Details

Time bar (total: 2.5m)

sample124.0ms

Algorithm
intervals
Results
29.0ms195×body80valid
23.0ms24×body2560valid
21.0ms30×body1280valid
14.0ms100×body80nan
9.0ms14×body640valid
4.0ms10×body320valid
4.0ms3×body5120valid
1.0ms2×body160valid

simplify176.0ms

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.2b

localize20.0ms

Local error

Found 4 expressions with local error:

21.9b
(sqrt (fma b b (* c (* -4 a))))
0.8b
(fma b b (* c (* -4 a)))
0.4b
(- (sqrt (fma b b (* c (* -4 a)))) b)
0.1b
(/ (/ (- (sqrt (fma b b (* c (* -4 a)))) 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
28.0ms
(/ (/ (- (sqrt (fma b b (* c (* -4 a)))) b) 2) a)
7.0ms
(- (sqrt (fma b b (* c (* -4 a)))) b)
1.0ms
(sqrt (fma b b (* c (* -4 a))))
0.0ms
(fma b b (* c (* -4 a)))

series544.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
165.0ms
(/ (/ (- (sqrt (fma b b (* c (* -4 a)))) b) 2) a)
157.0ms
(- (sqrt (fma b b (* c (* -4 a)))) b)
136.0ms
(sqrt (fma b b (* c (* -4 a))))
86.0ms
(fma b b (* c (* -4 a)))

simplify23.4s

Counts
282 → 191
Calls
282 calls:
Slowest
552.0ms
(* (* (/ (/ (- (sqrt (fma b b (* c (* -4 a)))) b) 2) a) (/ (/ (- (sqrt (fma b b (* c (* -4 a)))) b) 2) a)) (/ (/ (- (sqrt (fma b b (* c (* -4 a)))) b) 2) a))
463.0ms
(/ (/ (* (cbrt (- (sqrt (fma b b (* c (* -4 a)))) b)) (cbrt (- (sqrt (fma b b (* c (* -4 a)))) b))) (* (cbrt 2) (cbrt 2))) (* (cbrt a) (cbrt a)))
427.0ms
(- (* (sqrt (fma b b (* c (* -4 a)))) (sqrt (fma b b (* c (* -4 a))))) (* b b))
390.0ms
(/ (/ 1 (* (cbrt 2) (cbrt 2))) 1)
346.0ms
(- (pow (sqrt (fma b b (* c (* -4 a)))) 3) (pow b 3))

prune2.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.0b

localize50.0ms

Local error

Found 4 expressions with local error:

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

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
274×times-frac
142×*-un-lft-identity
113×add-sqr-sqrt
112×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×fma-def prod-exp sqrt-prod cbrt-unprod add-log-exp
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u
2×clear-num frac-2neg
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 pow1/2 associate-/l/
Counts
4 → 230
Calls
4 calls:
Slowest
54.0ms
(/ (/ (/ (* c (* -4 a)) (+ (sqrt (fma b b (* c (* -4 a)))) b)) 2) a)
40.0ms
(/ (* c (* -4 a)) (+ (sqrt (fma b b (* c (* -4 a)))) b))
12.0ms
(+ (sqrt (fma b b (* c (* -4 a)))) b)
3.0ms
(sqrt (fma b b (* c (* -4 a))))

series748.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
270.0ms
(/ (* c (* -4 a)) (+ (sqrt (fma b b (* c (* -4 a)))) b))
247.0ms
(/ (/ (/ (* c (* -4 a)) (+ (sqrt (fma b b (* c (* -4 a)))) b)) 2) a)
117.0ms
(+ (sqrt (fma b b (* c (* -4 a)))) b)
113.0ms
(sqrt (fma b b (* c (* -4 a))))

simplify1.3m

Counts
346 → 242
Calls
346 calls:
Slowest
1.2s
(/ (/ (/ (* (* (* c c) c) (* (* (* -4 a) (* -4 a)) (* -4 a))) (* (* (+ (sqrt (fma b b (* c (* -4 a)))) b) (+ (sqrt (fma b b (* c (* -4 a)))) b)) (+ (sqrt (fma b b (* c (* -4 a)))) b))) (* (* 2 2) 2)) (* (* a a) a))
1.2s
(/ (/ (/ (* (* (* c (* -4 a)) (* c (* -4 a))) (* c (* -4 a))) (* (* (+ (sqrt (fma b b (* c (* -4 a)))) b) (+ (sqrt (fma b b (* c (* -4 a)))) b)) (+ (sqrt (fma b b (* c (* -4 a)))) b))) (* (* 2 2) 2)) (* (* a a) a))
1.1s
(/ (/ (/ (* (* (* c c) c) (* (* (* -4 -4) -4) (* (* a a) a))) (* (* (+ (sqrt (fma b b (* c (* -4 a)))) b) (+ (sqrt (fma b b (* c (* -4 a)))) b)) (+ (sqrt (fma b b (* c (* -4 a)))) b))) (* (* 2 2) 2)) (* (* a a) a))
645.0ms
(/ (/ (/ (* -4 a) (+ (sqrt (fma b b (* c (* -4 a)))) b)) (cbrt 2)) a)
622.0ms
(/ (/ (sqrt (/ (* c (* -4 a)) (+ (sqrt (fma b b (* c (* -4 a)))) b))) (* (cbrt 2) (cbrt 2))) (* (cbrt a) (cbrt a)))

