Details

Time bar (total: 21.4s)

sample111.0ms

Algorithm
intervals
Results
22.0ms147×body160valid
21.0ms282×body80nan
17.0ms538×pre80true
11.0ms45×body320valid
5.0ms64×body80valid

simplify165.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
01417
12517
24616
38616
410816
511616
done11616

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.7b

localize24.0ms

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))
39.1b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite164.0ms

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:
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(- (* b b) (* (* 4.0 a) c))
95.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
43.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series463.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
65.0ms
(- (* b b) (* (* 4.0 a) c))
203.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
98.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.2s

Counts
102 → 102
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01671697
14331584
214811361
done50001347

prune848.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize19.0ms

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)))))

rewrite336.0ms

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:
50.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(- (* b b) (* (* 4.0 a) c))
144.0ms
(/ (/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
123.0ms
(/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series753.0ms

Counts
4 → 12
Calls
4 calls:
148.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
65.0ms
(- (* b b) (* (* 4.0 a) c))
237.0ms
(/ (/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
302.0ms
(/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify2.1s

Counts
243 → 243
Iterations

Useful iterations: done (2.1s)

IterNodesCost
034010026
18127598
232366483
done50016397

prune818.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

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

rewrite385.0ms

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:
42.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(- (* b b) (* (* 4.0 a) c))
140.0ms
(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
163.0ms
(/ (+ 0 (* (* a c) 4.0)) (* (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) 2.0))

series618.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
82.0ms
(- (* b b) (* (* 4.0 a) c))
202.0ms
(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
223.0ms
(/ (+ 0 (* (* a c) 4.0)) (* (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) 2.0))

simplify2.4s

Counts
297 → 297
Iterations

Useful iterations: done (2.4s)

IterNodesCost
037517028
178611195
232458620
done50018367

prune746.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma (* (* c 4.0) a) (fma b b (* 4.0 (* a c))) (pow b 4)))))) (* 2.0 a))
0.3b
(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma (* (* c 4.0) a) (fma b b (* 4.0 (* a c))) (pow b 4)))
0.3b
(/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma (* (* c 4.0) a) (fma b b (* 4.0 (* a c))) (pow b 4))))))
0.7b
(pow (* (* 4.0 a) c) 3)

rewrite682.0ms

Algorithm
rewrite-expression-head
Rules
155×add-sqr-sqrt
142×times-frac
105×*-un-lft-identity
57×add-cube-cbrt
54×difference-of-squares
43×associate-/l*
26×add-exp-log add-cbrt-cube
24×distribute-lft-out--
21×sqr-pow
20×sqrt-prod
12×associate-/r*
10×pow1 distribute-rgt-neg-in
9×unpow-prod-down
8×cbrt-undiv div-exp
6×associate-/r/
5×prod-exp cbrt-unprod div-inv associate-/l/
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u add-log-exp
3×pow-unpow pow-pow frac-2neg pow-prod-down pow-exp clear-num rem-cube-cbrt
1×cube-mult pow-to-exp flip3-+ unpow3 div-sub cube-prod flip-+
Counts
4 → 222
Calls
4 calls:
348.0ms
(/ (/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma (* (* c 4.0) a) (fma b b (* 4.0 (* a c))) (pow b 4)))))) (* 2.0 a))
64.0ms
(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma (* (* c 4.0) a) (fma b b (* 4.0 (* a c))) (pow b 4)))
217.0ms
(/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma (* (* c 4.0) a) (fma b b (* 4.0 (* a c))) (pow b 4))))))
40.0ms
(pow (* (* 4.0 a) c) 3)

series1.0s

Counts
4 → 12
Calls
4 calls:
319.0ms
(/ (/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma (* (* c 4.0) a) (fma b b (* 4.0 (* a c))) (pow b 4)))))) (* 2.0 a))
209.0ms
(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma (* (* c 4.0) a) (fma b b (* 4.0 (* a c))) (pow b 4)))
410.0ms
(/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma (* (* c 4.0) a) (fma b b (* 4.0 (* a c))) (pow b 4))))))
99.0ms
(pow (* (* 4.0 a) c) 3)

simplify2.4s

Counts
234 → 234
Iterations

Useful iterations: done (2.4s)

IterNodesCost
039212095
191911333
2377810629
done500010621

prune1.7s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes189.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
01925
12623
done2623

end0.0ms

sample4.2s

Algorithm
intervals
Results
1.3s8502×body80nan
889.0ms4786×body160valid
628.0ms16502×pre80true
382.0ms1349×body320valid
225.0ms1865×body80valid