Details

Time bar (total: 11.7s)

sample58.0ms

Algorithm
intervals
Results
11.0ms153×body160valid
9.0ms287×body80nan
9.0ms543×pre80true
4.0ms42×body320valid
2.0ms61×body80valid

simplify73.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
01417
12517
24616
38616
410816
511616
done11616

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
38.9b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
11×add-sqr-sqrt
10×add-cube-cbrt fma-def add-log-exp
9×add-exp-log add-cbrt-cube
6×distribute-rgt-neg-in distribute-lft-out
5×pow1 times-frac associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-neg-in sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 90
Calls
4 calls:
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
8.0ms
(- (* b b) (* (* 4.0 a) c))
66.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
22.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series315.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
49.0ms
(- (* b b) (* (* 4.0 a) c))
109.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
83.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify893.0ms

Counts
102 → 102
Iterations

Useful iterations: done (890.0ms)

IterNodesCost
01671697
14331584
214811361
done50001347

prune248.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b
(/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite191.0ms

Algorithm
rewrite-expression-head
Rules
123×add-sqr-sqrt *-un-lft-identity
90×times-frac
79×add-cube-cbrt
61×prod-diff
41×sqrt-prod
32×distribute-rgt-neg-in
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
21×distribute-lft-neg-in
18×add-exp-log add-cbrt-cube
11×fma-neg
10×add-log-exp
8×associate-/r*
7×cbrt-undiv neg-mul-1 div-exp
6×associate-/r/
5×flip3-- flip--
4×pow1 expm1-log1p-u log1p-expm1-u div-inv
3×diff-log associate-/l/
2×sub-neg frac-2neg prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 flip3-+ neg-log flip-+
Counts
4 → 231
Calls
4 calls:
30.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms
(- (* b b) (* (* 4.0 a) c))
84.0ms
(/ (/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
58.0ms
(/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series465.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
45.0ms
(- (* b b) (* (* 4.0 a) c))
153.0ms
(/ (/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
188.0ms
(/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify1.3s

Counts
243 → 243
Iterations

Useful iterations: done (1.3s)

IterNodesCost
034010026
18127598
232366483
done50016397

prune535.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (+ 0 (* (* a c) 4.0)) (* (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) 2.0))

rewrite249.0ms

Algorithm
rewrite-expression-head
Rules
181×prod-diff
135×add-sqr-sqrt
133×*-un-lft-identity
125×add-cube-cbrt
92×sqrt-prod
62×distribute-rgt-in distribute-lft-in
59×distribute-rgt-neg-in
57×distribute-lft-neg-in
19×neg-mul-1
15×add-exp-log add-cbrt-cube
11×fma-neg
10×add-log-exp
7×associate-*r*
6×pow1
4×expm1-log1p-u sub-neg flip3-- associate-*r/ prod-exp flip-- cbrt-unprod log1p-expm1-u distribute-lft-out-- difference-of-squares
3×cbrt-undiv times-frac diff-log div-exp associate-*l* associate-/l*
2×associate-*l/ associate-/r/ associate-/l/
1×associate--l- neg-sub0 frac-2neg flip3-+ pow-prod-down neg-log clear-num associate-/r* *-commutative flip-+ div-inv unswap-sqr
Counts
4 → 285
Calls
4 calls:
93.0ms
(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
29.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms
(- (* b b) (* (* 4.0 a) c))
104.0ms
(/ (+ 0 (* (* a c) 4.0)) (* (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) 2.0))

series398.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
81.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
46.0ms
(- (* b b) (* (* 4.0 a) c))
160.0ms
(/ (+ 0 (* (* a c) 4.0)) (* (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) 2.0))

simplify1.5s

Counts
297 → 297
Iterations

Useful iterations: done (1.4s)

IterNodesCost
037517028
178611195
232448620
done50028367

prune413.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
0.3b
(* (/ (* 4.0 (* a c)) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

rewrite273.0ms

Algorithm
rewrite-expression-head
Rules
317×times-frac
280×add-sqr-sqrt
269×*-un-lft-identity
180×add-cube-cbrt
103×add-exp-log
85×associate-*r*
63×add-cbrt-cube
61×prod-diff
52×sqrt-prod
45×div-exp
44×distribute-lft-out-- difference-of-squares
43×distribute-rgt-neg-in
35×prod-exp
27×associate-/l*
24×cbrt-undiv
21×distribute-lft-neg-in cbrt-unprod
14×associate-/r/
11×fma-neg
10×div-inv add-log-exp
9×flip3-- flip--
7×neg-mul-1 associate-*l*
6×pow1
5×rec-exp 1-exp
4×expm1-log1p-u log1p-expm1-u unswap-sqr
3×diff-log associate-/r*
2×sub-neg
1×associate--l- neg-sub0 frac-times frac-2neg associate-*r/ pow-prod-down neg-log associate-*l/ clear-num *-commutative associate-/l/
Counts
4 → 378
Calls
4 calls:
29.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(- (* b b) (* (* 4.0 a) c))
64.0ms
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
147.0ms
(* (/ (* 4.0 (* a c)) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

series405.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
48.0ms
(- (* b b) (* (* 4.0 a) c))
121.0ms
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
157.0ms
(* (/ (* 4.0 (* a c)) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

simplify1.8s

Counts
390 → 390
Iterations

Useful iterations: 2 (835.0ms)

IterNodesCost
052514301
1140511489
246089771
done50009771

prune736.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes108.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
01925
12623
done2623

end0.0ms

sample1.6s

Algorithm
intervals
Results
332.0ms4761×body160valid
281.0ms8389×body80nan
271.0ms16389×pre80true
147.0ms1428×body320valid
64.0ms1811×body80valid