Details

Time bar (total: 4.2m)

sample84.0ms

Algorithm
intervals
Results
26.0ms35×body2560valid
16.0ms181×body80valid
16.0ms36×body1280valid
6.0ms80×body80nan
4.0ms12×body640valid
2.0ms9×body320valid
0.0ms2×body160valid

simplify193.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
193.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.7b

localize44.0ms

Local error

Found 4 expressions with local error:

20.8b
(sqrt (fma (* a c) -4 (* b b)))
1.1b
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
0.2b
(fma (* a c) -4 (* b b))
0.1b
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
169×add-sqr-sqrt
168×*-un-lft-identity
159×times-frac
116×add-cube-cbrt
60×prod-diff
46×sqrt-prod
34×distribute-rgt-neg-in
26×distribute-lft-out-- difference-of-squares
25×associate-/l*
21×distribute-lft-neg-in
10×fma-neg
9×add-cbrt-cube add-exp-log
8×add-log-exp
7×neg-mul-1
5×pow1 div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×cbrt-undiv associate-/r* div-exp
2×diff-log div-sub
1×associate--l- neg-sub0 rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 neg-log fma-udef flip-- associate-/l/
Counts
4 → 240
Calls
4 calls:
Slowest
22.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
20.0ms
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)
2.0ms
(sqrt (fma (* a c) -4 (* b b)))
0.0ms
(fma (* a c) -4 (* b b))

series476.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
155.0ms
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)
139.0ms
(sqrt (fma (* a c) -4 (* b b)))
109.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
73.0ms
(fma (* a c) -4 (* b b))

simplify32.0s

Counts
334 → 252
Calls
334 calls:
Slowest
473.0ms
(/ (/ (sqrt (- (- b) (sqrt (fma (* a c) -4 (* b b))))) (sqrt 2)) (sqrt a))
456.0ms
(/ (/ (* (cbrt (- (- b) (sqrt (fma (* a c) -4 (* b b))))) (cbrt (- (- b) (sqrt (fma (* a c) -4 (* b b)))))) (* (cbrt 2) (cbrt 2))) (* (cbrt a) (cbrt a)))
266.0ms
(fma (- 1) 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))))))))
262.0ms
(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))))))))
259.0ms
(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))))))))

prune3.3s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.1b

localize23.0ms

Local error

Found 4 expressions with local error:

20.8b
(sqrt (fma c (* -4 a) (* b b)))
1.1b
(- (- (sqrt (fma c (* -4 a) (* b b)))) b)
0.1b
(/ (/ (+ (- (- (sqrt (fma c (* -4 a) (* b b)))) b) 0) 2) a)
0.0b
(fma c (* -4 a) (* b b))

rewrite186.0ms

Algorithm
rewrite-expression-head
Rules
204×*-un-lft-identity
138×times-frac
107×add-sqr-sqrt
104×add-cube-cbrt
48×prod-diff
37×distribute-rgt-neg-in
36×distribute-lft-out
27×sqrt-prod
26×distribute-lft-out--
24×distribute-lft-neg-in
22×associate-/l*
16×fma-neg
9×add-cbrt-cube add-exp-log
8×add-log-exp
5×pow1 div-inv
4×expm1-log1p-u neg-mul-1 insert-posit16 log1p-expm1-u
3×cbrt-undiv associate-/r* div-exp
2×diff-log div-sub
1×associate--l- neg-sub0 rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 neg-log associate-+l- fma-udef flip-- difference-of-squares associate-/l/
Counts
4 → 221
Calls
4 calls:
Slowest
159.0ms
(/ (/ (+ (- (- (sqrt (fma c (* -4 a) (* b b)))) b) 0) 2) a)
17.0ms
(- (- (sqrt (fma c (* -4 a) (* b b)))) b)
1.0ms
(sqrt (fma c (* -4 a) (* b b)))
1.0ms
(fma c (* -4 a) (* b b))

series398.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
120.0ms
(- (- (sqrt (fma c (* -4 a) (* b b)))) b)
105.0ms
(/ (/ (+ (- (- (sqrt (fma c (* -4 a) (* b b)))) b) 0) 2) a)
100.0ms
(sqrt (fma c (* -4 a) (* b b)))
72.0ms
(fma c (* -4 a) (* b b))

