Details

Time bar (total: 30.5s)

sample125.0ms

Algorithm
intervals
Results
28.0ms108×body80nan
26.0ms194×body80valid
25.0ms34×body2560valid
23.0ms36×body1280valid
4.0ms8×body640valid
2.0ms1×body5120valid
1.0ms3×body320valid
0.0ms1×body160valid

simplify166.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
166.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.2b

localize48.0ms

Local error

Found 4 expressions with local error:

18.8b
(sqrt (fma c (* -4 a) (* b b)))
0.4b
(- (sqrt (fma c (* -4 a) (* b b))) b)
0.1b
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
0.0b
(fma c (* -4 a) (* b b))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
135×add-sqr-sqrt
108×*-un-lft-identity
82×add-cube-cbrt
28×sqrt-prod
26×difference-of-squares
22×associate-/l*
18×prod-diff
13×distribute-lft-out--
9×add-cbrt-cube add-exp-log
6×fma-neg add-log-exp
5×pow1 div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×cbrt-undiv associate-/r* div-exp
2×div-sub
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 diff-log fma-udef flip-- associate-/l/
Counts
4 → 179
Calls
4 calls:
Slowest
33.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
16.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
3.0ms
(sqrt (fma c (* -4 a) (* b b)))
0.0ms
(fma c (* -4 a) (* b b))

series515.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
147.0ms
(sqrt (fma c (* -4 a) (* b b)))
140.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
121.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
107.0ms
(fma c (* -4 a) (* b b))

simplify14.8s

Counts
225 → 191
Calls
225 calls:
Slowest
402.0ms
(/ (/ (* (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)))
235.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (sqrt 2)) (* (cbrt a) (cbrt a)))
212.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (* (cbrt 2) (cbrt 2))) (sqrt a))
192.0ms
(/ (* (* (/ (- (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))
190.0ms
(/ (/ (* (* (- (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)) (* (* a a) a))

prune2.7s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 22.3b

localize37.0ms

Local error

Found 4 expressions with local error:

18.8b
(sqrt (fma c (* -4 a) (* b b)))
0.4b
(- (sqrt (fma c (* -4 a) (* b b))) b)
0.2b
(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))
0.0b
(fma c (* -4 a) (* b b))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
70×add-sqr-sqrt
46×*-un-lft-identity
36×add-cube-cbrt
34×times-frac
26×add-exp-log
22×associate-*l*
19×sqrt-prod
18×prod-diff
16×add-cbrt-cube
13×associate-*r*
8×div-exp prod-exp difference-of-squares
7×pow1
6×fma-neg add-log-exp unswap-sqr
4×expm1-log1p-u cbrt-undiv cbrt-unprod insert-posit16 log1p-expm1-u distribute-lft-out--
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 fma-udef flip--
Counts
4 → 138
Calls
4 calls:
Slowest
35.0ms
(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))
7.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
1.0ms
(sqrt (fma c (* -4 a) (* b b)))
1.0ms
(fma c (* -4 a) (* b b))

series845.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
543.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
122.0ms
(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))
103.0ms
(sqrt (fma c (* -4 a) (* b b)))
76.0ms
(fma c (* -4 a) (* b b))

simplify8.1s

Counts
126 → 150
Calls
126 calls:
Slowest
386.0ms
(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))
276.0ms
(+ (log (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (- (log 1) (log a)))
273.0ms
(+ (- (log (- (sqrt (fma c (* -4 a) (* b b))) b)) (log 2)) (- 0 (log a)))
268.0ms
(* (/ (* (* (- (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)))
265.0ms
(+ (- (log (- (sqrt (fma c (* -4 a) (* b b))) b)) (log 2)) (- (log 1) (log a)))

prune2.0s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 22.3b

localize44.0ms

Local error

Found 4 expressions with local error:

18.8b
(sqrt (fma c (* -4 a) (* b b)))
4.6b
(- (/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a) (/ (/ b 2) a))
0.1b
(/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a)
0.0b
(fma c (* -4 a) (* b b))

rewrite313.0ms

Algorithm
rewrite-expression-head
Rules
10113×times-frac
5326×add-sqr-sqrt
5300×*-un-lft-identity
5274×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
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
1×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 → 3262
Calls
4 calls:
Slowest
61.0ms
(- (/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a) (/ (/ b 2) a))
18.0ms
(/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a)
2.0ms
(sqrt (fma c (* -4 a) (* b b)))
0.0ms
(fma c (* -4 a) (* b b))

series570.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
192.0ms
(/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a)
152.0ms
(sqrt (fma c (* -4 a) (* b b)))
144.0ms
(- (/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a) (/ (/ b 2) a))
83.0ms
(fma c (* -4 a) (* b b))