Details

Time bar (total: 17.8s)

sample111.0ms

Algorithm
intervals
Results
9.0ms32×body2560valid
9.0ms185×body80valid
9.0ms31×body1280valid
5.0ms108×body80nan
2.0ms6×body5120valid
2.0ms11×body640valid
1.0ms8×body320valid
1.0ms5×body160valid

simplify72.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
01013
11813
23213
34113
44413
done4413

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b
(- (* b_2 b_2) (* a c))
1.2b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.3b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite222.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
37×*-un-lft-identity
21×times-frac
17×add-cube-cbrt
10×distribute-lft-out-- add-log-exp difference-of-squares
8×sqrt-prod
7×associate-/l*
6×add-exp-log add-cbrt-cube
5×pow1 distribute-rgt-neg-in
4×flip3-- flip--
3×diff-log associate-/r*
2×sub-neg sqrt-div associate-/l/
1×cbrt-undiv associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub div-exp neg-log clear-num div-inv
Counts
4 → 91
Calls
4 calls:
116.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
17.0ms
(- (* b_2 b_2) (* a c))
62.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series397.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
53.0ms
(- (* b_2 b_2) (* a c))
124.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
103.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify894.0ms

Counts
103 → 103
Iterations

Useful iterations: done (890.0ms)

IterNodesCost
01561821
13871727
215081613
done50011603

prune416.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.8b

localize15.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.7b
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
7.9b
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
23.3b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite355.0ms

Algorithm
rewrite-expression-head
Rules
162×times-frac
150×add-sqr-sqrt
115×*-un-lft-identity
81×add-cube-cbrt
34×difference-of-squares
27×associate-/l*
20×sqrt-prod
17×distribute-lft-out--
11×add-exp-log add-cbrt-cube
10×associate-/r/
9×associate-/r*
7×flip3-- flip--
6×div-inv add-log-exp
5×pow1
4×cbrt-undiv div-exp
3×associate-/l/
2×frac-2neg sqrt-div clear-num
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 187
Calls
4 calls:
62.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
148.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
121.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
10.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series699.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
209.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
305.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
92.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.3s

Counts
199 → 199
Iterations

Useful iterations: 2 (719.0ms)

IterNodesCost
03045659
17654902
241264722
done50014722

prune741.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.8b

localize30.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.8b
(* (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
7.9b
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
23.3b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite408.0ms

Algorithm
rewrite-expression-head
Rules
83×add-sqr-sqrt
52×times-frac
51×*-un-lft-identity
33×add-cube-cbrt
28×add-exp-log
24×associate-*l*
18×add-cbrt-cube
16×difference-of-squares
13×associate-*r*
11×sqrt-prod
9×div-exp
8×prod-exp distribute-lft-out--
7×pow1
6×associate-/r* add-log-exp unswap-sqr
5×cbrt-undiv
4×flip3-- associate-/r/ flip-- cbrt-unprod
3×div-inv associate-/l*
2×rec-exp sqrt-div 1-exp associate-/l/
1×frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 diff-log associate-*r/ pow-prod-down associate-*l/ clear-num un-div-inv *-commutative flip-+
Counts
4 → 141
Calls
4 calls:
83.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
175.0ms
(* (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
126.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
17.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series714.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
239.0ms
(* (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
281.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
88.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify3.9s

Counts
153 → 153
Iterations

Useful iterations: 2 (968.0ms)

IterNodesCost
02503533
17303010
246052710
done50002710

prune500.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b_2 b_2) (* a c))
1.4b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
11.8b
(/ (* a c) a)
23.3b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
9×add-exp-log *-un-lft-identity add-cbrt-cube
8×add-log-exp
7×add-cube-cbrt
5×pow1
4×sqrt-prod
3×flip3-- times-frac associate-/r* flip--
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp difference-of-squares
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 prod-exp clear-num cbrt-unprod div-inv associate-/l* distribute-lft-out--
Counts
4 → 63
Calls
4 calls:
12.0ms
(- (* b_2 b_2) (* a c))
52.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
20.0ms
(/ (* a c) a)
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series248.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(- (* b_2 b_2) (* a c))
103.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
12.0ms
(/ (* a c) a)
85.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.7s

Counts
75 → 75
Iterations

Useful iterations: done (1.7s)

IterNodesCost
0125880
1313806
21698726
done5002698

prune256.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.8b

regimes173.0ms

Accuracy

95.9% (1.0b remaining)

Error of 6.2b against oracle of 5.2b and baseline of 29.3b

bsearch222.0ms

Steps
ItersRangePoint
6
1.9101351599902807e+102
2.525038855038462e+103
5.550864523265887e+102
8
1.0408663060912465e-291
3.4349488111407062e-289
2.7156356358044857e-290
9
-2.501158360438979e+160
-5.198860796817705e+153
-1.3152753346874725e+154

simplify8.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03051
13649
23749
done3749

end0.0ms

sample3.2s

Algorithm
intervals
Results
947.0ms5806×body80valid
630.0ms1053×body2560valid
466.0ms935×body1280valid
273.0ms2894×body80nan
171.0ms466×body640valid
58.0ms111×body5120valid
46.0ms233×body320valid
14.0ms106×body160valid