Details

Time bar (total: 29.1s)

sample138.0ms

Algorithm
intervals
Results
36.0ms42×body2560valid
22.0ms163×body80valid
21.0ms30×body1280valid
20.0ms18×body640valid
12.0ms89×body80nan
6.0ms7×body5120valid
3.0ms9×body320valid
1.0ms3×body160valid

simplify228.0ms

Calls
1 calls:
Slowest
228.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.7b

localize22.0ms

Local error

Found 4 expressions with local error:

25.3b
(sqrt (fma (* a c) -4 (* b b)))
0.7b
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
0.6b
(fma (* a c) -4 (* b b))
0.1b
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
24×prod-diff
23×*-un-lft-identity
21×add-cube-cbrt
16×sqrt-prod
7×neg-mul-1
6×add-log-exp
4×expm1-log1p-u pow1 add-cbrt-cube fma-neg add-exp-log insert-posit16 log1p-expm1-u associate-/l*
2×div-sub div-inv difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square clear-num sub-neg frac-2neg flip3-- pow1/2 diff-log fma-udef flip-- distribute-lft-out-- associate-/l/
Calls
4 calls:
Slowest
16.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
16.0ms
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)
1.0ms
(sqrt (fma (* a c) -4 (* b b)))
0.0ms
(fma (* a c) -4 (* b b))

series431.0ms

Calls
4 calls:
Slowest
127.0ms
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)
124.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
93.0ms
(fma (* a c) -4 (* b b))
86.0ms
(sqrt (fma (* a c) -4 (* b b)))

simplify5.0s

Calls
77 calls:
Slowest
126.0ms
(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (- (* (sqrt (fma (* a c) -4 (* b b))) 1)))
117.0ms
(- (* 2 (/ (* a c) b)) (* 2 b))
116.0ms
(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (- (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b))))))))
115.0ms
(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (- (* (sqrt (cbrt (fma (* a c) -4 (* b b)))) (sqrt (* (cbrt (fma (* a c) -4 (* b b))) (cbrt (fma (* a c) -4 (* b b))))))))
111.0ms
(fma (sqrt (- b)) (sqrt (- b)) (- (* (sqrt (sqrt (fma (* a c) -4 (* b b)))) (sqrt (sqrt (fma (* a c) -4 (* b b)))))))

prune1.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.2b

localize4.0ms

Local error

Found 0 expressions with local error:

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Calls
0 calls:
Slowest

series0.0ms

Calls
0 calls:
Slowest

simplify0.0ms

Calls
0 calls:
Slowest

prune37.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.2b

localize7.0ms

Local error

Found 4 expressions with local error:

25.3b
(sqrt (fma (* a c) -4 (* b b)))
0.7b
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
0.6b
(fma (* a c) -4 (* b b))
0.1b
(/ 1 (/ a (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
24×prod-diff
23×*-un-lft-identity
21×add-cube-cbrt
16×sqrt-prod
7×neg-mul-1
6×add-log-exp
5×pow1 associate-/r* add-exp-log
4×expm1-log1p-u add-cbrt-cube fma-neg insert-posit16 log1p-expm1-u
2×associate-/r/ div-inv difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square rec-exp clear-num sub-neg frac-2neg flip3-- pow1/2 diff-log fma-udef pow-flip flip-- distribute-lft-out-- inv-pow
Calls
4 calls:
Slowest
6.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
1.0ms
(sqrt (fma (* a c) -4 (* b b)))
1.0ms
(/ 1 (/ a (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)))
0.0ms
(fma (* a c) -4 (* b b))

series478.0ms

Calls
4 calls:
Slowest
142.0ms
(/ 1 (/ a (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)))
133.0ms
(sqrt (fma (* a c) -4 (* b b)))
109.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
94.0ms
(fma (* a c) -4 (* b b))

