Details

Time bar (total: 3.3m)

sample150.0ms

Algorithm
intervals
Results
55.0ms41×body2560valid
31.0ms189×body80valid
18.0ms25×body1280valid
13.0ms91×body80nan
8.0ms11×body640valid
5.0ms10×body320valid
1.0ms4×body160valid

simplify155.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
155.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.0b

localize24.0ms

Local error

Found 4 expressions with local error:

21.6b
(sqrt (fma c (* -4 a) (* b b)))
1.3b
(- (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))

rewrite48.0ms

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)
9.0ms
(- (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))

series436.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
134.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
115.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
98.0ms
(sqrt (fma c (* -4 a) (* b b)))
89.0ms
(fma c (* -4 a) (* b b))

simplify19.7s

Counts
282 → 191
Calls
282 calls:
Slowest
816.0ms
(- (* (sqrt (fma c (* -4 a) (* b b))) (sqrt (fma c (* -4 a) (* b b)))) (* b b))
659.0ms
(* (* (/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a) (/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)) (/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a))
418.0ms
(/ (/ (* (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)))
359.0ms
(- (pow (sqrt (fma c (* -4 a) (* b b))) 3) (pow b 3))
353.0ms
(* (* (- (sqrt (fma c (* -4 a) (* b b))) b) (- (sqrt (fma c (* -4 a) (* b b))) b)) (- (sqrt (fma c (* -4 a) (* b b))) b))

prune2.5s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 28.6b

localize37.0ms

Local error

Found 4 expressions with local error:

21.6b
(sqrt (fma c (* -4 a) (* b b)))
1.3b
(- (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))

rewrite56.0ms

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))
16.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
2.0ms
(sqrt (fma c (* -4 a) (* b b)))
0.0ms
(fma c (* -4 a) (* b b))

series437.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
126.0ms
(sqrt (fma c (* -4 a) (* b b)))
111.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
107.0ms
(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))
93.0ms
(fma c (* -4 a) (* b b))

simplify21.8s

Counts
178 → 150
Calls
178 calls:
Slowest
620.0ms
(- (* (sqrt (fma c (* -4 a) (* b b))) (sqrt (fma c (* -4 a) (* b b)))) (* b b))
498.0ms
(* (- (sqrt (fma c (* -4 a) (* b b))) b) (/ 1 a))
436.0ms
(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))
410.0ms
(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) (cbrt 2)) (/ 1 a))
402.0ms
(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 (* (cbrt a) (cbrt a))))

prune1.8s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 28.6b

localize30.0ms

Local error

Found 4 expressions with local error:

21.6b
(sqrt (fma c (* -4 a) (* b b)))
1.3b
(- (sqrt (fma c (* -4 a) (* b b))) b)
0.2b
(/ 1 (/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)))
0.1b
(/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
831×times-frac
563×add-sqr-sqrt
464×*-un-lft-identity
366×add-cube-cbrt
98×difference-of-squares
93×associate-/r*
64×sqrt-prod
49×distribute-lft-out--
30×add-exp-log
22×div-inv
18×add-cbrt-cube div-exp prod-diff
9×cbrt-undiv
6×pow1 fma-neg associate-/r/ associate-/l* add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×rec-exp 1-exp
2×clear-num frac-2neg
1×rem-sqrt-square sub-neg sqrt-pow1 flip3-- pow1/2 diff-log pow-flip flip-- inv-pow
Counts
4 → 482
Calls
4 calls:
Slowest
15.0ms
(/ 1 (/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)))
14.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
11.0ms
(/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))
1.0ms
(sqrt (fma c (* -4 a) (* b b)))

series682.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
316.0ms
(/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))
167.0ms
(/ 1 (/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)))
102.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
97.0ms
(sqrt (fma c (* -4 a) (* b b)))

simplify2.4m

Counts
797 → 494
Calls
797 calls:
Slowest
1.2s
(* (* (/ 1 (/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))) (/ 1 (/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)))) (/ 1 (/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))))
847.0ms
(/ 1 (/ (sqrt a) (/ (+ (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt b)) (* (cbrt 2) (cbrt 2)))))
813.0ms
(/ (sqrt 1) (/ 1 (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (* (cbrt 2) (cbrt 2)))))
702.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (sqrt a) (/ (+ (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt b)) (* (cbrt 2) (cbrt 2)))))
698.0ms
(/ (sqrt 1) (/ (* (cbrt a) (cbrt a)) (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (sqrt 2))))

prune6.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 11.8b

localize41.0ms

Local error

Found 4 expressions with local error:

21.6b
(sqrt (fma c (* -4 a) (* b b)))
6.8b
(- (/ (/ (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))

rewrite288.0ms

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
31.0ms
(- (/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a) (/ (/ b 2) a))
13.0ms
(/ (/ (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))

series456.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
142.0ms
(/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a)
132.0ms
(- (/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a) (/ (/ b 2) a))
113.0ms
(sqrt (fma c (* -4 a) (* b b)))
68.0ms
(fma c (* -4 a) (* b b))