Details

Time bar (total: 45.0s)

sample176.0ms

Algorithm
intervals
Results
58.0ms145×body160valid
40.0ms304×body80nan
35.0ms560×pre80true
15.0ms111×body80valid

simplify103.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
103.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.1b

localize38.0ms

Local error

Found 4 expressions with local error:

28.9b
(- (sqrt (fma c (* -4 a) (* b b))) b)
0.3b
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
0.2b
(fma c (* -4 a) (* b b))
0.1b
(sqrt (fma c (* -4 a) (* b b)))

rewrite30.0ms

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

series473.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
149.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
118.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
110.0ms
(sqrt (fma c (* -4 a) (* b b)))
95.0ms
(fma c (* -4 a) (* b b))

simplify14.7s

Counts
225 → 191
Calls
225 calls:
Slowest
544.0ms
(/ (/ (- (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt b)) (sqrt 2)) (cbrt a))
342.0ms
(/ (/ (* (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)))
225.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (* (cbrt 2) (cbrt 2))) (sqrt a))
218.0ms
(/ (/ (* (* (- (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))
218.0ms
(/ (* (* (/ (- (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))

prune2.3s

Pruning

30 alts after pruning (30 fresh and 0 done)

Merged error: 26.5b

localize51.0ms

Local error

Found 4 expressions with local error:

28.9b
(- (sqrt (fma b b (* (* a -4) c))) b)
0.4b
(* (- (sqrt (fma b b (* (* a -4) c))) b) (/ 1/2 a))
0.1b
(sqrt (fma b b (* (* a -4) c)))
0.0b
(fma b b (* (* a -4) c))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
31×*-un-lft-identity
27×add-cube-cbrt
18×prod-diff
17×sqrt-prod
13×associate-*r*
10×times-frac
9×add-cbrt-cube add-exp-log
7×pow1
6×fma-neg associate-*l* add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u difference-of-squares
3×flip3-- flip--
2×frac-times associate-*l/ prod-exp cbrt-unprod distribute-lft-out-- unswap-sqr
1×cbrt-undiv rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log div-exp pow-prod-down associate-*r/ *-commutative fma-udef div-inv
Counts
4 → 111
Calls
4 calls:
Slowest
24.0ms
(* (- (sqrt (fma b b (* (* a -4) c))) b) (/ 1/2 a))
11.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)
2.0ms
(sqrt (fma b b (* (* a -4) c)))
1.0ms
(fma b b (* (* a -4) c))

series544.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
199.0ms
(* (- (sqrt (fma b b (* (* a -4) c))) b) (/ 1/2 a))
156.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)
97.0ms
(sqrt (fma b b (* (* a -4) c)))
91.0ms
(fma b b (* (* a -4) c))

simplify5.8s

Counts
96 → 123
Calls
96 calls:
Slowest
505.0ms
(* (- (* (sqrt (fma b b (* (* a -4) c))) (sqrt (fma b b (* (* a -4) c)))) (* b b)) 1/2)
264.0ms
(* (+ (* (sqrt (fma b b (* (* a -4) c))) (sqrt (fma b b (* (* a -4) c)))) (+ (* b b) (* (sqrt (fma b b (* (* a -4) c))) b))) a)
243.0ms
(* (- (pow (sqrt (fma b b (* (* a -4) c))) 3) (pow b 3)) (/ 1/2 a))
223.0ms
(- b (* 2 (/ (* a c) b)))
218.0ms
(* (- (* (sqrt (fma b b (* (* a -4) c))) (sqrt (fma b b (* (* a -4) c)))) (* b b)) (/ 1/2 a))

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 1/2 a) (fma a (* c -4) 0))
0.2b
(+ (sqrt (fma b b (* (* a -4) c))) b)
0.2b
(/ (* (/ 1/2 a) (fma a (* c -4) 0)) (+ (sqrt (fma b b (* (* a -4) c))) b))
0.1b
(sqrt (fma b b (* (* a -4) c)))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt *-un-lft-identity
18×add-cbrt-cube add-exp-log
17×add-cube-cbrt
14×times-frac
13×associate-*l*
7×pow1
6×fma-def sqrt-prod add-log-exp
5×cbrt-undiv div-exp
4×expm1-log1p-u associate-/r* prod-exp cbrt-unprod insert-posit16 log1p-expm1-u
3×associate-*r* distribute-lft-out
2×flip3-+ associate-*l/ associate-/r/ flip-+ fma-udef div-inv unswap-sqr
1×distribute-rgt-in +-commutative rem-sqrt-square clear-num sum-log frac-2neg distribute-lft-in sqrt-pow1 pow1/2 pow-prod-down *-commutative associate-/l* associate-/l/
Counts
4 → 105
Calls
4 calls:
Slowest
35.0ms
(/ (* (/ 1/2 a) (fma a (* c -4) 0)) (+ (sqrt (fma b b (* (* a -4) c))) b))
12.0ms
(* (/ 1/2 a) (fma a (* c -4) 0))
12.0ms
(+ (sqrt (fma b b (* (* a -4) c))) b)
2.0ms
(sqrt (fma b b (* (* a -4) c)))

