Details

Time bar (total: 29.6s)

sample141.0ms

Algorithm
intervals
Results
31.0ms34×body2560valid
28.0ms194×body80valid
26.0ms36×body1280valid
15.0ms108×body80nan
3.0ms8×body640valid
1.0ms3×body320valid
1.0ms1×body5120valid
0.0ms1×body160valid

simplify460.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
460.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.2b

localize42.0ms

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))

rewrite64.0ms

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
32.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
22.0ms
(- (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))

series417.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
118.0ms
(sqrt (fma c (* -4 a) (* b b)))
116.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
94.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
89.0ms
(fma c (* -4 a) (* b b))

simplify15.0s

Counts
225 → 191
Calls
225 calls:
Slowest
395.0ms
(/ (/ (* (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)))
257.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (sqrt 2)) (* (cbrt a) (cbrt a)))
227.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (* (cbrt 2) (cbrt 2))) (sqrt a))
213.0ms
(/ (* (* (/ (- (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))
168.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (* (cbrt 2) (cbrt 2))) 1)

prune2.4s

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))

rewrite46.0ms

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
33.0ms
(* (/ (- (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)))
0.0ms
(fma c (* -4 a) (* b b))

series402.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
124.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
100.0ms
(sqrt (fma c (* -4 a) (* b b)))
94.0ms
(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))
85.0ms
(fma c (* -4 a) (* b b))

simplify8.0s

Counts
126 → 150
Calls
126 calls:
Slowest
364.0ms
(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))
289.0ms
(* (/ (* (* (- (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)))
267.0ms
(+ (log (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (log (/ 1 a)))
265.0ms
(+ (log (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (- (log 1) (log a)))
256.0ms
(+ (log (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (- 0 (log a)))

prune1.8s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 22.3b

localize27.0ms

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))

rewrite293.0ms

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
68.0ms
(- (/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a) (/ (/ b 2) a))
16.0ms
(/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a)
1.0ms
(sqrt (fma c (* -4 a) (* b b)))
0.0ms
(fma c (* -4 a) (* b b))

series431.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
181.0ms
(/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a)
97.0ms
(sqrt (fma c (* -4 a) (* b b)))
90.0ms
(- (/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a) (/ (/ b 2) a))
63.0ms
(fma c (* -4 a) (* b b))