simplify27.2s

Counts
293 → 233
Calls
293 calls:
Slowest
453.0ms
(/ (/ (* (cbrt (+ (- (- (sqrt (fma c (* -4 a) (* b b)))) b) 0)) (cbrt (+ (- (- (sqrt (fma c (* -4 a) (* b b)))) b) 0))) (* (cbrt 2) (cbrt 2))) (* (cbrt a) (cbrt a)))
306.0ms
(/ (/ (+ (- (- (sqrt (fma c (* -4 a) (* b b)))) b) 0) (cbrt 2)) (cbrt a))
305.0ms
(/ (/ (* (* (+ (- (- (sqrt (fma c (* -4 a) (* b b)))) b) 0) (+ (- (- (sqrt (fma c (* -4 a) (* b b)))) b) 0)) (+ (- (- (sqrt (fma c (* -4 a) (* b b)))) b) 0)) (* (* 2 2) 2)) (* (* a a) a))
301.0ms
(/ (/ (+ (- (- (sqrt (fma c (* -4 a) (* b b)))) b) 0) (sqrt 2)) (cbrt a))
281.0ms
(/ (/ (* (cbrt (+ (- (- (sqrt (fma c (* -4 a) (* b b)))) b) 0)) (cbrt (+ (- (- (sqrt (fma c (* -4 a) (* b b)))) b) 0))) (* (cbrt 2) (cbrt 2))) (sqrt a))

prune3.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.1b

localize44.0ms

Local error

Found 4 expressions with local error:

20.8b
(sqrt (fma b b (* (* -4 c) a)))
1.1b
(- (- b) (sqrt (fma b b (* (* -4 c) a))))
0.3b
(fma b b (* (* -4 c) a))
0.1b
(/ (/ (+ (+ (- (- b) (sqrt (fma b b (* (* -4 c) a)))) (+ (- b) b)) 0) 2) a)

rewrite731.0ms

Algorithm
rewrite-expression-head
Rules
654×*-un-lft-identity
300×distribute-lft-out
285×times-frac
163×add-sqr-sqrt
158×add-cube-cbrt
94×distribute-rgt-neg-in
74×distribute-lft-out--
60×prod-diff
43×associate-/l*
34×sqrt-prod
21×distribute-lft-neg-in
10×fma-neg
9×add-cbrt-cube add-exp-log
8×add-log-exp
7×neg-mul-1
5×pow1 div-inv
4×expm1-log1p-u div-sub associate-+l- insert-posit16 log1p-expm1-u
3×cbrt-undiv associate-/r* div-exp
2×neg-sub0 diff-log difference-of-squares
1×associate--l- rem-sqrt-square clear-num associate-+r- sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 neg-log fma-udef flip-- associate-/l/
Counts
4 → 313
Calls
4 calls:
Slowest
690.0ms
(/ (/ (+ (+ (- (- b) (sqrt (fma b b (* (* -4 c) a)))) (+ (- b) b)) 0) 2) a)
20.0ms
(- (- b) (sqrt (fma b b (* (* -4 c) a))))
2.0ms
(sqrt (fma b b (* (* -4 c) a)))
0.0ms
(fma b b (* (* -4 c) a))

series438.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
124.0ms
(- (- b) (sqrt (fma b b (* (* -4 c) a))))
116.0ms
(/ (/ (+ (+ (- (- b) (sqrt (fma b b (* (* -4 c) a)))) (+ (- b) b)) 0) 2) a)
115.0ms
(sqrt (fma b b (* (* -4 c) a)))
84.0ms
(fma b b (* (* -4 c) a))

