Details

Time bar (total: 24.6s)

sample470.0ms

Algorithm
intervals
Results
100.0ms35×body2560valid
67.0ms194×body80valid
23.0ms28×body1280valid
12.0ms79×body80nan
7.0ms11×body640valid
5.0ms4×body5120valid
3.0ms5×body320valid
1.0ms4×body160valid

simplify100.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
99.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize19.0ms

Local error

Found 4 expressions with local error:

22.4b
(sqrt (- (* b_2 b_2) (* a c)))
1.0b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.8b
(- (* b_2 b_2) (* a c))
0.1b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)

rewrite139.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×*-un-lft-identity
18×times-frac
16×add-cube-cbrt
10×difference-of-squares
8×sqrt-prod add-log-exp
6×add-cbrt-cube add-exp-log associate-/l*
5×pow1 distribute-lft-out--
4×flip3-- insert-posit16 flip--
3×associate-/r*
2×sub-neg sqrt-div diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-sub div-exp div-inv
Counts
4 → 88
Calls
4 calls:
Slowest
72.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
39.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
12.0ms
(sqrt (- (* b_2 b_2) (* a c)))
7.0ms
(- (* b_2 b_2) (* a c))

series535.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
259.0ms
(sqrt (- (* b_2 b_2) (* a c)))
112.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
111.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
53.0ms
(- (* b_2 b_2) (* a c))

simplify4.0s

Counts
73 → 100
Calls
73 calls:
Slowest
366.0ms
(- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2))
336.0ms
(- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3))
273.0ms
(/ (* (* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (* (* a a) a))
259.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
205.0ms
(- b_2 (* 1/2 (/ (* a c) b_2)))

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.5b

localize26.0ms

Local error

Found 4 expressions with local error:

22.4b
(sqrt (- (* b_2 b_2) (* a c)))
1.0b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.8b
(- (* b_2 b_2) (* a c))
0.1b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×*-un-lft-identity
18×times-frac
16×add-cube-cbrt
10×difference-of-squares
8×sqrt-prod add-log-exp
6×add-cbrt-cube add-exp-log associate-/l*
5×pow1 distribute-lft-out--
4×flip3-- insert-posit16 flip--
3×associate-/r*
2×sub-neg sqrt-div diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-sub div-exp div-inv
Counts
4 → 88
Calls
4 calls:
Slowest
77.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
36.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
8.0ms
(- (* b_2 b_2) (* a c))
7.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series432.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
163.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
109.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
95.0ms
(sqrt (- (* b_2 b_2) (* a c)))
65.0ms
(- (* b_2 b_2) (* a c))

simplify3.9s

Counts
73 → 100
Calls
73 calls:
Slowest
432.0ms
(- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2))
304.0ms
(/ (* (* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (* (* a a) a))
266.0ms
(- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3))
260.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
249.0ms
(- b_2 (* 1/2 (/ (* a c) b_2)))

prune990.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.5b

localize44.0ms

Local error

Found 4 expressions with local error:

22.4b
(sqrt (- (* b_2 b_2) (* a c)))
22.4b
(sqrt (- (* b_2 b_2) (* a c)))
1.0b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.0b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×*-un-lft-identity
8×sqrt-prod add-log-exp
6×pow1 add-cube-cbrt
4×flip3-- add-cbrt-cube sqrt-div add-exp-log insert-posit16 flip-- difference-of-squares
2×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log distribute-lft-out--
Counts
4 → 64
Calls
4 calls:
Slowest
41.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
39.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.0ms
(sqrt (- (* b_2 b_2) (* a c)))
10.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series358.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
102.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
95.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
81.0ms
(sqrt (- (* b_2 b_2) (* a c)))
78.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.9s

Counts
38 → 76
Calls
38 calls:
Slowest
317.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
299.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
281.0ms
(- b_2 (* 1/2 (/ (* a c) b_2)))
262.0ms
(- b_2 (* 1/2 (/ (* a c) b_2)))
192.0ms
(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))

prune839.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 6.5b

localize30.0ms

Local error

Found 4 expressions with local error:

22.4b
(sqrt (- (* b_2 b_2) (* a c)))
22.4b
(sqrt (- (* b_2 b_2) (* a c)))
1.0b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.0b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)

rewrite118.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×*-un-lft-identity
8×sqrt-prod add-log-exp
6×pow1 add-cube-cbrt
4×flip3-- add-cbrt-cube sqrt-div add-exp-log insert-posit16 flip-- difference-of-squares
2×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log distribute-lft-out--
Counts
4 → 64
Calls
4 calls:
Slowest
47.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
34.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.0ms
(sqrt (- (* b_2 b_2) (* a c)))
14.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series380.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
109.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
108.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
86.0ms
(sqrt (- (* b_2 b_2) (* a c)))
76.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.9s

Counts
38 → 76
Calls
38 calls:
Slowest
356.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
324.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
256.0ms
(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))
231.0ms
(- b_2 (* 1/2 (/ (* a c) b_2)))
221.0ms
(- b_2 (* 1/2 (/ (* a c) b_2)))

prune901.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 6.5b

regimes357.0ms

Accuracy

83.7% (4.5b remaining)

Error of 9.9b against oracle of 5.4b and baseline of 33.1b

bsearch128.0ms

end0.0ms

sample3.7s

Algorithm
intervals
Results
855.0ms1024×body2560valid
829.0ms2988×body80nan
654.0ms5880×body80valid
594.0ms950×body1280valid
211.0ms437×body640valid
104.0ms109×body5120valid
94.0ms226×body320valid
23.0ms121×body160valid