Details

Time bar (total: 57.7s)

sample113.0ms

Algorithm
intervals
Results
31.0ms34×body1280valid
26.0ms200×body80valid
17.0ms22×body2560valid
13.0ms104×body80nan
6.0ms11×body640valid
2.0ms5×body320valid
1.0ms2×body5120valid
0.0ms1×body160valid

simplify157.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
157.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.0b

localize41.0ms

Local error

Found 4 expressions with local error:

20.6b
(sqrt (fma b b (* (* a c) -4)))
1.8b
(fma b b (* (* a c) -4))
0.2b
(- (sqrt (fma b b (* (* a c) -4))) b)
0.1b
(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)

rewrite52.0ms

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
30.0ms
(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)
16.0ms
(- (sqrt (fma b b (* (* a c) -4))) b)
3.0ms
(sqrt (fma b b (* (* a c) -4)))
1.0ms
(fma b b (* (* a c) -4))

series410.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
141.0ms
(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)
112.0ms
(sqrt (fma b b (* (* a c) -4)))
96.0ms
(- (sqrt (fma b b (* (* a c) -4))) b)
62.0ms
(fma b b (* (* a c) -4))

simplify16.3s

Counts
225 → 191
Calls
225 calls:
Slowest
497.0ms
(/ (/ (- (sqrt (sqrt (fma b b (* (* a c) -4)))) (sqrt b)) 2) a)
417.0ms
(/ (/ (* (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)))
249.0ms
(- b (* 2 (/ (* a c) b)))
222.0ms
(/ (* (* (/ (- (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))
219.0ms
(/ (/ (* (cbrt (- (sqrt (fma b b (* (* a c) -4))) b)) (cbrt (- (sqrt (fma b b (* (* a c) -4))) b))) (sqrt 2)) (* (cbrt a) (cbrt a)))

prune2.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.9b

localize33.0ms

Local error

Found 3 expressions with local error:

20.6b
(sqrt (fma (* -4 c) a (* b b)))
0.2b
(- (sqrt (fma (* -4 c) a (* b b))) b)
0.2b
(* (- (sqrt (fma (* -4 c) a (* b b))) b) (/ 1/2 a))

rewrite69.0ms

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
43.0ms
(* (- (sqrt (fma (* -4 c) a (* b b))) b) (/ 1/2 a))
16.0ms
(- (sqrt (fma (* -4 c) a (* b b))) b)
2.0ms
(sqrt (fma (* -4 c) a (* b b)))

series320.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
121.0ms
(* (- (sqrt (fma (* -4 c) a (* b b))) b) (/ 1/2 a))
107.0ms
(sqrt (fma (* -4 c) a (* b b)))
92.0ms
(- (sqrt (fma (* -4 c) a (* b b))) b)

simplify5.2s

Counts
93 → 109
Calls
93 calls:
Slowest
569.0ms
(* (- (* (sqrt (fma (* -4 c) a (* b b))) (sqrt (fma (* -4 c) a (* b b)))) (* b b)) 1/2)
289.0ms
(* (- (pow (sqrt (fma (* -4 c) a (* b b))) 3) (pow b 3)) (/ 1/2 a))
283.0ms
(* (+ (* (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)
209.0ms
(* (- (* (sqrt (fma (* -4 c) a (* b b))) (sqrt (fma (* -4 c) a (* b b)))) (* b b)) (/ 1/2 a))
205.0ms
(* (- (pow (sqrt (fma (* -4 c) a (* b b))) 3) (pow b 3)) 1/2)

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.9b

localize37.0ms

Local error

Found 3 expressions with local error:

20.6b
(sqrt (fma (* -4 c) a (* b b)))
0.2b
(- (sqrt (fma (* -4 c) a (* b b))) b)
0.1b
(/ (* (- (sqrt (fma (* -4 c) a (* b b))) b) 1/2) a)

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
22×*-un-lft-identity
20×add-cube-cbrt
18×prod-diff
16×sqrt-prod
8×add-cbrt-cube add-exp-log
6×fma-neg
5×add-log-exp
4×pow1
3×expm1-log1p-u associate-/r* times-frac insert-posit16 log1p-expm1-u
2×cbrt-undiv flip3-- div-exp associate-*l/ flip-- difference-of-squares associate-/l/
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log prod-exp cbrt-unprod div-inv associate-/l* distribute-lft-out--
Counts
3 → 84
Calls
3 calls:
Slowest
32.0ms
(/ (* (- (sqrt (fma (* -4 c) a (* b b))) b) 1/2) a)
7.0ms
(- (sqrt (fma (* -4 c) a (* b b))) b)
1.0ms
(sqrt (fma (* -4 c) a (* b b)))

series358.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
125.0ms
(- (sqrt (fma (* -4 c) a (* b b))) b)
122.0ms
(/ (* (- (sqrt (fma (* -4 c) a (* b b))) b) 1/2) a)
111.0ms
(sqrt (fma (* -4 c) a (* b b)))

