Details

Time bar (total: 53.1s)

sample117.0ms

Algorithm
intervals
Results
35.0ms141×body160valid
26.0ms263×body80nan
24.0ms519×pre80true
12.0ms115×body80valid

simplify139.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
139.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize46.0ms

Local error

Found 4 expressions with local error:

29.1b
(- (sqrt (- (* b b) (* (* c a) 4))) b)
0.3b
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
0.2b
(- (* b b) (* (* c a) 4))
0.1b
(sqrt (- (* b b) (* (* c a) 4)))

rewrite198.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
13×*-un-lft-identity
9×add-cbrt-cube add-exp-log
8×add-log-exp
7×add-cube-cbrt
6×times-frac sqrt-prod associate-/l* difference-of-squares
5×pow1
4×flip3-- insert-posit16 flip--
3×distribute-lft-out--
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/l/
1×rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 pow1/2 div-sub prod-exp cbrt-unprod div-inv
Counts
4 → 76
Calls
4 calls:
Slowest
115.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
51.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
15.0ms
(sqrt (- (* b b) (* (* c a) 4)))
15.0ms
(- (* b b) (* (* c a) 4))

series486.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
151.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
138.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
120.0ms
(sqrt (- (* b b) (* (* c a) 4)))
77.0ms
(- (* b b) (* (* c a) 4))

simplify12.7s

Counts
105 → 88
Calls
105 calls:
Slowest
595.0ms
(- (* (sqrt (- (* b b) (* (* c a) 4))) (sqrt (- (* b b) (* (* c a) 4)))) (* b b))
447.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* c a) 4) (* (* c a) 4))))
396.0ms
(+ (* (* b b) (* b b)) (+ (* (* (* c a) 4) (* (* c a) 4)) (* (* b b) (* (* c a) 4))))
374.0ms
(- (* (* b b) (* b b)) (* (* (* c a) 4) (* (* c a) 4)))
350.0ms
(- (pow (sqrt (- (* b b) (* (* c a) 4))) 3) (pow b 3))

prune1000.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 8.4b

localize6.0ms

Local error

Found 0 expressions with local error:

rewrite0.0ms

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

series0.0ms

Counts
0 → 0
Calls
0 calls:
Slowest

simplify0.0ms

Counts
0 → 0
Calls
0 calls:
Slowest

prune67.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 8.4b

localize22.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (* a c) b)
0.2b
(/ (* -2 (/ (* a c) b)) (* 2 a))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
39×add-cbrt-cube add-exp-log
14×cbrt-undiv div-exp
13×prod-exp cbrt-unprod
4×add-sqr-sqrt associate-/r* *-un-lft-identity times-frac add-cube-cbrt
2×pow1 clear-num frac-2neg insert-posit16 div-inv associate-/l* add-log-exp
1×associate-*r/ associate-/l/
Counts
2 → 53
Calls
2 calls:
Slowest
37.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))
19.0ms
(/ (* a c) b)

series79.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
43.0ms
(/ (* a c) b)
36.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))

simplify15.2s

Counts
65 → 59
Calls
65 calls:
Slowest
1.3s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.3s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.2s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* 2 2) 2) (* (* a a) a)))
1.1s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 2 2) 2) (* (* a a) a)))
831.0ms
(/ (* (* (* -2 (/ (* a c) b)) (* -2 (/ (* a c) b))) (* -2 (/ (* a c) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))

prune557.0ms

Pruning

26 alts after pruning (25 fresh and 1 done)

Merged error: 8.3b

localize9.0ms

Local error

Found 1 expressions with local error:

0.3b
(/ 1 (/ (- b) c))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
222×times-frac
116×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
36×distribute-lft-neg-in distribute-rgt-neg-in
34×associate-/r*
12×neg-mul-1 add-exp-log
7×div-exp
6×add-cbrt-cube
5×div-inv
3×cbrt-undiv associate-/l*
2×pow1 rec-exp 1-exp
1×clear-num frac-2neg associate-/r/ insert-posit16 pow-flip inv-pow add-log-exp
Counts
1 → 161
Calls
1 calls:
Slowest
15.0ms
(/ 1 (/ (- b) c))

series18.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
18.0ms
(/ 1 (/ (- b) c))

simplify15.0s

Counts
266 → 164
Calls
266 calls:
Slowest
581.0ms
(* (* (/ 1 (/ (- b) c)) (/ 1 (/ (- b) c))) (/ 1 (/ (- b) c)))
484.0ms
(/ (* (* 1 1) 1) (/ (* (* (- b) (- b)) (- b)) (* (* c c) c)))
412.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (- (* (cbrt b) (cbrt b))) (* (cbrt c) (cbrt c))))
311.0ms
(/ (sqrt 1) (/ (* (cbrt (- b)) (cbrt (- b))) (* (cbrt c) (cbrt c))))
306.0ms
(/ (sqrt 1) (/ (- (* (cbrt b) (cbrt b))) (* (cbrt c) (cbrt c))))

prune1.3s

Pruning

29 alts after pruning (28 fresh and 1 done)

Merged error: 8.3b

regimes649.0ms

Accuracy

43.4% (7.6b remaining)

Error of 16.9b against oracle of 9.3b and baseline of 22.7b

bsearch39.0ms

end0.0ms

sample5.4s

Algorithm
intervals
Results
1.8s4484×body160valid
1.6s8539×body80nan
990.0ms16539×pre80true
450.0ms3516×body80valid