Details

Time bar (total: 20.8s)

sample185.0ms

Algorithm
intervals
Results
58.0ms113×body320valid
13.0ms262×body80nan
12.0ms518×pre80true
10.0ms107×body160valid
2.0ms8×body640valid
1.0ms28×body80valid

simplify105.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
01417
12517
24616
38716
412016
512916
done12916

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(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))
30.5b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite195.0ms

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:
24.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
19.0ms
(- (* b b) (* (* 4.0 a) c))
111.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
34.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series453.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
63.0ms
(- (* b b) (* (* 4.0 a) c))
147.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
135.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify2.0s

Counts
102 → 102
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01671697
14521588
221181361
done50011352

prune380.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

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

rewrite380.0ms

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:
45.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms
(- (* b b) (* (* 4.0 a) c))
174.0ms
(/ (/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
129.0ms
(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series717.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
53.0ms
(- (* b b) (* (* 4.0 a) c))
248.0ms
(/ (/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
292.0ms
(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify709.0ms

Counts
243 → 243
Iterations

Useful iterations: done (690.0ms)

IterNodesCost
033910026
18617622
done50006606

prune860.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (/ (fma b (pow b 3) (- (* (* (* 4.0 a) c) (* (* 4.0 a) c)))) (fma b b (* (* 4.0 a) c))))))
0.3b
(fma b (pow b 3) (- (* (* (* 4.0 a) c) (* (* 4.0 a) c))))
0.5b
(/ (fma b (pow b 3) (- (* (* (* 4.0 a) c) (* (* 4.0 a) c)))) (fma b b (* (* 4.0 a) c)))
0.5b
(* (* (* 4.0 a) c) (* (* 4.0 a) c))

rewrite273.0ms

Algorithm
rewrite-expression-head
Rules
118×pow1
66×pow-prod-down
53×add-sqr-sqrt
44×add-exp-log add-cbrt-cube
41×*-un-lft-identity
37×times-frac
27×prod-exp cbrt-unprod
25×add-cube-cbrt
12×difference-of-squares
11×associate-/r*
9×pow-sqr pow-prod-up
8×sqrt-prod distribute-lft-out--
6×associate-/l*
4×expm1-log1p-u distribute-rgt-neg-in log1p-expm1-u add-log-exp
3×pow-plus
2×cbrt-undiv frac-2neg div-exp clear-num associate-/r/ div-inv associate-/l/
1×pow2 flip3-- flip3-+ swap-sqr associate-*r* associate-*l* *-commutative flip-- flip-+ fma-udef
Counts
4 → 154
Calls
4 calls:
71.0ms
(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (/ (fma b (pow b 3) (- (* (* (* 4.0 a) c) (* (* 4.0 a) c)))) (fma b b (* (* 4.0 a) c))))))
1.0ms
(fma b (pow b 3) (- (* (* (* 4.0 a) c) (* (* 4.0 a) c))))
14.0ms
(/ (fma b (pow b 3) (- (* (* (* 4.0 a) c) (* (* 4.0 a) c)))) (fma b b (* (* 4.0 a) c)))
174.0ms
(* (* (* 4.0 a) c) (* (* 4.0 a) c))

series722.0ms

Counts
4 → 12
Calls
4 calls:
360.0ms
(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (/ (fma b (pow b 3) (- (* (* (* 4.0 a) c) (* (* 4.0 a) c)))) (fma b b (* (* 4.0 a) c))))))
129.0ms
(fma b (pow b 3) (- (* (* (* 4.0 a) c) (* (* 4.0 a) c))))
181.0ms
(/ (fma b (pow b 3) (- (* (* (* 4.0 a) c) (* (* 4.0 a) c)))) (fma b b (* (* 4.0 a) c)))
51.0ms
(* (* (* 4.0 a) c) (* (* 4.0 a) c))

simplify5.4s

Counts
166 → 166
Iterations

Useful iterations: 2 (880.0ms)

IterNodesCost
02345357
15915001
242554298
done50004298

prune715.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite567.0ms

Algorithm
rewrite-expression-head
Rules
152×add-exp-log
121×prod-diff
92×add-cbrt-cube
90×add-sqr-sqrt
88×*-un-lft-identity
84×add-cube-cbrt
73×prod-exp
62×distribute-rgt-in distribute-lft-in
61×sqrt-prod
46×div-exp
41×cbrt-unprod
37×distribute-rgt-neg-in
36×distribute-lft-neg-in
26×cbrt-undiv
12×neg-mul-1
9×pow1
8×rec-exp 1-exp
7×associate-*r*
6×add-log-exp
5×flip3-- times-frac associate-*l* associate-/r/ flip--
4×expm1-log1p-u frac-times associate-*r/ log1p-expm1-u associate-/l*
3×sub-neg div-inv
2×pow-flip frac-2neg pow-prod-down associate-*l/ clear-num associate-/r* distribute-lft-out-- difference-of-squares
1×fma-neg diff-log *-commutative inv-pow unswap-sqr
Counts
4 → 269
Calls
4 calls:
17.0ms
(- (* b b) (* (* 4.0 a) c))
23.0ms
(/ (* 2.0 a) (* (* 4.0 a) c))
225.0ms
(/ 1 (* (/ (* 2.0 a) (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
265.0ms
(* (/ (* 2.0 a) (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series456.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(- (* b b) (* (* 4.0 a) c))
20.0ms
(/ (* 2.0 a) (* (* 4.0 a) c))
223.0ms
(/ 1 (* (/ (* 2.0 a) (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
138.0ms
(* (/ (* 2.0 a) (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify1.4s

Counts
281 → 281
Iterations

Useful iterations: done (1.4s)

IterNodesCost
043316195
1132712154
done50009342

prune665.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes110.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify23.0ms

Iterations

Useful iterations: 3 (8.0ms)

IterNodesCost
02132
13328
24228
36327
49127
59927
done9927

end0.0ms

sample4.3s

Algorithm
intervals
Results
1.1s3682×body320valid
727.0ms16139×pre80true
688.0ms8139×body80nan
493.0ms2945×body160valid
345.0ms894×body80valid
178.0ms479×body640valid