prune3.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.9b

localize32.0ms

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

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity
9×add-sqr-sqrt add-cbrt-cube add-exp-log
8×add-cube-cbrt
6×add-log-exp
5×pow1
4×expm1-log1p-u associate-/r* times-frac insert-posit16 log1p-expm1-u
3×fma-def sqrt-prod 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 → 73
Calls
4 calls:
Slowest
15.0ms
(/ (* -2 c) (+ b (sqrt (fma b b (* (* a -4) c)))))
5.0ms
(+ b (sqrt (fma b b (* (* a -4) c))))
1.0ms
(sqrt (fma b b (* (* a -4) c)))
0.0ms
(fma b b (* (* a -4) c))

series583.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
257.0ms
(/ (* -2 c) (+ b (sqrt (fma b b (* (* a -4) c)))))
124.0ms
(+ b (sqrt (fma b b (* (* a -4) c))))
110.0ms
(sqrt (fma b b (* (* a -4) c)))
92.0ms
(fma b b (* (* a -4) c))

simplify8.2s

Counts
89 → 85
Calls
89 calls:
Slowest
640.0ms
(/ (* -2 c) (+ (pow b 3) (pow (sqrt (fma b b (* (* a -4) c))) 3)))
401.0ms
(* (* (/ (* -2 c) (+ b (sqrt (fma b b (* (* a -4) c))))) (/ (* -2 c) (+ b (sqrt (fma b b (* (* a -4) c)))))) (/ (* -2 c) (+ b (sqrt (fma b b (* (* a -4) c))))))
368.0ms
(/ (* -2 c) (- (* b b) (* (sqrt (fma b b (* (* a -4) c))) (sqrt (fma b b (* (* a -4) c))))))
318.0ms
(/ (* (* (* -2 -2) -2) (* (* c c) c)) (* (* (+ b (sqrt (fma b b (* (* a -4) c)))) (+ b (sqrt (fma b b (* (* a -4) c))))) (+ b (sqrt (fma b b (* (* a -4) c))))))
308.0ms
(- (* 2 b) (* 2 (/ (* a c) b)))

prune930.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.9b

localize25.0ms

Local error

Found 4 expressions with local error:

21.9b
(sqrt (fma (* a c) -4 (* b b)))
0.6b
(fma (* a c) -4 (* b b))
0.4b
(- (sqrt (fma (* a c) -4 (* b b))) b)
0.1b
(/ (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2) a)

rewrite46.0ms

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 (* a c) -4 (* b b))) b) 2) a)
7.0ms
(- (sqrt (fma (* a c) -4 (* b b))) b)
1.0ms
(sqrt (fma (* a c) -4 (* b b)))
0.0ms
(fma (* a c) -4 (* b b))

series486.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
160.0ms
(/ (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2) a)
137.0ms
(- (sqrt (fma (* a c) -4 (* b b))) b)
108.0ms
(sqrt (fma (* a c) -4 (* b b)))
80.0ms
(fma (* a c) -4 (* b b))

simplify23.4s

Counts
282 → 191
Calls
282 calls:
Slowest
689.0ms
(- (* (sqrt (fma (* a c) -4 (* b b))) (sqrt (fma (* a c) -4 (* b b)))) (* b b))
670.0ms
(* (* (/ (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2) a) (/ (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2) a)) (/ (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2) a))
415.0ms
(/ (/ (* (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)))
378.0ms
(- (pow (sqrt (fma (* a c) -4 (* b b))) 3) (pow b 3))
319.0ms
(* (* (- (sqrt (fma (* a c) -4 (* b b))) b) (- (sqrt (fma (* a c) -4 (* b b))) b)) (- (sqrt (fma (* a c) -4 (* b b))) b))

prune2.3s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 6.9b

regimes257.0ms

Accuracy

96.1% (0.9b remaining)

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

bsearch237.0ms

end0.0ms

sample5.0s

Algorithm
intervals
Results
1.5s5843×body80valid
1.5s1049×body2560valid
688.0ms889×body1280valid
434.0ms2926×body80nan
369.0ms490×body640valid
117.0ms223×body320valid
107.0ms107×body5120valid
30.0ms114×body160valid