Details

Time bar (total: 55.9s)

sample169.0ms

Algorithm
intervals
Results
52.0ms149×body160valid
40.0ms315×body80nan
34.0ms571×pre80true
15.0ms107×body80valid

simplify175.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
175.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize20.0ms

Local error

Found 4 expressions with local error:

29.9b
(- (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)))

rewrite56.0ms

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)
8.0ms
(- (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))

series452.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
135.0ms
(sqrt (fma c (* -4 a) (* b b)))
120.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
113.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
83.0ms
(fma c (* -4 a) (* b b))

simplify14.1s

Counts
225 → 191
Calls
225 calls:
Slowest
439.0ms
(/ (/ (* (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)))
234.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (sqrt 2)) (* (cbrt a) (cbrt a)))
184.0ms
(/ (/ (* (* (- (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))
175.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (* (cbrt 2) (cbrt 2))) 1)
161.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (* (cbrt 2) (cbrt 2))) (sqrt a))

prune2.4s

Pruning

32 alts after pruning (32 fresh and 0 done)

Merged error: 27.4b

localize43.0ms

Local error

Found 4 expressions with local error:

29.9b
(- (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))

rewrite72.0ms

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
47.0ms
(* (- (sqrt (fma b b (* (* a -4) c))) b) (/ 1/2 a))
22.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)
1.0ms
(sqrt (fma b b (* (* a -4) c)))
0.0ms
(fma b b (* (* a -4) c))

series856.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
487.0ms
(fma b b (* (* a -4) c))
166.0ms
(* (- (sqrt (fma b b (* (* a -4) c))) b) (/ 1/2 a))
105.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)
99.0ms
(sqrt (fma b b (* (* a -4) c)))

simplify5.6s

Counts
96 → 123
Calls
96 calls:
Slowest
426.0ms
(* (- (* (sqrt (fma b b (* (* a -4) c))) (sqrt (fma b b (* (* a -4) c)))) (* b b)) 1/2)
298.0ms
(* (+ (* (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)
291.0ms
(* (- (pow (sqrt (fma b b (* (* a -4) c))) 3) (pow b 3)) (/ 1/2 a))
239.0ms
(* (* (* (- (sqrt (fma b b (* (* a -4) c))) b) (- (sqrt (fma b b (* (* a -4) c))) b)) (- (sqrt (fma b b (* (* a -4) c))) b)) (/ (* (* 1/2 1/2) 1/2) (* (* a a) a)))
233.0ms
(* (- (pow (sqrt (fma b b (* (* a -4) c))) 3) (pow b 3)) 1/2)

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

localize59.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (* -2 (* a c)) (* (+ (sqrt (fma b b (* (* a -4) c))) b) a))
0.2b
(* (+ (sqrt (fma b b (* (* a -4) c))) b) a)
0.2b
(+ (sqrt (fma b b (* (* a -4) c))) b)
0.1b
(sqrt (fma b b (* (* a -4) c)))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
27×add-cbrt-cube add-exp-log
13×*-un-lft-identity
12×add-sqr-sqrt
10×prod-exp cbrt-unprod
9×add-cube-cbrt
7×pow1
6×cbrt-undiv fma-def div-exp sqrt-prod add-log-exp
4×expm1-log1p-u associate-*l* associate-*l/ insert-posit16 log1p-expm1-u
3×flip3-+ associate-*r* flip-+
2×associate-/r/ distribute-lft-out
1×+-commutative rem-sqrt-square clear-num associate-/r* sum-log frac-2neg sqrt-pow1 times-frac pow1/2 pow-prod-down *-commutative div-inv associate-/l* unswap-sqr
Counts
4 → 91
Calls
4 calls:
Slowest
47.0ms
(/ (* -2 (* a c)) (* (+ (sqrt (fma b b (* (* a -4) c))) b) a))
18.0ms
(* (+ (sqrt (fma b b (* (* a -4) c))) b) a)
6.0ms
(+ (sqrt (fma b b (* (* a -4) c))) b)
1.0ms
(sqrt (fma b b (* (* a -4) c)))

series560.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
220.0ms
(/ (* -2 (* a c)) (* (+ (sqrt (fma b b (* (* a -4) c))) b) a))
146.0ms
(* (+ (sqrt (fma b b (* (* a -4) c))) b) a)
105.0ms
(+ (sqrt (fma b b (* (* a -4) c))) b)
89.0ms
(sqrt (fma b b (* (* a -4) c)))

