Details

Time bar (total: 23.0s)

sample213.0ms

Algorithm
intervals
Results
13.0ms37×body2560valid
12.0ms184×body80valid
10.0ms31×body1280valid
4.0ms90×body80nan
2.0ms12×body640valid
2.0ms11×body320valid
1.0ms2×body5120valid
0.0ms2×body160valid

simplify38.0ms

Counts
1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

localize67.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b
(- (* b_2 b_2) (* a c))
22.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite169.0ms

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:
112.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
27.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
8.0ms
(- (* b_2 b_2) (* a c))
14.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series421.0ms

Counts
4 → 12
Calls
4 calls:
129.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
105.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
71.0ms
(- (* b_2 b_2) (* a c))
115.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.0s

Counts
103 → 103

prune436.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.0b

localize24.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.6b
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
9.6b
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
22.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite302.0ms

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:
48.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
149.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
76.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series740.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
213.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
299.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
113.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.6s

Counts
199 → 199

prune763.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.0b

localize30.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.0b
(/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)
4.6b
(/ (/ 1 (/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)) a)
22.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite600.0ms

Algorithm
rewrite-expression-head
Rules
3063×times-frac
1689×add-sqr-sqrt
1446×*-un-lft-identity
1204×add-cube-cbrt
242×difference-of-squares
237×associate-/l*
124×sqrt-prod
121×distribute-lft-out--
58×div-inv
41×add-exp-log
28×div-exp
23×add-cbrt-cube
13×cbrt-undiv
6×associate-/r* add-log-exp
5×pow1
4×associate-/r/
3×rec-exp 1-exp
2×flip3-- frac-2neg sqrt-div div-sub clear-num flip-- associate-/l/
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 1025
Calls
4 calls:
84.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
122.0ms
(/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)
188.0ms
(/ (/ 1 (/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)) a)
26.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series467.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
155.0ms
(/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)
134.0ms
(/ (/ 1 (/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)) a)
84.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.3s

Counts
1037 → 1037

prune4.8s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.0b

localize16.0ms

Local error

Found 4 expressions with local error:

1.1b
(+ (sqrt (- (* b_2 b_2) (* a c))) (- b_2))
4.6b
(/ (/ (+ 0 (* a c)) (+ (sqrt (- (* b_2 b_2) (* a c))) (- b_2))) a)
9.6b
(/ (+ 0 (* a c)) (+ (sqrt (- (* b_2 b_2) (* a c))) (- b_2)))
22.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite355.0ms

Algorithm
rewrite-expression-head
Rules
141×*-un-lft-identity
138×times-frac
74×add-sqr-sqrt
73×add-cube-cbrt
34×distribute-lft-out
24×associate-/l*
17×distribute-rgt-neg-in
11×add-exp-log add-cbrt-cube
10×associate-/r/
8×associate-/r* add-log-exp
7×flip3-+ flip-+
6×div-inv
5×pow1
4×cbrt-undiv div-exp
3×sqrt-prod associate-/l/
2×frac-2neg sqrt-div clear-num sum-log
1×+-commutative neg-sub0 associate-+r- rem-sqrt-square flip3-- sqrt-pow1 pow1/2 unsub-neg neg-log flip--
Counts
4 → 173
Calls
4 calls:
36.0ms
(+ (sqrt (- (* b_2 b_2) (* a c))) (- b_2))
153.0ms
(/ (/ (+ 0 (* a c)) (+ (sqrt (- (* b_2 b_2) (* a c))) (- b_2))) a)
122.0ms
(/ (+ 0 (* a c)) (+ (sqrt (- (* b_2 b_2) (* a c))) (- b_2)))
27.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series741.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(+ (sqrt (- (* b_2 b_2) (* a c))) (- b_2))
229.0ms
(/ (/ (+ 0 (* a c)) (+ (sqrt (- (* b_2 b_2) (* a c))) (- b_2))) a)
281.0ms
(/ (+ 0 (* a c)) (+ (sqrt (- (* b_2 b_2) (* a c))) (- b_2)))
100.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.6s

Counts
185 → 185

prune691.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.0b

regimes323.0ms

Accuracy

95.9% (1.0b remaining)

Error of 6.7b against oracle of 5.7b and baseline of 29.7b

bsearch245.0ms

Steps
ItersRangePoint
8
1.8560558009645164e+92
4.334214702125778e+95
4.275810729145967e+95
7
6.280116215398226e-292
4.284365751511997e-290
2.999993907961032e-290
9
-3.494733358578083e+156
-1.1278306941613648e+148
-3.7099499749986014e+149

simplify679.0ms

end0.0ms

sample3.3s

Algorithm
intervals
Results
767.0ms2962×body80nan
522.0ms1107×body2560valid
514.0ms5894×body80valid
506.0ms106×body5120valid
267.0ms845×body1280valid
159.0ms467×body640valid
39.0ms227×body320valid
12.0ms100×body160valid