series605.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
315.0ms
(/ (* (/ 1/2 a) (fma a (* c -4) 0)) (+ (sqrt (fma b b (* (* a -4) c))) b))
120.0ms
(sqrt (fma b b (* (* a -4) c)))
111.0ms
(+ (sqrt (fma b b (* (* a -4) c))) b)
59.0ms
(* (/ 1/2 a) (fma a (* c -4) 0))

simplify7.5s

Counts
72 → 117
Calls
72 calls:
Slowest
1.2s
(* (* (* (/ 1/2 a) (/ 1/2 a)) (/ 1/2 a)) (* (* (fma a (* c -4) 0) (fma a (* c -4) 0)) (fma a (* c -4) 0)))
554.0ms
(/ (* (* (* (/ 1/2 a) (fma a (* c -4) 0)) (* (/ 1/2 a) (fma a (* c -4) 0))) (* (/ 1/2 a) (fma a (* c -4) 0))) (* (* (+ (sqrt (fma b b (* (* a -4) c))) b) (+ (sqrt (fma b b (* (* a -4) c))) b)) (+ (sqrt (fma b b (* (* a -4) c))) b)))
524.0ms
(/ (* (/ (* (* 1/2 1/2) 1/2) (* (* a a) a)) (* (* (fma a (* c -4) 0) (fma a (* c -4) 0)) (fma a (* c -4) 0))) (* (* (+ (sqrt (fma b b (* (* a -4) c))) b) (+ (sqrt (fma b b (* (* a -4) c))) b)) (+ (sqrt (fma b b (* (* a -4) c))) b)))
425.0ms
(+ (- (log 1/2) (log a)) (log (fma a (* c -4) 0)))
422.0ms
(/ (* (* (* (/ 1/2 a) (/ 1/2 a)) (/ 1/2 a)) (* (* (fma a (* c -4) 0) (fma a (* c -4) 0)) (fma a (* c -4) 0))) (* (* (+ (sqrt (fma b b (* (* a -4) c))) b) (+ (sqrt (fma b b (* (* a -4) c))) b)) (+ (sqrt (fma b b (* (* a -4) c))) b)))

prune1.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b
(+ (sqrt (fma b b (* (* a -4) c))) b)
0.2b
(/ (* -2 c) (+ (sqrt (fma b b (* (* a -4) c))) b))
0.1b
(sqrt (fma b b (* (* a -4) c)))
0.0b
(fma b b (* (* a -4) c))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
10×add-sqr-sqrt
9×add-cbrt-cube add-exp-log add-cube-cbrt
6×fma-def sqrt-prod add-log-exp
5×pow1
4×expm1-log1p-u associate-/r* times-frac insert-posit16 log1p-expm1-u
3×distribute-lft-out
2×cbrt-undiv flip3-+ div-exp associate-/r/ flip-+
1×+-commutative rem-sqrt-square clear-num sum-log frac-2neg sqrt-pow1 pow1/2 prod-exp cbrt-unprod fma-udef div-inv associate-/l*
Counts
4 → 76
Calls
4 calls:
Slowest
28.0ms
(/ (* -2 c) (+ (sqrt (fma b b (* (* a -4) c))) b))
12.0ms
(+ (sqrt (fma b b (* (* a -4) c))) b)
3.0ms
(sqrt (fma b b (* (* a -4) c)))
0.0ms
(fma b b (* (* a -4) c))

series562.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
232.0ms
(/ (* -2 c) (+ (sqrt (fma b b (* (* a -4) c))) b))
144.0ms
(+ (sqrt (fma b b (* (* a -4) c))) b)
112.0ms
(sqrt (fma b b (* (* a -4) c)))
73.0ms
(fma b b (* (* a -4) c))

simplify2.8s

Counts
42 → 88
Calls
42 calls:
Slowest
340.0ms
(+ (* (sqrt (fma b b (* (* a -4) c))) (sqrt (fma b b (* (* a -4) c)))) (- (* b b) (* (sqrt (fma b b (* (* a -4) c))) b)))
309.0ms
(/ (* (* (* -2 -2) -2) (* (* c c) c)) (* (* (+ (sqrt (fma b b (* (* a -4) c))) b) (+ (sqrt (fma b b (* (* a -4) c))) b)) (+ (sqrt (fma b b (* (* a -4) c))) b)))
251.0ms
(/ (* (* (* -2 c) (* -2 c)) (* -2 c)) (* (* (+ (sqrt (fma b b (* (* a -4) c))) b) (+ (sqrt (fma b b (* (* a -4) c))) b)) (+ (sqrt (fma b b (* (* a -4) c))) b)))
250.0ms
(- (* 2 b) (* 2 (/ (* a c) b)))
240.0ms
(- b (* 2 (/ (* a c) b)))

prune992.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

regimes241.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch2.0ms

end0.0ms

sample5.3s

Algorithm
intervals
Results
2.0s4468×body160valid
1.2s8706×body80nan
1.2s16706×pre80true
515.0ms3532×body80valid