simplify15.5s

Counts
51 → 103
Calls
51 calls:
Slowest
2.1s
(/ (* (* (* -2 (* a c)) (* -2 (* a c))) (* -2 (* a c))) (* (* (* (+ (sqrt (fma b b (* (* a -4) c))) b) a) (* (+ (sqrt (fma b b (* (* a -4) c))) b) a)) (* (+ (sqrt (fma b b (* (* a -4) c))) b) a)))
2.1s
(/ (* (* (* -2 -2) -2) (* (* (* a a) a) (* (* c c) c))) (* (* (* (+ (sqrt (fma b b (* (* a -4) c))) b) a) (* (+ (sqrt (fma b b (* (* a -4) c))) b) a)) (* (+ (sqrt (fma b b (* (* a -4) c))) b) a)))
1.9s
(/ (* (* (* -2 -2) -2) (* (* (* a c) (* a c)) (* a c))) (* (* (* (+ (sqrt (fma b b (* (* a -4) c))) b) a) (* (+ (sqrt (fma b b (* (* a -4) c))) b) a)) (* (+ (sqrt (fma b b (* (* a -4) c))) b) a)))
1.6s
(/ (* (* (* -2 (* a c)) (* -2 (* a c))) (* -2 (* a 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)) (* (* a a) a)))
1.5s
(/ (* (* (* -2 -2) -2) (* (* (* a c) (* a c)) (* a 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)) (* (* a a) a)))

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
41×*-un-lft-identity
31×add-sqr-sqrt
25×times-frac add-cube-cbrt
18×associate-*l*
11×add-cbrt-cube add-exp-log
8×distribute-lft-out
7×pow1
6×fma-def sqrt-prod add-log-exp
4×expm1-log1p-u associate-/r* associate-/r/ insert-posit16 log1p-expm1-u
3×flip3-+ associate-*r* flip-+ associate-/l*
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
1×+-commutative rem-sqrt-square clear-num sum-log frac-2neg sqrt-pow1 pow1/2 pow-prod-down associate-*l/ *-commutative
Counts
4 → 113
Calls
4 calls:
Slowest
22.0ms
(* (/ -2 (+ (sqrt (fma b b (* (* a -4) c))) b)) c)
9.0ms
(/ -2 (+ (sqrt (fma b b (* (* a -4) c))) b))
6.0ms
(sqrt (fma b b (* (* a -4) c)))
6.0ms
(+ (sqrt (fma b b (* (* a -4) c))) b)

series584.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
185.0ms
(* (/ -2 (+ (sqrt (fma b b (* (* a -4) c))) b)) c)
143.0ms
(/ -2 (+ (sqrt (fma b b (* (* a -4) c))) b))
129.0ms
(sqrt (fma b b (* (* a -4) c)))
127.0ms
(+ (sqrt (fma b b (* (* a -4) c))) b)

simplify5.5s

Counts
86 → 125
Calls
86 calls:
Slowest
512.0ms
(/ -2 (- (* (sqrt (fma b b (* (* a -4) c))) (sqrt (fma b b (* (* a -4) c)))) (* b b)))
411.0ms
(* (* (* (/ -2 (+ (sqrt (fma b b (* (* a -4) c))) b)) (/ -2 (+ (sqrt (fma b b (* (* a -4) c))) b))) (/ -2 (+ (sqrt (fma b b (* (* a -4) c))) b))) (* (* c c) c))
399.0ms
(+ (* (sqrt (fma b b (* (* a -4) c))) (sqrt (fma b b (* (* a -4) c)))) (- (* b b) (* (sqrt (fma b b (* (* a -4) c))) b)))
320.0ms
(/ (* (* -2 -2) -2) (* (* (+ (sqrt (fma b b (* (* a -4) c))) b) (+ (sqrt (fma b b (* (* a -4) c))) b)) (+ (sqrt (fma b b (* (* a -4) c))) b)))
277.0ms
(- b (* 2 (/ (* a c) b)))

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes279.0ms

Accuracy

0% (0.3b remaining)

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

bsearch3.0ms

end0.0ms

sample5.5s

Algorithm
intervals
Results
1.8s4518×body160valid
1.6s8848×body80nan
1.1s16848×pre80true
544.0ms3481×body80valid
0.0ms1×body320valid