Details

Time bar (total: 1.0m)

sample171.0ms

Algorithm
intervals
Results
50.0ms191×body80valid
34.0ms35×body2560valid
32.0ms37×body1280valid
16.0ms106×body80nan
10.0ms16×body640valid
2.0ms4×body320valid
1.0ms4×body160valid
1.0ms1×body5120valid

simplify171.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
171.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.8b

localize52.0ms

Local error

Found 4 expressions with local error:

20.3b
(sqrt (fma b b (* (* a c) -4)))
0.9b
(- (sqrt (fma b b (* (* a c) -4))) b)
0.8b
(fma b b (* (* a c) -4))
0.1b
(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)

rewrite55.0ms

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 b b (* (* a c) -4))) b) 2) a)
14.0ms
(- (sqrt (fma b b (* (* a c) -4))) b)
2.0ms
(sqrt (fma b b (* (* a c) -4)))
0.0ms
(fma b b (* (* a c) -4))

series458.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
146.0ms
(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)
138.0ms
(sqrt (fma b b (* (* a c) -4)))
111.0ms
(- (sqrt (fma b b (* (* a c) -4))) b)
63.0ms
(fma b b (* (* a c) -4))

simplify15.7s

Counts
225 → 191
Calls
225 calls:
Slowest
540.0ms
(/ (/ (* (cbrt (- (sqrt (fma b b (* (* a c) -4))) b)) (cbrt (- (sqrt (fma b b (* (* a c) -4))) b))) (sqrt 2)) (* (cbrt a) (cbrt a)))
499.0ms
(/ (/ (* (cbrt (- (sqrt (fma b b (* (* a c) -4))) b)) (cbrt (- (sqrt (fma b b (* (* a c) -4))) b))) (* (cbrt 2) (cbrt 2))) (* (cbrt a) (cbrt a)))
267.0ms
(- b (* 2 (/ (* a c) b)))
213.0ms
(/ (* (* (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2)) (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2)) (* (* a a) a))
187.0ms
(/ (/ (* (* (- (sqrt (fma b b (* (* a c) -4))) b) (- (sqrt (fma b b (* (* a c) -4))) b)) (- (sqrt (fma b b (* (* a c) -4))) b)) (* (* 2 2) 2)) (* (* a a) a))

prune2.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.5b

localize44.0ms

Local error

Found 4 expressions with local error:

20.3b
(sqrt (fma (* a c) -4 (* b b)))
0.9b
(- (sqrt (fma (* a c) -4 (* b b))) b)
0.6b
(fma (* a c) -4 (* b b))
0.1b
(/ (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2) a)

rewrite65.0ms

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
40.0ms
(/ (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2) a)
15.0ms
(- (sqrt (fma (* a c) -4 (* b b))) b)
2.0ms
(sqrt (fma (* a c) -4 (* b b)))
0.0ms
(fma (* a c) -4 (* b b))

series546.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
209.0ms
(/ (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2) a)
146.0ms
(- (sqrt (fma (* a c) -4 (* b b))) b)
113.0ms
(sqrt (fma (* a c) -4 (* b b)))
78.0ms
(fma (* a c) -4 (* b b))

simplify15.7s

Counts
225 → 191
Calls
225 calls:
Slowest
440.0ms
(/ (/ (* (cbrt (- (sqrt (fma (* a c) -4 (* b b))) b)) (cbrt (- (sqrt (fma (* a c) -4 (* b b))) b))) (* (cbrt 2) (cbrt 2))) (* (cbrt a) (cbrt a)))
204.0ms
(/ (/ (* (cbrt (- (sqrt (fma (* a c) -4 (* b b))) b)) (cbrt (- (sqrt (fma (* a c) -4 (* b b))) b))) (sqrt 2)) (* (cbrt a) (cbrt a)))
186.0ms
(/ (/ (* (* (- (sqrt (fma (* a c) -4 (* b b))) b) (- (sqrt (fma (* a c) -4 (* b b))) b)) (- (sqrt (fma (* a c) -4 (* b b))) b)) (* (* 2 2) 2)) (* (* a a) a))
172.0ms
(/ (/ (* (cbrt (- (sqrt (fma (* a c) -4 (* b b))) b)) (cbrt (- (sqrt (fma (* a c) -4 (* b b))) b))) 1) (* (cbrt a) (cbrt a)))
166.0ms
(/ (/ (* (cbrt (- (sqrt (fma (* a c) -4 (* b b))) b)) (cbrt (- (sqrt (fma (* a c) -4 (* b b))) b))) (* (cbrt 2) (cbrt 2))) (sqrt a))

prune2.4s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.5b

localize43.0ms

Local error

Found 3 expressions with local error:

20.3b
(sqrt (fma (* -4 c) a (* b b)))
0.9b
(- (sqrt (fma (* -4 c) a (* b b))) b)
0.2b
(* (- (sqrt (fma (* -4 c) a (* b b))) b) (/ 1/2 a))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
30×*-un-lft-identity
26×add-cube-cbrt
18×prod-diff
17×sqrt-prod
13×associate-*r*
10×times-frac
8×add-cbrt-cube add-exp-log
6×pow1 fma-neg associate-*l*
5×add-log-exp
4×difference-of-squares
3×expm1-log1p-u flip3-- insert-posit16 log1p-expm1-u 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 div-inv
Counts
3 → 100
Calls
3 calls:
Slowest
31.0ms
(* (- (sqrt (fma (* -4 c) a (* b b))) b) (/ 1/2 a))
14.0ms
(- (sqrt (fma (* -4 c) a (* b b))) b)
2.0ms
(sqrt (fma (* -4 c) a (* b b)))

series355.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
136.0ms
(- (sqrt (fma (* -4 c) a (* b b))) b)
124.0ms
(* (- (sqrt (fma (* -4 c) a (* b b))) b) (/ 1/2 a))
94.0ms
(sqrt (fma (* -4 c) a (* b b)))

simplify5.2s

Counts
93 → 109
Calls
93 calls:
Slowest
606.0ms
(* (- (* (sqrt (fma (* -4 c) a (* b b))) (sqrt (fma (* -4 c) a (* b b)))) (* b b)) 1/2)
294.0ms
(* (- (pow (sqrt (fma (* -4 c) a (* b b))) 3) (pow b 3)) (/ 1/2 a))
267.0ms
(* (+ (* (sqrt (fma (* -4 c) a (* b b))) (sqrt (fma (* -4 c) a (* b b)))) (+ (* b b) (* (sqrt (fma (* -4 c) a (* b b))) b))) a)
236.0ms
(* (- (* (sqrt (fma (* -4 c) a (* b b))) (sqrt (fma (* -4 c) a (* b b)))) (* b b)) (/ 1/2 a))
196.0ms
(* (- (pow (sqrt (fma (* -4 c) a (* b b))) 3) (pow b 3)) 1/2)

prune1.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.4b

localize53.0ms

Local error

Found 4 expressions with local error:

20.3b
(sqrt (fma (* -4 c) a (* b b)))
0.9b
(- (sqrt (fma (* -4 c) a (* b b))) b)
0.4b
(/ (sqrt 1/2) a)
0.3b
(* (- (sqrt (fma (* -4 c) a (* b b))) b) (/ (sqrt 1/2) 1))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
69×add-sqr-sqrt
54×*-un-lft-identity
48×add-cube-cbrt
40×times-frac sqrt-prod
22×associate-*r*
18×prod-diff
13×add-exp-log
11×add-cbrt-cube
7×pow1
6×fma-neg associate-*l* associate-/l* add-log-exp
5×unswap-sqr
4×expm1-log1p-u insert-posit16 log1p-expm1-u difference-of-squares
3×associate-/r* flip3-- div-exp prod-exp flip--
2×frac-times cbrt-undiv associate-*l/ cbrt-unprod div-inv distribute-lft-out--
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log 1-exp pow-prod-down associate-*r/ *-commutative
Counts
4 → 155
Calls
4 calls:
Slowest
30.0ms
(* (- (sqrt (fma (* -4 c) a (* b b))) b) (/ (sqrt 1/2) 1))
10.0ms
(- (sqrt (fma (* -4 c) a (* b b))) b)
5.0ms
(/ (sqrt 1/2) a)
2.0ms
(sqrt (fma (* -4 c) a (* b b)))

series554.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
215.0ms
(* (- (sqrt (fma (* -4 c) a (* b b))) b) (/ (sqrt 1/2) 1))
136.0ms
(- (sqrt (fma (* -4 c) a (* b b))) b)
117.0ms
(sqrt (fma (* -4 c) a (* b b)))
86.0ms
(/ (sqrt 1/2) a)

simplify7.5s

Counts
157 → 167
Calls
157 calls:
Slowest
905.0ms
(* (- (* (sqrt (fma (* -4 c) a (* b b))) (sqrt (fma (* -4 c) a (* b b)))) (* b b)) (sqrt 1/2))
436.0ms
(* (* (* (- (sqrt (fma (* -4 c) a (* b b))) b) (- (sqrt (fma (* -4 c) a (* b b))) b)) (- (sqrt (fma (* -4 c) a (* b b))) b)) (* (* (/ (sqrt 1/2) 1) (/ (sqrt 1/2) 1)) (/ (sqrt 1/2) 1)))
377.0ms
(* (* (* (- (sqrt (fma (* -4 c) a (* b b))) b) (- (sqrt (fma (* -4 c) a (* b b))) b)) (- (sqrt (fma (* -4 c) a (* b b))) b)) (/ (* (* (sqrt 1/2) (sqrt 1/2)) (sqrt 1/2)) (* (* 1 1) 1)))
346.0ms
(* (+ (* (sqrt (fma (* -4 c) a (* b b))) (sqrt (fma (* -4 c) a (* b b)))) (+ (* b b) (* (sqrt (fma (* -4 c) a (* b b))) b))) 1)
262.0ms
(* (- (pow (sqrt (fma (* -4 c) a (* b b))) 3) (pow b 3)) (/ (sqrt 1/2) 1))

prune2.1s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.4b

regimes379.0ms

Accuracy

84.8% (4.3b remaining)

Error of 10.2b against oracle of 5.9b and baseline of 33.9b

bsearch201.0ms

end0.0ms

sample4.8s

Algorithm
intervals
Results
1.3s935×body1280valid
1.1s1072×body2560valid
1.0s5821×body80valid
476.0ms2839×body80nan
249.0ms428×body640valid
151.0ms92×body5120valid
102.0ms233×body320valid
36.0ms127×body160valid