Details

Time bar (total: 7.3s)

sample48.0ms

Algorithm
intervals
Results
8.0ms181×body80valid
7.0ms27×body2560valid
7.0ms31×body1280valid
4.0ms21×body640valid
4.0ms81×body80nan
3.0ms8×body5120valid
1.0ms8×body320valid
0.0ms4×body160valid

simplify90.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01417
12917
26417
311917
414117
514717
615017
done15017

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b
(- (* b b) (* 4.0 (* a c)))
0.9b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt prod-diff
60×*-un-lft-identity
48×add-cube-cbrt
36×sqrt-prod
24×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×neg-mul-1 times-frac associate-/l*
6×distribute-lft-out-- difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 157
Calls
4 calls:
45.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms
(- (* b b) (* 4.0 (* a c)))
17.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series292.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
44.0ms
(- (* b b) (* 4.0 (* a c)))
79.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
74.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify701.0ms

Counts
169 → 169
Iterations

Useful iterations: done (695.0ms)

IterNodesCost
02436690
15784705
217893760
done50013759

prune392.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.4b
(- (* b b) (* 4.0 (* a c)))
0.9b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
89×add-sqr-sqrt
88×*-un-lft-identity
68×add-cube-cbrt
67×times-frac
61×prod-diff
38×sqrt-prod
26×distribute-rgt-neg-in
25×add-exp-log
21×distribute-lft-neg-in
13×associate-/r* add-cbrt-cube
12×div-exp
11×fma-neg
10×distribute-lft-out-- add-log-exp difference-of-squares
9×associate-/r/
7×neg-mul-1 flip3-- flip--
6×pow1
5×cbrt-undiv div-inv
4×expm1-log1p-u log1p-expm1-u
3×rec-exp diff-log 1-exp prod-exp associate-/l*
2×sub-neg sqrt-div
1×associate--l- neg-sub0 rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 neg-log clear-num cbrt-unprod inv-pow
Counts
4 → 205
Calls
4 calls:
26.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
20.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series311.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
45.0ms
(- (* b b) (* 4.0 (* a c)))
79.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify971.0ms

Counts
217 → 217
Iterations

Useful iterations: done (963.0ms)

IterNodesCost
03118365
17066123
219905076
done50005068

prune405.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (/ 1 2.0) a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
0.4b
(- (* b b) (* 4.0 (* a c)))
0.9b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite118.0ms

Algorithm
rewrite-expression-head
Rules
181×prod-diff
179×add-sqr-sqrt
167×*-un-lft-identity
158×add-cube-cbrt
95×sqrt-prod
71×times-frac
62×distribute-rgt-in distribute-lft-in
59×distribute-rgt-neg-in
57×distribute-lft-neg-in
43×associate-*l*
19×add-exp-log neg-mul-1
13×add-cbrt-cube
11×fma-neg
10×add-log-exp
7×pow1 associate-*r*
6×div-exp
5×flip3-- prod-exp flip--
4×expm1-log1p-u sub-neg log1p-expm1-u div-inv distribute-lft-out-- difference-of-squares unswap-sqr
3×cbrt-undiv diff-log cbrt-unprod
2×frac-times sqrt-div associate-*r/
1×associate--l- neg-sub0 rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp pow-prod-down neg-log associate-*l/ *-commutative
Counts
4 → 325
Calls
4 calls:
76.0ms
(* (/ (/ 1 2.0) a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
16.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series317.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(* (/ (/ 1 2.0) a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
45.0ms
(- (* b b) (* 4.0 (* a c)))
79.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.2s

Counts
337 → 337
Iterations

Useful iterations: 2 (629.0ms)

IterNodesCost
043818702
1113112903
230809948
done50009948

prune591.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.3b

localize4.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify1.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000
done00

prune0.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.3b

regimes252.0ms

Accuracy

83.9% (4.6b remaining)

Error of 10.2b against oracle of 5.6b and baseline of 34.4b

bsearch124.0ms

Steps
ItersRangePoint
10
1.1889782913455773e+76
6.845935134449847e+90
1.964008874546701e+84
8
-2.5526520307548834e-35
-5.158362140144754e-39
-9.665680960493338e-39

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02535
13035
done3035

end0.0ms

sample1.3s

Algorithm
intervals
Results
287.0ms1059×body2560valid
267.0ms5841×body80valid
203.0ms909×body1280valid
137.0ms2943×body80nan
82.0ms464×body640valid
33.0ms102×body5120valid
30.0ms234×body320valid
10.0ms111×body160valid