(* (* (* (- (+ b (sqrt (fma a (* c -4) (* b b))))) (- (+ b (sqrt (fma a (* c -4) (* b b)))))) (- (+ b (sqrt (fma a (* c -4) (* b b)))))) (/ (* (* 1/2 1/2) 1/2) (* (* a a) a)))
332.0ms
(* (+ (* b b) (- (* (sqrt (fma a (* c -4) (* b b))) (sqrt (fma a (* c -4) (* b b)))) (* b (sqrt (fma a (* c -4) (* b b)))))) a)
312.0ms
(* (* (* (- (+ b (sqrt (fma a (* c -4) (* b b))))) (- (+ b (sqrt (fma a (* c -4) (* b b)))))) (- (+ b (sqrt (fma a (* c -4) (* b b)))))) (* (* (/ 1/2 a) (/ 1/2 a)) (/ 1/2 a)))
298.0ms
(* (- (+ (pow b 3) (pow (sqrt (fma a (* c -4) (* b b))) 3))) (/ 1/2 a))
281.0ms
(- (* 2 b) (* 2 (/ (* a c) b)))

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.5b

localize50.0ms

Local error

Found 4 expressions with local error:

22.3b
(sqrt (fma (* a c) -4 (* b b)))
7.5b
(- (/ (/ (- b) 2) a) (/ (/ (sqrt (fma (* a c) -4 (* b b))) 2) a))
0.8b
(fma (* a c) -4 (* b b))
0.1b
(/ (/ (sqrt (fma (* a c) -4 (* b b))) 2) a)

rewrite910.0ms

Algorithm
rewrite-expression-head
Rules
26601×times-frac
13477×add-sqr-sqrt
13469×*-un-lft-identity
13425×add-cube-cbrt
7420×prod-diff
2904×sqrt-prod
1926×distribute-rgt-neg-in
1917×distribute-lft-neg-in
721×div-inv
639×neg-mul-1
106×fma-neg
22×associate-/l* distribute-lft-out--
12×difference-of-squares
9×add-cbrt-cube add-exp-log
6×add-log-exp
5×pow1
4×expm1-log1p-u distribute-rgt-out-- insert-posit16 log1p-expm1-u
3×cbrt-undiv associate-/r* div-exp
2×div-sub
1×associate--l- neg-sub0 rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 diff-log frac-sub fma-udef flip-- sub-div associate-/l/
Counts
4 → 7718
Calls
4 calls:
Slowest
98.0ms
(- (/ (/ (- b) 2) a) (/ (/ (sqrt (fma (* a c) -4 (* b b))) 2) a))
17.0ms
(/ (/ (sqrt (fma (* a c) -4 (* b b))) 2) a)
3.0ms
(sqrt (fma (* a c) -4 (* b b)))
1.0ms
(fma (* a c) -4 (* b b))

series573.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
177.0ms
(- (/ (/ (- b) 2) a) (/ (/ (sqrt (fma (* a c) -4 (* b b))) 2) a))
157.0ms
(/ (/ (sqrt (fma (* a c) -4 (* b b))) 2) a)
141.0ms
(sqrt (fma (* a c) -4 (* b b)))
96.0ms
(fma (* a c) -4 (* b b))