simplify4.2s

Counts
76 → 93
Calls
76 calls:
Slowest
667.0ms
(* (- (* (sqrt (fma (* -4 c) a (* b b))) (sqrt (fma (* -4 c) a (* b b)))) (* b b)) 1/2)
312.0ms
(/ (* (* (* (- (sqrt (fma (* -4 c) a (* b b))) b) 1/2) (* (- (sqrt (fma (* -4 c) a (* b b))) b) 1/2)) (* (- (sqrt (fma (* -4 c) a (* b b))) b) 1/2)) (* (* a a) a))
286.0ms
(/ (* (* (* (- (sqrt (fma (* -4 c) a (* b b))) b) (- (sqrt (fma (* -4 c) a (* b b))) b)) (- (sqrt (fma (* -4 c) a (* b b))) b)) (* (* 1/2 1/2) 1/2)) (* (* a a) a))
204.0ms
(* (- (pow (sqrt (fma (* -4 c) a (* b b))) 3) (pow b 3)) 1/2)
136.0ms
(- (log (* (- (sqrt (fma (* -4 c) a (* b b))) b) 1/2)) (log a))

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.9b

localize28.0ms

Local error

Found 4 expressions with local error:

20.6b
(sqrt (fma (* -4 c) a (* b b)))
0.4b
(/ (sqrt 1/2) a)
0.3b
(* (- (sqrt (fma (* -4 c) a (* b b))) b) (/ (sqrt 1/2) 1))
0.2b
(* (* (- (sqrt (fma (* -4 c) a (* b b))) b) (/ (sqrt 1/2) 1)) (/ (sqrt 1/2) a))

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
64×add-sqr-sqrt
58×times-frac
51×*-un-lft-identity
47×add-cube-cbrt
44×associate-*r*
41×add-exp-log
36×sqrt-prod
32×add-cbrt-cube
17×prod-exp
12×pow1 cbrt-unprod
11×frac-times div-exp associate-*l/
7×cbrt-undiv associate-*l*
6×flip3-- flip-- associate-/l*
5×unswap-sqr
4×expm1-log1p-u pow-prod-down associate-*r/ insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* 1-exp div-inv
2×*-commutative difference-of-squares
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 distribute-lft-out--
Counts
4 → 174
Calls
4 calls:
Slowest
75.0ms
(* (* (- (sqrt (fma (* -4 c) a (* b b))) b) (/ (sqrt 1/2) 1)) (/ (sqrt 1/2) a))
31.0ms
(* (- (sqrt (fma (* -4 c) a (* b b))) b) (/ (sqrt 1/2) 1))
5.0ms
(/ (sqrt 1/2) a)
1.0ms
(sqrt (fma (* -4 c) a (* b b)))

series839.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
402.0ms
(* (* (- (sqrt (fma (* -4 c) a (* b b))) b) (/ (sqrt 1/2) 1)) (/ (sqrt 1/2) a))
246.0ms
(* (- (sqrt (fma (* -4 c) a (* b b))) b) (/ (sqrt 1/2) 1))
120.0ms
(sqrt (fma (* -4 c) a (* b b)))
71.0ms
(/ (sqrt 1/2) a)

simplify16.5s

Counts
164 → 186
Calls
164 calls:
Slowest
764.0ms
(* (+ (* (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)
649.0ms
(* (- (* (sqrt (fma (* -4 c) a (* b b))) (sqrt (fma (* -4 c) a (* b b)))) (* b b)) (sqrt 1/2))
590.0ms
(+ (+ (log (- (sqrt (fma (* -4 c) a (* b b))) b)) (- (log (sqrt 1/2)) (log 1))) (log (/ (sqrt 1/2) a)))
509.0ms
(+ (+ (log (- (sqrt (fma (* -4 c) a (* b b))) b)) (- (log (sqrt 1/2)) 0)) (log (/ (sqrt 1/2) a)))
508.0ms
(* (* (* (* (- (sqrt (fma (* -4 c) a (* b b))) b) (/ (sqrt 1/2) 1)) (* (- (sqrt (fma (* -4 c) a (* b b))) b) (/ (sqrt 1/2) 1))) (* (- (sqrt (fma (* -4 c) a (* b b))) b) (/ (sqrt 1/2) 1))) (/ (* (* (sqrt 1/2) (sqrt 1/2)) (sqrt 1/2)) (* (* a a) a)))

prune2.6s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.9b

regimes378.0ms

Accuracy

81.2% (4.8b remaining)

Error of 10.6b against oracle of 5.8b and baseline of 31.4b

bsearch371.0ms

end0.0ms

sample4.4s

Algorithm
intervals
Results
1.4s1113×body2560valid
911.0ms5763×body80valid
763.0ms883×body1280valid
469.0ms2958×body80nan
287.0ms486×body640valid
132.0ms115×body5120valid
110.0ms224×body320valid
56.0ms122×body160valid