Details

Time bar (total: 59.6s)

sample122.0ms

Algorithm
intervals
Results
33.0ms35×body2560valid
24.0ms182×body80valid
20.0ms29×body1280valid
13.0ms97×body80nan
7.0ms12×body640valid
3.0ms6×body320valid
2.0ms2×body5120valid
1.0ms2×body160valid

simplify239.0ms

Calls
1 calls:
Slowest
238.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.2b

localize25.0ms

Local error

Found 4 expressions with local error:

25.7b
(sqrt (fma (* a c) -4 (* b b)))
0.8b
(fma (* a c) -4 (* b b))
0.5b
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
0.1b
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)

rewrite49.0ms

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/
Calls
4 calls:
Slowest
22.0ms
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)
21.0ms
(- (- 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))

series389.0ms

Calls
4 calls:
Slowest
135.0ms
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)
107.0ms
(sqrt (fma (* a c) -4 (* b b)))
82.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
65.0ms
(fma (* a c) -4 (* b b))

simplify30.2s

Calls
334 calls:
Slowest
459.0ms
(/ (/ (* (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)))
284.0ms
(fma (- (sqrt b)) (sqrt 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))))))))
266.0ms
(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))))))))
261.0ms
(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))))))))
236.0ms
(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))))))))

prune3.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.8b

localize44.0ms

Local error

Found 3 expressions with local error:

25.7b
(sqrt (fma a (* c -4) (* b b)))
0.5b
(+ b (sqrt (fma a (* c -4) (* b b))))
0.2b
(* (- (+ b (sqrt (fma a (* c -4) (* b b))))) (/ 1/2 a))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt *-un-lft-identity
15×add-cube-cbrt
13×associate-*r*
12×associate-*l*
10×times-frac
8×add-cbrt-cube add-exp-log
6×pow1
5×add-log-exp
4×distribute-lft-neg-in distribute-rgt-neg-in distribute-neg-frac
3×expm1-log1p-u fma-def flip3-+ sqrt-prod flip-+ insert-posit16 log1p-expm1-u 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 div-inv
Calls
3 calls:
Slowest
50.0ms
(* (- (+ b (sqrt (fma a (* c -4) (* b b))))) (/ 1/2 a))
10.0ms
(+ b (sqrt (fma a (* c -4) (* b b))))
3.0ms
(sqrt (fma a (* c -4) (* b b)))

series350.0ms

Calls
3 calls:
Slowest
129.0ms
(* (- (+ b (sqrt (fma a (* c -4) (* b b))))) (/ 1/2 a))
127.0ms
(+ b (sqrt (fma a (* c -4) (* b b))))
93.0ms
(sqrt (fma a (* c -4) (* b b)))

simplify4.2s

Calls
55 calls:
Slowest
613.0ms
(* (- (+ (pow b 3) (pow (sqrt (fma a (* c -4) (* b b))) 3))) (/ 1/2 a))
392.0ms
(* (* (* (- (+ 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)))
287.0ms
(- (* 2 b) (* 2 (/ (* a c) b)))
271.0ms
(* (* (* (- (+ 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)))
258.0ms
(* (- (+ b (sqrt (fma a (* c -4) (* b b))))) (/ 1/2 a))

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.8b

localize58.0ms

Local error

Found 4 expressions with local error:

25.7b
(sqrt (fma (* a c) -4 (* b b)))
1.0b
(/ 1 (sqrt 2))
0.8b
(fma (* a c) -4 (* b b))
0.5b
(- (- b) (sqrt (fma (* a c) -4 (* b b))))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
66×add-sqr-sqrt
65×*-un-lft-identity
61×add-cube-cbrt
60×prod-diff
46×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
18×times-frac
10×fma-neg
8×add-exp-log add-log-exp
7×pow1 neg-mul-1
6×associate-/r* add-cbrt-cube
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×pow-flip associate-/l*
2×sqrt-pow1 pow1/2 diff-log div-exp distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 cbrt-undiv rem-sqrt-square rec-exp clear-num sub-neg frac-2neg flip3-- 1-exp neg-log fma-udef div-inv flip-- inv-pow
Calls
4 calls:
Slowest
31.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
10.0ms
(/ 1 (sqrt 2))
3.0ms
(sqrt (fma (* a c) -4 (* b b)))
0.0ms
(fma (* a c) -4 (* b b))

series321.0ms

Calls
4 calls:
Slowest
126.0ms
(sqrt (fma (* a c) -4 (* b b)))
122.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
72.0ms
(fma (* a c) -4 (* b b))
0.0ms
(/ 1 (sqrt 2))

simplify14.5s

Calls
200 calls:
Slowest
283.0ms
(fma (sqrt (- b)) (sqrt (- 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))))))))
275.0ms
(* (/ 1 (sqrt 2)) (/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) (sqrt 2)) a))
241.0ms
(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))))))))
240.0ms
(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))))))))
230.0ms
(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))))))))

prune2.5s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 7.8b

localize49.0ms

Local error

Found 4 expressions with local error:

25.7b
(sqrt (fma (* a c) -4 (* b b)))
5.7b
(- (/ (/ (- 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)

rewrite848.0ms

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/
Calls
4 calls:
Slowest
74.0ms
(- (/ (/ (- b) 2) a) (/ (/ (sqrt (fma (* a c) -4 (* b b))) 2) a))
8.0ms
(/ (/ (sqrt (fma (* a c) -4 (* b b))) 2) a)
2.0ms
(sqrt (fma (* a c) -4 (* b b)))
0.0ms
(fma (* a c) -4 (* b b))

series1.0s

Calls
4 calls:
Slowest
591.0ms
(fma (* a c) -4 (* b b))
171.0ms
(/ (/ (sqrt (fma (* a c) -4 (* b b))) 2) a)
127.0ms
(- (/ (/ (- b) 2) a) (/ (/ (sqrt (fma (* a c) -4 (* b b))) 2) a))
114.0ms
(sqrt (fma (* a c) -4 (* b b)))