Details

Time bar (total: 21.4s)

sample139.0ms

Algorithm
intervals
Results
38.0ms318×body80nan
25.0ms146×body160valid
21.0ms574×pre80true
10.0ms110×body80valid

simplify125.0ms

Counts
1 → 1
Iterations
IterNodes
done128
5128
4119
386
246
125
014

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.5b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (fma (- a) (* 4.0 c) (* b b)))
0.2b
(/ (- (sqrt (fma (- a) (* 4.0 c) (* b b))) b) a)
0.2b
(fma (- a) (* 4.0 c) (* b b))
28.3b
(- (sqrt (fma (- a) (* 4.0 c) (* b b))) b)

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
40×*-un-lft-identity
30×add-cube-cbrt
20×sqrt-prod
18×times-frac prod-diff
10×difference-of-squares
6×add-cbrt-cube fma-neg add-exp-log associate-/l* add-log-exp
5×pow1 distribute-lft-out--
4×expm1-log1p-u log1p-expm1-u
3×associate-/r*
2×flip3-- flip-- associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-sub div-exp fma-udef div-inv
Counts
4 → 110
Calls
4 calls:
2.0ms
(sqrt (fma (- a) (* 4.0 c) (* b b)))
47.0ms
(/ (- (sqrt (fma (- a) (* 4.0 c) (* b b))) b) a)
0.0ms
(fma (- a) (* 4.0 c) (* b b))
9.0ms
(- (sqrt (fma (- a) (* 4.0 c) (* b b))) b)

series583.0ms

Counts
4 → 12
Calls
4 calls:
152.0ms
(sqrt (fma (- a) (* 4.0 c) (* b b)))
185.0ms
(/ (- (sqrt (fma (- a) (* 4.0 c) (* b b))) b) a)
104.0ms
(fma (- a) (* 4.0 c) (* b b))
143.0ms
(- (sqrt (fma (- a) (* 4.0 c) (* b b))) b)

simplify894.0ms

Counts
122 → 122
Iterations
IterNodes
done5000
21071
1336
0152

prune724.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
114×times-frac
100×*-un-lft-identity
67×add-sqr-sqrt
66×add-cube-cbrt
21×associate-/l*
17×distribute-lft-out
11×add-cbrt-cube add-exp-log
10×associate-/r/
7×associate-/r*
6×flip3-+ flip-+ div-inv add-log-exp
5×pow1
4×expm1-log1p-u cbrt-undiv div-exp log1p-expm1-u
3×fma-def sqrt-prod
2×clear-num frac-2neg
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 pow1/2 associate-/l/
Counts
4 → 159
Calls
4 calls:
1.0ms
(sqrt (fma b b (* c (- (* a 4.0)))))
32.0ms
(/ (/ (fma (- (* a 4.0)) c 0) (+ b (sqrt (fma b b (* c (- (* a 4.0))))))) a)
12.0ms
(+ b (sqrt (fma b b (* c (- (* a 4.0))))))
11.0ms
(/ (fma (- (* a 4.0)) c 0) (+ b (sqrt (fma b b (* c (- (* a 4.0)))))))

series995.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(sqrt (fma b b (* c (- (* a 4.0)))))
370.0ms
(/ (/ (fma (- (* a 4.0)) c 0) (+ b (sqrt (fma b b (* c (- (* a 4.0))))))) a)
132.0ms
(+ b (sqrt (fma b b (* c (- (* a 4.0))))))
392.0ms
(/ (fma (- (* a 4.0)) c 0) (+ b (sqrt (fma b b (* c (- (* a 4.0)))))))

simplify1.3s

Counts
171 → 171
Iterations
IterNodes
done5000
22633
1621
0256

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma b b (* (- c) (* a 4.0)))
0.1b
(sqrt (fma b b (* (- c) (* a 4.0))))
0.2b
(/ c (+ (sqrt (fma b b (* (- c) (* a 4.0)))) b))
0.2b
(+ (sqrt (fma b b (* (- c) (* a 4.0)))) b)

