Details

Time bar (total: 17.4s)

sample118.0ms

Algorithm
intervals
Results
36.0ms35×body1280valid
18.0ms33×body2560valid
15.0ms168×body80valid
8.0ms92×body80nan
5.0ms15×body640valid
4.0ms6×body5120valid
2.0ms9×body320valid
1.0ms8×body160valid

simplify146.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
01217
12217
24216
38216
410416
511216
done11216

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
1.2b
(- (* b b) (* (* 3.0 a) c))
2.0b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.4b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite143.0ms

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:
78.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
9.0ms
(- (* b b) (* (* 3.0 a) c))
39.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
15.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series436.0ms

Counts
4 → 12
Calls
4 calls:
152.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
62.0ms
(- (* b b) (* (* 3.0 a) c))
125.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
96.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.3s

Counts
102 → 102
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01671697
14271586
214451363
done50011349

prune352.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.3b

localize24.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 3.0 a) c))
3.9b
(/ (/ (+ 0 (* (* c 3.0) a)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
11.6b
(/ (+ 0 (* (* c 3.0) a)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
24.4b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite231.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
80×add-sqr-sqrt
79×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
20×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
13×sqrt-prod
10×distribute-rgt-neg-in
8×associate-/r*
7×cbrt-undiv div-exp
6×associate-/r/ add-log-exp
5×pow1 flip3-- flip--
4×expm1-log1p-u log1p-expm1-u div-inv
3×associate-/l/
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 fma-neg diff-log prod-diff flip-+
Counts
4 → 158
Calls
4 calls:
16.0ms
(- (* b b) (* (* 3.0 a) c))
105.0ms
(/ (/ (+ 0 (* (* c 3.0) a)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
71.0ms
(/ (+ 0 (* (* c 3.0) a)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
32.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series637.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(- (* b b) (* (* 3.0 a) c))
266.0ms
(/ (/ (+ 0 (* (* c 3.0) a)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
203.0ms
(/ (+ 0 (* (* c 3.0) a)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
95.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.8s

Counts
170 → 170
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02645076
16504511
228424181
done50014179

prune759.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 7.2b

localize28.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 3.0 a) c))
3.9b
(/ (* 3.0 a) (/ (* (* c 3.0) a) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
11.6b
(/ (* (* c 3.0) a) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
24.4b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite178.0ms

Algorithm
rewrite-expression-head
Rules
45×add-exp-log add-cbrt-cube
34×times-frac
28×add-sqr-sqrt
27×*-un-lft-identity
20×associate-/r*
17×cbrt-undiv div-exp
13×prod-exp cbrt-unprod
11×add-cube-cbrt
8×distribute-lft-out-- difference-of-squares
7×sqrt-prod associate-/r/
6×add-log-exp
5×pow1 flip3-- flip--
4×expm1-log1p-u distribute-rgt-neg-in log1p-expm1-u div-inv
2×frac-2neg sqrt-div clear-num associate-/l*
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff
Counts
4 → 124
Calls
4 calls:
9.0ms
(- (* b b) (* (* 3.0 a) c))
63.0ms
(/ (* 3.0 a) (/ (* (* c 3.0) a) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
88.0ms
(/ (* (* c 3.0) a) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
13.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series570.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(- (* b b) (* (* 3.0 a) c))
132.0ms
(/ (* 3.0 a) (/ (* (* c 3.0) a) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
269.0ms
(/ (* (* c 3.0) a) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
105.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.7s

Counts
136 → 136
Iterations

Useful iterations: done (2.7s)

IterNodesCost
02383538
16423334
231992606
done50002605

prune426.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.2b

localize52.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (/ 1 1) (* (/ 3.0 (* c 3.0)) (* 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))))
0.7b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.2b
(- (* b b) (* (* 3.0 a) c))
24.4b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite292.0ms

Algorithm
rewrite-expression-head
Rules
281×add-exp-log
152×div-exp
126×prod-exp
71×1-exp
69×add-cbrt-cube
65×add-sqr-sqrt
64×*-un-lft-identity
61×prod-diff
60×add-cube-cbrt
34×sqrt-prod
31×times-frac
29×cbrt-undiv
22×distribute-rgt-neg-in cbrt-unprod
21×distribute-lft-neg-in
20×rec-exp
13×associate-/l*
11×fma-neg
10×add-log-exp
7×neg-mul-1
6×associate-*r/
5×pow1 flip3-- associate-/r/ flip--
4×expm1-log1p-u log1p-expm1-u
3×diff-log div-inv
2×frac-times sub-neg sqrt-div distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log associate-*l/ clear-num associate-/r* associate-/l/
Counts
4 → 252
Calls
4 calls:
184.0ms
(/ (/ 1 1) (* (/ 3.0 (* c 3.0)) (* 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))))
36.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
10.0ms
(- (* b b) (* (* 3.0 a) c))
25.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series554.0ms

Counts
4 → 12
Calls
4 calls:
261.0ms
(/ (/ 1 1) (* (/ 3.0 (* c 3.0)) (* 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))))
106.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
67.0ms
(- (* b b) (* (* 3.0 a) c))
119.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.5s

Counts
264 → 264
Iterations

Useful iterations: done (1.5s)

IterNodesCost
041410252
18957292
224275781
done50005697

prune1.0s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 7.2b

regimes532.0ms

Accuracy

93.7% (1.5b remaining)

Error of 7.1b against oracle of 5.6b and baseline of 29.8b

bsearch277.0ms

Steps
ItersRangePoint
5
1.2073698495971617e+61
2.9312978430050554e+61
2.269665110513951e+61
10
-1.7644224511749593e-214
-4.3193946104502796e-226
-2.3122726808272165e-225
10
-3.742210988141449e+103
-1.1204690717208776e+87
-8.594947000714855e+98

simplify10.0ms

Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
03969
14965
done4965

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.1s1051×body2560valid
597.0ms5868×body80valid
387.0ms891×body1280valid
253.0ms480×body640valid
211.0ms2845×body80nan
96.0ms217×body320valid
52.0ms100×body5120valid
37.0ms111×body160valid