simplify5.0s

Calls
78 calls:
Slowest
135.0ms
(fma (sqrt (- b)) (sqrt (- b)) (- (* (sqrt (cbrt (fma (* a c) -4 (* b b)))) (sqrt (* (cbrt (fma (* a c) -4 (* b b))) (cbrt (fma (* a c) -4 (* b b))))))))
122.0ms
(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (- (* (sqrt (fma (* a c) -4 (* b b))) 1)))
117.0ms
(fma 1 (- b) (- (* (sqrt (fma (* a c) -4 (* b b))) 1)))
110.0ms
(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (- (* (sqrt (cbrt (fma (* a c) -4 (* b b)))) (sqrt (* (cbrt (fma (* a c) -4 (* b b))) (cbrt (fma (* a c) -4 (* b b))))))))
109.0ms
(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (- (* (sqrt (fma (* a c) -4 (* b b))) (sqrt 1))))

prune1.1s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.2b

localize13.0ms

Local error

Found 4 expressions with local error:

25.3b
(sqrt (fma (* a c) -4 (* b b)))
6.9b
(- (/ (/ (- b) 2) a) (/ (/ (sqrt (fma (* a c) -4 (* b b))) 2) a))
0.6b
(fma (* a c) -4 (* b b))
0.1b
(/ (/ (sqrt (fma (* a c) -4 (* b b))) 2) a)

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
17×*-un-lft-identity
16×prod-diff
15×add-cube-cbrt
13×div-inv
6×add-log-exp
4×expm1-log1p-u pow1 add-cbrt-cube fma-neg add-exp-log insert-posit16 log1p-expm1-u associate-/l*
3×sqrt-prod
2×div-sub
1×associate--l- neg-sub0 rem-sqrt-square clear-num sub-neg frac-2neg flip3-- distribute-rgt-out-- pow1/2 diff-log frac-sub fma-udef flip-- distribute-lft-out-- sub-div difference-of-squares associate-/l/
Calls
4 calls:
Slowest
12.0ms
(- (/ (/ (- b) 2) a) (/ (/ (sqrt (fma (* a c) -4 (* b b))) 2) a))
9.0ms
(/ (/ (sqrt (fma (* a c) -4 (* b b))) 2) a)
1.0ms
(sqrt (fma (* a c) -4 (* b b)))
0.0ms
(fma (* a c) -4 (* b b))

series455.0ms

Calls
4 calls:
Slowest
162.0ms
(/ (/ (sqrt (fma (* a c) -4 (* b b))) 2) a)
136.0ms
(- (/ (/ (- b) 2) a) (/ (/ (sqrt (fma (* a c) -4 (* b b))) 2) a))
78.0ms
(fma (* a c) -4 (* b b))
78.0ms
(sqrt (fma (* a c) -4 (* b b)))

simplify8.1s

Calls
65 calls:
Slowest
465.0ms
(fma (/ (- b) 2) (/ 1 a) (- (* (/ (/ (sqrt (fma (* a c) -4 (* b b))) 2) a) 1)))
365.0ms
(fma 1 (/ (/ (- b) 2) a) (- (* (sqrt (/ (/ (sqrt (fma (* a c) -4 (* b b))) 2) a)) (sqrt (/ (/ (sqrt (fma (* a c) -4 (* b b))) 2) a)))))
343.0ms
(fma (sqrt (/ (/ (- b) 2) a)) (sqrt (/ (/ (- b) 2) a)) (- (* (/ 1 a) (/ (sqrt (fma (* a c) -4 (* b b))) 2))))
311.0ms
(fma 1 (/ (/ (- b) 2) a) (- (* (/ 1 a) (/ (sqrt (fma (* a c) -4 (* b b))) 2))))
309.0ms
(fma (* (cbrt (/ (/ (- b) 2) a)) (cbrt (/ (/ (- b) 2) a))) (cbrt (/ (/ (- b) 2) a)) (- (* (/ (/ (sqrt (fma (* a c) -4 (* b b))) 2) a) 1)))

prune1.3s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 4.2b

regimes424.0ms

Accuracy

86.8% (4.5b remaining)

Error of 9.8b against oracle of 5.4b and baseline of 39.1b

bsearch232.0ms

end0.0ms

sample4.5s

Algorithm
intervals
Results
1.5s5754×body80valid
911.0ms1070×body2560valid
760.0ms918×body1280valid
399.0ms482×body640valid
383.0ms2916×body80nan
148.0ms117×body5120valid
88.0ms243×body320valid
61.0ms122×body160valid