Details

Time bar (total: 2.1m)

sample129.0ms

Algorithm
intervals
Results
38.0ms24×body2560valid
26.0ms195×body80valid
21.0ms30×body1280valid
13.0ms100×body80nan
7.0ms14×body640valid
4.0ms10×body320valid
2.0ms3×body5120valid
1.0ms2×body160valid

simplify119.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
119.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.2b

localize35.0ms

Local error

Found 4 expressions with local error:

21.9b
(sqrt (fma b b (* (* a c) -4)))
0.8b
(fma b b (* (* a c) -4))
0.4b
(- (sqrt (fma b b (* (* a c) -4))) b)
0.1b
(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)

rewrite43.0ms

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
29.0ms
(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)
8.0ms
(- (sqrt (fma b b (* (* a c) -4))) b)
1.0ms
(sqrt (fma b b (* (* a c) -4)))
0.0ms
(fma b b (* (* a c) -4))

series409.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
134.0ms
(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)
112.0ms
(- (sqrt (fma b b (* (* a c) -4))) b)
99.0ms
(sqrt (fma b b (* (* a c) -4)))
64.0ms
(fma b b (* (* a c) -4))

simplify21.4s

Counts
282 → 191
Calls
282 calls:
Slowest
661.0ms
(* (* (/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a) (/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)) (/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a))
448.0ms
(/ (/ (sqrt (- (sqrt (fma b b (* (* a c) -4))) b)) 2) a)
419.0ms
(/ (/ (* (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)))
415.0ms
(- (* (sqrt (fma b b (* (* a c) -4))) (sqrt (fma b b (* (* a c) -4)))) (* b b))
373.0ms
(- (pow (sqrt (fma b b (* (* a c) -4))) 3) (pow b 3))

prune2.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.0b

localize47.0ms

Local error

Found 4 expressions with local error:

21.9b
(sqrt (fma (* a -4) c (* b b)))
11.4b
(/ (* (* a -4) c) (+ b (sqrt (fma (* a -4) c (* b b)))))
2.8b
(/ (/ (/ (* (* a -4) c) (+ b (sqrt (fma (* a -4) c (* b b))))) 2) a)
0.9b
(+ b (sqrt (fma (* a -4) c (* b b))))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
274×times-frac
141×*-un-lft-identity
112×add-sqr-sqrt
111×add-cube-cbrt
35×associate-/l*
33×add-cbrt-cube add-exp-log
26×associate-/r/
18×div-inv
15×cbrt-undiv div-exp distribute-lft-out
14×flip3-+ flip-+
7×associate-/r*
6×prod-exp cbrt-unprod add-log-exp
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×fma-def sqrt-prod
2×clear-num frac-2neg
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 pow1/2 associate-/l/
Counts
4 → 227
Calls
4 calls:
Slowest
35.0ms
(/ (* (* a -4) c) (+ b (sqrt (fma (* a -4) c (* b b)))))
31.0ms
(/ (/ (/ (* (* a -4) c) (+ b (sqrt (fma (* a -4) c (* b b))))) 2) a)
5.0ms
(+ b (sqrt (fma (* a -4) c (* b b))))
3.0ms
(sqrt (fma (* a -4) c (* b b)))

series640.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
246.0ms
(/ (* (* a -4) c) (+ b (sqrt (fma (* a -4) c (* b b)))))
189.0ms
(/ (/ (/ (* (* a -4) c) (+ b (sqrt (fma (* a -4) c (* b b))))) 2) a)
112.0ms
(sqrt (fma (* a -4) c (* b b)))
93.0ms
(+ b (sqrt (fma (* a -4) c (* b b))))

simplify1.2m

Counts
346 → 239
Calls
346 calls:
Slowest
1.3s
(/ (/ (/ (* (* (* (* a a) a) (* (* -4 -4) -4)) (* (* c c) c)) (* (* (+ b (sqrt (fma (* a -4) c (* b b)))) (+ b (sqrt (fma (* a -4) c (* b b))))) (+ b (sqrt (fma (* a -4) c (* b b)))))) (* (* 2 2) 2)) (* (* a a) a))
1.2s
(/ (/ (/ (* (* (* (* a -4) (* a -4)) (* a -4)) (* (* c c) c)) (* (* (+ b (sqrt (fma (* a -4) c (* b b)))) (+ b (sqrt (fma (* a -4) c (* b b))))) (+ b (sqrt (fma (* a -4) c (* b b)))))) (* (* 2 2) 2)) (* (* a a) a))
1.1s
(/ (/ (/ (* (* (* (* a -4) c) (* (* a -4) c)) (* (* a -4) c)) (* (* (+ b (sqrt (fma (* a -4) c (* b b)))) (+ b (sqrt (fma (* a -4) c (* b b))))) (+ b (sqrt (fma (* a -4) c (* b b)))))) (* (* 2 2) 2)) (* (* a a) a))
875.0ms
(/ (/ (/ (* (* a -4) c) (+ (pow b 3) (pow (sqrt (fma (* a -4) c (* b b))) 3))) 1) (sqrt a))
731.0ms
(/ (sqrt (/ (/ (* (* a -4) c) (+ b (sqrt (fma (* a -4) c (* b b))))) 2)) (sqrt a))

prune3.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.9b

localize51.0ms

Local error

Found 4 expressions with local error:

21.9b
(sqrt (fma b b (* (* a -4) c)))
0.9b
(+ b (sqrt (fma b b (* (* a -4) c))))
0.8b
(fma b b (* (* a -4) c))
0.1b
(/ (/ c -1/2) (+ b (sqrt (fma b b (* (* a -4) c)))))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
97×times-frac
85×*-un-lft-identity
56×add-sqr-sqrt
55×add-cube-cbrt
15×distribute-lft-out
13×associate-/l*
9×add-cbrt-cube add-exp-log
6×div-inv add-log-exp
5×pow1
4×expm1-log1p-u associate-/r* insert-posit16 log1p-expm1-u
3×cbrt-undiv fma-def div-exp sqrt-prod
2×flip3-+ associate-/r/ flip-+
1×+-commutative rem-sqrt-square clear-num sum-log frac-2neg sqrt-pow1 pow1/2 fma-udef associate-/l/
Counts
4 → 134
Calls
4 calls:
Slowest
18.0ms
(/ (/ c -1/2) (+ b (sqrt (fma b b (* (* a -4) c)))))
10.0ms
(+ b (sqrt (fma b b (* (* a -4) c))))
3.0ms
(sqrt (fma b b (* (* a -4) c)))
0.0ms
(fma b b (* (* a -4) c))

series590.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
272.0ms
(/ (/ c -1/2) (+ b (sqrt (fma b b (* (* a -4) c)))))
122.0ms
(sqrt (fma b b (* (* a -4) c)))
111.0ms
(+ b (sqrt (fma b b (* (* a -4) c))))
85.0ms
(fma b b (* (* a -4) c))

simplify14.3s

Counts
198 → 146
Calls
198 calls:
Slowest
406.0ms
(/ (/ (* (cbrt c) (cbrt c)) (* (cbrt -1/2) (cbrt -1/2))) (* (cbrt (+ b (sqrt (fma b b (* (* a -4) c))))) (cbrt (+ b (sqrt (fma b b (* (* a -4) c)))))))
347.0ms
(* (* (/ (/ c -1/2) (+ b (sqrt (fma b b (* (* a -4) c))))) (/ (/ c -1/2) (+ b (sqrt (fma b b (* (* a -4) c)))))) (/ (/ c -1/2) (+ b (sqrt (fma b b (* (* a -4) c))))))
329.0ms
(+ (* b b) (- (* (sqrt (fma b b (* (* a -4) c))) (sqrt (fma b b (* (* a -4) c)))) (* b (sqrt (fma b b (* (* a -4) c))))))
323.0ms
(/ (/ c -1/2) (- (* b b) (* (sqrt (fma b b (* (* a -4) c))) (sqrt (fma b b (* (* a -4) c))))))
293.0ms
(/ (/ c -1/2) (+ (pow b 3) (pow (sqrt (fma b b (* (* a -4) c))) 3)))

prune1.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.9b

localize34.0ms

Local error

Found 4 expressions with local error:

21.9b
(sqrt (fma b b (* (* a -4) c)))
21.9b
(sqrt (fma b b (* (* a -4) c)))
7.0b
(+ b (* (sqrt (sqrt (fma b b (* (* a -4) c)))) (sqrt (sqrt (fma b b (* (* a -4) c))))))
0.8b
(fma b b (* (* a -4) c))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
6×pow1 sqrt-prod add-log-exp
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×fma-def
2×rem-sqrt-square sqrt-pow1 pow1/2
1×+-commutative sum-log flip3-+ flip-+ fma-udef
Counts
4 → 60
Calls
4 calls:
Slowest
10.0ms
(+ b (* (sqrt (sqrt (fma b b (* (* a -4) c)))) (sqrt (sqrt (fma b b (* (* a -4) c))))))
2.0ms
(sqrt (fma b b (* (* a -4) c)))
2.0ms
(sqrt (fma b b (* (* a -4) c)))
0.0ms
(fma b b (* (* a -4) c))

series454.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
147.0ms
(+ b (* (sqrt (sqrt (fma b b (* (* a -4) c)))) (sqrt (sqrt (fma b b (* (* a -4) c))))))
128.0ms
(sqrt (fma b b (* (* a -4) c)))
96.0ms
(sqrt (fma b b (* (* a -4) c)))
83.0ms
(fma b b (* (* a -4) c))

simplify5.8s

Counts
72 → 72
Calls
72 calls:
Slowest
654.0ms
(- b (* 2 (/ (* a c) b)))
404.0ms
(* (* (+ b (* (sqrt (sqrt (fma b b (* (* a -4) c)))) (sqrt (sqrt (fma b b (* (* a -4) c)))))) (+ b (* (sqrt (sqrt (fma b b (* (* a -4) c)))) (sqrt (sqrt (fma b b (* (* a -4) c))))))) (+ b (* (sqrt (sqrt (fma b b (* (* a -4) c)))) (sqrt (sqrt (fma b b (* (* a -4) c)))))))
389.0ms
(+ (pow b 3) (pow (* (sqrt (sqrt (fma b b (* (* a -4) c)))) (sqrt (sqrt (fma b b (* (* a -4) c))))) 3))
311.0ms
(+ (* b b) (- (* (* (sqrt (sqrt (fma b b (* (* a -4) c)))) (sqrt (sqrt (fma b b (* (* a -4) c))))) (* (sqrt (sqrt (fma b b (* (* a -4) c)))) (sqrt (sqrt (fma b b (* (* a -4) c)))))) (* b (* (sqrt (sqrt (fma b b (* (* a -4) c)))) (sqrt (sqrt (fma b b (* (* a -4) c))))))))
290.0ms
(- b (* 2 (/ (* a c) b)))

prune1.0s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.9b

regimes249.0ms

Accuracy

96.1% (0.9b remaining)

Error of 6.4b against oracle of 5.5b and baseline of 28.9b

bsearch267.0ms

end0.0ms

sample4.6s

Algorithm
intervals
Results
1.5s5843×body80valid
1.1s1049×body2560valid
645.0ms889×body1280valid
474.0ms2926×body80nan
257.0ms490×body640valid
165.0ms107×body5120valid
91.0ms223×body320valid
30.0ms114×body160valid