simplify1.1m

Counts
461 → 325
Calls
461 calls:
Slowest
820.0ms
(/ (/ (sqrt (+ (+ (- (- b) (sqrt (fma b b (* (* -4 c) a)))) (+ (- b) b)) 0)) 2) (cbrt a))
664.0ms
(/ (/ (* (cbrt (+ (+ (- (- b) (sqrt (fma b b (* (* -4 c) a)))) (+ (- b) b)) 0)) (cbrt (+ (+ (- (- b) (sqrt (fma b b (* (* -4 c) a)))) (+ (- b) b)) 0))) (* (cbrt 2) (cbrt 2))) (sqrt a))
570.0ms
(- (log (/ (+ (+ (- (- b) (sqrt (fma b b (* (* -4 c) a)))) (+ (- b) b)) 0) 2)) (log a))
561.0ms
(/ (/ (* (cbrt (+ (+ (- (- b) (sqrt (fma b b (* (* -4 c) a)))) (+ (- b) b)) 0)) (cbrt (+ (+ (- (- b) (sqrt (fma b b (* (* -4 c) a)))) (+ (- b) b)) 0))) (sqrt 2)) (* (cbrt a) (cbrt a)))
558.0ms
(/ (* (cbrt (/ (+ (+ (- (- b) (sqrt (fma b b (* (* -4 c) a)))) (+ (- b) b)) 0) 2)) (cbrt (/ (+ (+ (- (- b) (sqrt (fma b b (* (* -4 c) a)))) (+ (- b) b)) 0) 2))) (* (cbrt a) (cbrt a)))

prune4.7s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.1b

localize28.0ms

Local error

Found 4 expressions with local error:

20.8b
(sqrt (fma (* a c) -4 (* b b)))
1.1b
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
0.2b
(fma (* a c) -4 (* b b))
0.2b
(/ 1 (/ a (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
792×times-frac
512×add-sqr-sqrt
511×*-un-lft-identity
363×add-cube-cbrt
80×associate-/r*
74×distribute-lft-out-- difference-of-squares
70×sqrt-prod
60×prod-diff
58×distribute-rgt-neg-in
25×add-exp-log
21×distribute-lft-neg-in
17×div-inv
15×div-exp
13×add-cbrt-cube
10×fma-neg
8×add-log-exp
7×neg-mul-1
6×pow1 cbrt-undiv
5×associate-/r/
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×rec-exp 1-exp associate-/l*
2×diff-log
1×associate--l- neg-sub0 rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 neg-log fma-udef pow-flip flip-- inv-pow
Counts
4 → 469
Calls
4 calls:
Slowest
38.0ms
(/ 1 (/ a (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)))
10.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
1.0ms
(sqrt (fma (* a c) -4 (* b b)))
0.0ms
(fma (* a c) -4 (* b b))

series433.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
162.0ms
(/ 1 (/ a (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)))
101.0ms
(sqrt (fma (* a c) -4 (* b b)))
99.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
71.0ms
(fma (* a c) -4 (* b b))

simplify1.8m

Counts
724 → 481
Calls
724 calls:
Slowest
707.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (sqrt a) (/ (sqrt (- (- b) (sqrt (fma (* a c) -4 (* b b))))) (* (cbrt 2) (cbrt 2)))))
606.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt a) (cbrt a)) (/ (* (cbrt (- (- b) (sqrt (fma (* a c) -4 (* b b))))) (cbrt (- (- b) (sqrt (fma (* a c) -4 (* b b)))))) 1)))
539.0ms
(/ (sqrt 1) (/ (cbrt a) (/ (- (sqrt (- b)) (sqrt (sqrt (fma (* a c) -4 (* b b))))) 2)))
505.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt a) (cbrt a)) (- (- b) (sqrt (fma (* a c) -4 (* b b))))))
500.0ms
(/ 1 (/ (cbrt a) (/ (- (sqrt (- b)) (sqrt (sqrt (fma (* a c) -4 (* b b))))) (sqrt 2))))

prune4.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.1b

regimes313.0ms

Accuracy

84.1% (4.4b remaining)

Error of 9.8b against oracle of 5.4b and baseline of 33.2b

bsearch133.0ms

end0.0ms

sample3.0s

Algorithm
intervals
Results
746.0ms5826×body80valid
708.0ms1073×body2560valid
451.0ms879×body1280valid
438.0ms467×body640valid
273.0ms2853×body80nan
85.0ms99×body5120valid
79.0ms217×body320valid
18.0ms106×body160valid