Details

Time bar (total: 2.1m)

sample125.0ms

Algorithm
intervals
Results
32.0ms141×body160valid
31.0ms519×pre80true
27.0ms263×body80nan
12.0ms115×body80valid

simplify165.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
165.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.1b

localize20.0ms

Local error

Found 4 expressions with local error:

29.1b
(- (sqrt (fma b b (* c (* -4 a)))) b)
0.3b
(/ (/ (- (sqrt (fma b b (* c (* -4 a)))) b) 2) a)
0.1b
(sqrt (fma b b (* c (* -4 a))))
0.0b
(fma b b (* c (* -4 a)))

rewrite61.0ms

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
31.0ms
(/ (/ (- (sqrt (fma b b (* c (* -4 a)))) b) 2) a)
15.0ms
(- (sqrt (fma b b (* c (* -4 a)))) b)
8.0ms
(sqrt (fma b b (* c (* -4 a))))
0.0ms
(fma b b (* c (* -4 a)))

series423.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
142.0ms
(/ (/ (- (sqrt (fma b b (* c (* -4 a)))) b) 2) a)
119.0ms
(- (sqrt (fma b b (* c (* -4 a)))) b)
93.0ms
(sqrt (fma b b (* c (* -4 a))))
69.0ms
(fma b b (* c (* -4 a)))

simplify21.6s

Counts
282 → 191
Calls
282 calls:
Slowest
592.0ms
(* (* (/ (/ (- (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))
444.0ms
(- (* (sqrt (fma b b (* c (* -4 a)))) (sqrt (fma b b (* c (* -4 a))))) (* b b))
397.0ms
(/ (/ 1 (* (cbrt 2) (cbrt 2))) (sqrt a))
363.0ms
(- (pow (sqrt (fma b b (* c (* -4 a)))) 3) (pow b 3))
359.0ms
(/ (/ (* (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)))

prune1.9s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite128.0ms

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
61.0ms
(/ (/ (/ (* c (* -4 a)) (+ (sqrt (fma b b (* c (* -4 a)))) b)) 2) a)
43.0ms
(/ (* c (* -4 a)) (+ (sqrt (fma b b (* c (* -4 a)))) b))
12.0ms
(+ (sqrt (fma b b (* c (* -4 a)))) b)
2.0ms
(sqrt (fma b b (* c (* -4 a))))

series815.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
299.0ms
(/ (/ (/ (* c (* -4 a)) (+ (sqrt (fma b b (* c (* -4 a)))) b)) 2) a)
266.0ms
(/ (* c (* -4 a)) (+ (sqrt (fma b b (* c (* -4 a)))) b))
135.0ms
(+ (sqrt (fma b b (* c (* -4 a)))) b)
115.0ms
(sqrt (fma b b (* c (* -4 a))))

simplify1.2m

Counts
346 → 242
Calls
346 calls:
Slowest
1.3s
(/ (/ (/ (* (* (* 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))
1.0s
(/ (/ (/ (* (* (* 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))
819.0ms
(/ (/ (* c (* -4 a)) 1) (sqrt a))
675.0ms
(/ (/ (* (cbrt (/ (* c (* -4 a)) (+ (sqrt (fma b b (* c (* -4 a)))) b))) (cbrt (/ (* c (* -4 a)) (+ (sqrt (fma b b (* c (* -4 a)))) b)))) (* (cbrt 2) (cbrt 2))) 1)

prune2.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (* -2 c) (+ b (sqrt (fma b b (* (* a -4) c)))))
0.2b
(+ b (sqrt (fma b b (* (* a -4) c))))
0.1b
(sqrt (fma b b (* (* a -4) c)))
0.0b
(fma b b (* (* a -4) c))

rewrite43.0ms

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
29.0ms
(/ (* -2 c) (+ b (sqrt (fma b b (* (* a -4) c)))))
10.0ms
(+ b (sqrt (fma b b (* (* a -4) c))))
2.0ms
(sqrt (fma b b (* (* a -4) c)))
0.0ms
(fma b b (* (* a -4) c))

