Details

Time bar (total: 57.5s)

sample124.0ms

Algorithm
intervals
Results
31.0ms30×body2560valid
28.0ms192×body80valid
23.0ms33×body1280valid
10.0ms80×body80nan
9.0ms15×body640valid
2.0ms6×body320valid
1.0ms1×body5120valid

simplify561.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
561.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.4b

localize22.0ms

Local error

Found 4 expressions with local error:

22.2b
(sqrt (fma c (* -4 a) (* b b)))
0.3b
(- (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))

rewrite51.0ms

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
23.0ms
(/ (/ (- (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))

series436.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
127.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
117.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
108.0ms
(sqrt (fma c (* -4 a) (* b b)))
83.0ms
(fma c (* -4 a) (* b b))

simplify13.3s

Counts
225 → 191
Calls
225 calls:
Slowest
359.0ms
(/ (/ (* (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)))
216.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (* (cbrt 2) (cbrt 2))) (sqrt a))
163.0ms
(/ (* (* (/ (- (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))
157.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (sqrt 2)) (* (cbrt a) (cbrt a)))
148.0ms
(/ (/ (* (* (- (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))

prune2.2s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 28.2b

localize35.0ms

Local error

Found 4 expressions with local error:

22.2b
(sqrt (fma c (* -4 a) (* b b)))
22.2b
(sqrt (fma c (* -4 a) (* b b)))
0.3b
(- (sqrt (fma c (* -4 a) (* b b))) b)
0.3b
(- (sqrt (fma c (* -4 a) (* b b))) b)

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
38×*-un-lft-identity
36×prod-diff
34×add-cube-cbrt
32×sqrt-prod
12×fma-neg
8×add-log-exp
6×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u difference-of-squares
2×rem-sqrt-square sub-neg sqrt-pow1 flip3-- pow1/2 diff-log flip-- distribute-lft-out--
Counts
4 → 116
Calls
4 calls:
Slowest
7.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
7.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
1.0ms
(sqrt (fma c (* -4 a) (* b b)))
1.0ms
(sqrt (fma c (* -4 a) (* b b)))

series459.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
124.0ms
(sqrt (fma c (* -4 a) (* b b)))
119.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
109.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
107.0ms
(sqrt (fma c (* -4 a) (* b b)))

simplify3.7s

Counts
116 → 128
Calls
116 calls:
Slowest
117.0ms
(fma (* (cbrt (sqrt (fma c (* -4 a) (* b b)))) (cbrt (sqrt (fma c (* -4 a) (* b b))))) (cbrt (sqrt (fma c (* -4 a) (* b b)))) (- (* b 1)))
106.0ms
(fma (* (cbrt (sqrt (fma c (* -4 a) (* b b)))) (cbrt (sqrt (fma c (* -4 a) (* b b))))) (cbrt (sqrt (fma c (* -4 a) (* b b)))) (- (* (cbrt b) (* (cbrt b) (cbrt b)))))
100.0ms
(fma (* (cbrt (sqrt (fma c (* -4 a) (* b b)))) (cbrt (sqrt (fma c (* -4 a) (* b b))))) (cbrt (sqrt (fma c (* -4 a) (* b b)))) (- (* (cbrt b) (* (cbrt b) (cbrt b)))))
86.0ms
(fma (* (cbrt (sqrt (fma c (* -4 a) (* b b)))) (cbrt (sqrt (fma c (* -4 a) (* b b))))) (cbrt (sqrt (fma c (* -4 a) (* b b)))) (- (* b 1)))
85.0ms
(fma (* (cbrt (sqrt (fma c (* -4 a) (* b b)))) (cbrt (sqrt (fma c (* -4 a) (* b b))))) (cbrt (sqrt (fma c (* -4 a) (* b b)))) (- (* (sqrt b) (sqrt b))))

prune2.0s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 28.2b

localize39.0ms

Local error

Found 4 expressions with local error:

22.2b
(sqrt (fma c (* -4 a) (* b b)))
22.2b
(sqrt (fma c (* -4 a) (* b b)))
0.3b
(* (/ (/ (sqrt (- (sqrt (fma c (* -4 a) (* b b))) b)) 1) 1) (/ (/ (sqrt (- (sqrt (fma c (* -4 a) (* b b))) b)) 2) a))
0.3b
(- (sqrt (fma c (* -4 a) (* b b))) b)

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
475×times-frac
437×add-sqr-sqrt
254×*-un-lft-identity
180×add-cube-cbrt
172×sqrt-prod
97×associate-*r* associate-*l*
82×add-exp-log
51×div-exp
44×unswap-sqr
40×add-cbrt-cube
38×difference-of-squares
21×prod-exp
19×distribute-lft-out--
18×cbrt-undiv prod-diff
15×1-exp
9×cbrt-unprod
8×pow1 div-inv
6×fma-neg add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times sub-neg flip3-- diff-log pow-prod-down associate-*l/ associate-*r/ *-commutative flip--
Counts
4 → 357
Calls
4 calls:
Slowest
75.0ms
(* (/ (/ (sqrt (- (sqrt (fma c (* -4 a) (* b b))) b)) 1) 1) (/ (/ (sqrt (- (sqrt (fma c (* -4 a) (* b b))) b)) 2) a))
8.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
1.0ms
(sqrt (fma c (* -4 a) (* b b)))
1.0ms
(sqrt (fma c (* -4 a) (* b b)))

series437.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
115.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
108.0ms
(sqrt (fma c (* -4 a) (* b b)))
107.0ms
(* (/ (/ (sqrt (- (sqrt (fma c (* -4 a) (* b b))) b)) 1) 1) (/ (/ (sqrt (- (sqrt (fma c (* -4 a) (* b b))) b)) 2) a))
106.0ms
(sqrt (fma c (* -4 a) (* b b)))

simplify29.5s

Counts
384 → 369
Calls
384 calls:
Slowest
517.0ms
(+ (- (- (log (sqrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (log 1)) (log 1)) (- (log (/ (sqrt (- (sqrt (fma c (* -4 a) (* b b))) b)) 2)) (log a)))
482.0ms
(+ (- (- (log (sqrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (log 1)) (log 1)) (log (/ (/ (sqrt (- (sqrt (fma c (* -4 a) (* b b))) b)) 2) a)))
478.0ms
(+ (- (- (log (sqrt (- (sqrt (fma c (* -4 a) (* b b))) b))) 0) 0) (log (/ (/ (sqrt (- (sqrt (fma c (* -4 a) (* b b))) b)) 2) a)))
454.0ms
(+ (- (log (/ (sqrt (- (sqrt (fma c (* -4 a) (* b b))) b)) 1)) 0) (- (- (log (sqrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (log 2)) (log a)))
445.0ms
(+ (log (/ (/ (sqrt (- (sqrt (fma c (* -4 a) (* b b))) b)) 1) 1)) (- (- (log (sqrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (log 2)) (log a)))

prune4.1s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 28.2b

localize29.0ms

Local error

Found 4 expressions with local error:

22.2b
(sqrt (fma c (* -4 a) (* b b)))
5.0b
(- (/ (/ (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))

rewrite224.0ms

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
30.0ms
(- (/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a) (/ (/ b 2) a))
14.0ms
(/ (/ (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))

series357.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
122.0ms
(/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a)
88.0ms
(sqrt (fma c (* -4 a) (* b b)))
87.0ms
(- (/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a) (/ (/ b 2) a))
59.0ms
(fma c (* -4 a) (* b b))