Details

Time bar (total: 16.0s)

sample125.0ms

Algorithm
intervals
Results
26.0ms146×body160valid
22.0ms257×body80nan
20.0ms513×pre80true
10.0ms110×body80valid

simplify137.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
01417
12517
24616
38616
411916
512816
done12816

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.6b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
29.5b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite141.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
11×add-sqr-sqrt
10×fma-def add-cube-cbrt add-log-exp
9×add-cbrt-cube add-exp-log
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×neg-sub0 cbrt-undiv sum-log flip3-+ flip3-- sqrt-div div-exp associate-+l- flip-+ flip-- associate-/l/
1×+-commutative rem-sqrt-square clear-num associate-/r* neg-mul-1 sub-neg frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff neg-log prod-exp cbrt-unprod div-inv
Counts
4 → 90
Calls
4 calls:
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms
(- (* b b) (* (* 4.0 a) c))
81.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
24.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series441.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
55.0ms
(- (* b b) (* (* 4.0 a) c))
166.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
109.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.4s

Counts
102 → 102
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01671697
14521588
221131361
done50001352

prune574.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite286.0ms

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-cbrt-cube add-exp-log
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×expm1-log1p-u pow1 log1p-expm1-u div-inv
3×diff-log associate-/l/
2×clear-num sub-neg frac-2neg prod-exp cbrt-unprod
1×associate--l- neg-sub0 flip3-+ neg-log flip-+
Counts
4 → 231
Calls
4 calls:
14.0ms
(- (* b b) (* (* 4.0 a) c))
51.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
138.0ms
(/ (/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
66.0ms
(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series677.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(- (* b b) (* (* 4.0 a) c))
84.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
286.0ms
(/ (/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
252.0ms
(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify564.0ms

Counts
243 → 243
Iterations

Useful iterations: done (551.0ms)

IterNodesCost
033910026
18607622
done50006606

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
0.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.4b
(* (/ (* (* 4.0 a) c) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

rewrite342.0ms

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×associate-/r* diff-log
2×sub-neg
1×associate--l- neg-sub0 frac-times clear-num frac-2neg pow-prod-down neg-log associate-*l/ associate-*r/ *-commutative associate-/l/
Counts
4 → 378
Calls
4 calls:
16.0ms
(- (* b b) (* (* 4.0 a) c))
80.0ms
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
44.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
171.0ms
(* (/ (* (* 4.0 a) c) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

series607.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(- (* b b) (* (* 4.0 a) c))
178.0ms
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
116.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
247.0ms
(* (/ (* (* 4.0 a) c) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

simplify744.0ms

Counts
390 → 390
Iterations

Useful iterations: done (723.0ms)

IterNodesCost
052414295
1158611621
done500010083

prune1.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite345.0ms

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-cbrt-cube add-exp-log
11×fma-neg
10×add-log-exp
7×associate-*r*
6×pow1
4×expm1-log1p-u sub-neg flip3-- prod-exp associate-*r/ cbrt-unprod log1p-expm1-u flip-- 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 clear-num associate-/r* frac-2neg flip3-+ pow-prod-down neg-log *-commutative flip-+ div-inv unswap-sqr
Counts
4 → 285
Calls
4 calls:
13.0ms
(- (* b b) (* (* 4.0 a) c))
106.0ms
(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
49.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
149.0ms
(/ (+ 0 (* c (* 4.0 a))) (* (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) 2.0))

series614.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(- (* b b) (* (* 4.0 a) c))
166.0ms
(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
125.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
273.0ms
(/ (+ 0 (* c (* 4.0 a))) (* (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) 2.0))

simplify563.0ms

Counts
297 → 297
Iterations

Useful iterations: done (544.0ms)

IterNodesCost
037417028
194211259
done50018985

prune1.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes341.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
01825
12223
done2223

end0.0ms

sample3.9s

Algorithm
intervals
Results
1.2s4521×body160valid
885.0ms8544×body80nan
749.0ms16544×pre80true
297.0ms3479×body80valid