series530.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
239.0ms
(/ (* -2 c) (+ b (sqrt (fma b b (* (* a -4) c)))))
136.0ms
(+ b (sqrt (fma b b (* (* a -4) c))))
97.0ms
(sqrt (fma b b (* (* a -4) c)))
57.0ms
(fma b b (* (* a -4) c))

simplify7.7s

Counts
89 → 85
Calls
89 calls:
Slowest
502.0ms
(log1p (/ (* -2 c) (+ b (sqrt (fma b b (* (* a -4) c))))))
450.0ms
(* (* (/ (* -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))))))
351.0ms
(/ (* -2 c) (- (* b b) (* (sqrt (fma b b (* (* a -4) c))) (sqrt (fma b b (* (* a -4) c))))))
344.0ms
(/ (* (* (* -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))))))
288.0ms
(- b (* 2 (/ (* a c) b)))

prune942.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
40×*-un-lft-identity
30×add-sqr-sqrt
25×times-frac
24×add-cube-cbrt
18×associate-*r*
11×add-cbrt-cube add-exp-log
8×distribute-lft-out
7×pow1
6×add-log-exp
4×expm1-log1p-u associate-/r* associate-/r/ insert-posit16 log1p-expm1-u
3×fma-def flip3-+ associate-*l* sqrt-prod 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-*r/ *-commutative
Counts
4 → 110
Calls
4 calls:
Slowest
38.0ms
(* c (/ -2 (+ b (sqrt (fma b b (* c (* -4 a)))))))
12.0ms
(/ -2 (+ b (sqrt (fma b b (* c (* -4 a))))))
5.0ms
(+ b (sqrt (fma b b (* c (* -4 a)))))
1.0ms
(sqrt (fma b b (* c (* -4 a))))

series683.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
256.0ms
(* c (/ -2 (+ b (sqrt (fma b b (* c (* -4 a)))))))
175.0ms
(/ -2 (+ b (sqrt (fma b b (* c (* -4 a))))))
144.0ms
(+ b (sqrt (fma b b (* c (* -4 a)))))
109.0ms
(sqrt (fma b b (* c (* -4 a))))

simplify10.5s

Counts
135 → 122
Calls
135 calls:
Slowest
384.0ms
(* (* (/ -2 (+ b (sqrt (fma b b (* c (* -4 a)))))) (/ -2 (+ b (sqrt (fma b b (* c (* -4 a))))))) (/ -2 (+ b (sqrt (fma b b (* c (* -4 a)))))))
329.0ms
(* (* (* c c) c) (* (* (/ -2 (+ b (sqrt (fma b b (* c (* -4 a)))))) (/ -2 (+ b (sqrt (fma b b (* c (* -4 a))))))) (/ -2 (+ b (sqrt (fma b b (* c (* -4 a))))))))
326.0ms
(* c (/ -2 (- (* b b) (* (sqrt (fma b b (* c (* -4 a)))) (sqrt (fma b b (* c (* -4 a))))))))
321.0ms
(* (* (* c (/ -2 (+ b (sqrt (fma b b (* c (* -4 a))))))) (* c (/ -2 (+ b (sqrt (fma b b (* c (* -4 a)))))))) (* c (/ -2 (+ b (sqrt (fma b b (* c (* -4 a))))))))
315.0ms
(/ (* (* -2 -2) -2) (* (* (+ b (sqrt (fma b b (* c (* -4 a))))) (+ b (sqrt (fma b b (* c (* -4 a)))))) (+ b (sqrt (fma b b (* c (* -4 a)))))))

prune1.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes259.0ms

Accuracy

0% (0.2b remaining)

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

bsearch5.0ms

end0.0ms

sample4.8s

Algorithm
intervals
Results
1.5s16539×pre80true
1.3s4484×body160valid
1.1s8539×body80nan
532.0ms3516×body80valid