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
26×*-un-lft-identity
17×add-sqr-sqrt
16×add-cube-cbrt
12×times-frac
6×fma-def add-cbrt-cube add-exp-log sqrt-prod add-log-exp
5×pow1 distribute-lft-out
4×expm1-log1p-u associate-/r* log1p-expm1-u
3×associate-/l*
2×flip3-+ associate-/r/ flip-+
1×cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log frac-2neg sqrt-pow1 pow1/2 div-exp fma-udef div-inv
Counts
4 → 80
Calls
4 calls:
0.0ms
(fma b b (* (- c) (* a 4.0)))
2.0ms
(sqrt (fma b b (* (- c) (* a 4.0))))
22.0ms
(/ c (+ (sqrt (fma b b (* (- c) (* a 4.0)))) b))
8.0ms
(+ (sqrt (fma b b (* (- c) (* a 4.0)))) b)

series611.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(fma b b (* (- c) (* a 4.0)))
96.0ms
(sqrt (fma b b (* (- c) (* a 4.0))))
275.0ms
(/ c (+ (sqrt (fma b b (* (- c) (* a 4.0)))) b))
148.0ms
(+ (sqrt (fma b b (* (- c) (* a 4.0)))) b)

simplify2.1s

Counts
92 → 92
Iterations
IterNodes
done5000
34551
2839
1258
0122

prune755.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize113.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ c (+ (pow b 3) (pow (sqrt (fma (- (* a c)) 4.0 (* b b))) 3))) (+ (* (sqrt (fma b b (* (- c) (* a 4.0)))) (sqrt (fma b b (* (- c) (* a 4.0))))) (- (* b b) (* (sqrt (fma b b (* (- c) (* a 4.0)))) b))))
0.4b
(* (sqrt (fma b b (* (- c) (* a 4.0)))) (sqrt (fma b b (* (- c) (* a 4.0)))))
0.6b
(pow (sqrt (fma (- (* a c)) 4.0 (* b b))) 3)
28.7b
(- (* b b) (* (sqrt (fma b b (* (- c) (* a 4.0)))) b))

rewrite265.0ms

Algorithm
rewrite-expression-head
Rules
61×*-un-lft-identity
48×add-sqr-sqrt
39×associate-*l*
31×add-cube-cbrt
28×times-frac
24×sqrt-prod
23×pow1
18×unpow-prod-down cube-prod
15×distribute-lft-out
12×add-cbrt-cube add-exp-log
9×sqrt-pow1 pow1/2 associate-*r*
8×swap-sqr
6×add-log-exp unswap-sqr
5×pow-prod-up
4×expm1-log1p-u pow-prod-down log1p-expm1-u
3×pow-unpow pow-pow flip3-+ prod-exp pow-sqr sum-cubes cbrt-unprod flip-+
2×frac-times associate-*r/ associate-/r/ *-commutative
1×pow2 distribute-rgt-in cube-mult pow-to-exp cbrt-undiv sub-neg rem-square-sqrt distribute-lft-in pow-plus flip3-- distribute-rgt-out-- fma-neg sqrt-unprod diff-log unpow3 div-exp prod-diff associate-*l/ pow-exp div-inv sqrt-pow2 flip-- rem-cube-cbrt sqr-pow
Counts
4 → 162
Calls
4 calls:
215.0ms
(* (/ c (+ (pow b 3) (pow (sqrt (fma (- (* a c)) 4.0 (* b b))) 3))) (+ (* (sqrt (fma b b (* (- c) (* a 4.0)))) (sqrt (fma b b (* (- c) (* a 4.0))))) (- (* b b) (* (sqrt (fma b b (* (- c) (* a 4.0)))) b))))
20.0ms
(* (sqrt (fma b b (* (- c) (* a 4.0)))) (sqrt (fma b b (* (- c) (* a 4.0)))))
6.0ms
(pow (sqrt (fma (- (* a c)) 4.0 (* b b))) 3)
14.0ms
(- (* b b) (* (sqrt (fma b b (* (- c) (* a 4.0)))) b))

series2.8s

Counts
4 → 12
Calls
4 calls:
1.6s
(* (/ c (+ (pow b 3) (pow (sqrt (fma (- (* a c)) 4.0 (* b b))) 3))) (+ (* (sqrt (fma b b (* (- c) (* a 4.0)))) (sqrt (fma b b (* (- c) (* a 4.0))))) (- (* b b) (* (sqrt (fma b b (* (- c) (* a 4.0)))) b))))
74.0ms
(* (sqrt (fma b b (* (- c) (* a 4.0)))) (sqrt (fma b b (* (- c) (* a 4.0)))))
904.0ms
(pow (sqrt (fma (- (* a c)) 4.0 (* b b))) 3)
162.0ms
(- (* b b) (* (sqrt (fma b b (* (- c) (* a 4.0)))) b))

simplify579.0ms

Counts
174 → 174
Iterations
IterNodes
done5000
1888
0261

prune1.5s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes333.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.2s

Iterations
IterNodes
done5001
123287
111735
10951
9551
8343
7231
6167
5127
494
359
243
133
018

end0.0ms

sample3.8s

Algorithm
intervals
Results
1.0s16646×pre80true
829.0ms4367×body160valid
702.0ms8646×body80nan
356.0ms3633×body80valid