Details

Time bar (total: 13.7s)

sample140.0ms

Algorithm
intervals
Results
15.0ms38×body2560valid
14.0ms178×body80valid
10.0ms29×body1280valid
5.0ms79×body80nan
3.0ms11×body640valid
2.0ms3×body5120valid
1.0ms5×body320valid
0.0ms2×body160valid

simplify40.0ms

Counts
1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize51.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.5b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.6b
(- (* b_2 b_2) (* a c))
20.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite181.0ms

Algorithm
rewrite-expression-head
Rules
35×*-un-lft-identity
16×add-sqr-sqrt
15×add-cube-cbrt times-frac
10×distribute-lft-out add-log-exp
6×add-exp-log add-cbrt-cube
5×pow1 distribute-rgt-neg-in associate-/l*
3×associate-/r* sqrt-prod
2×neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div sum-log flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub div-exp neg-log clear-num div-inv
Counts
4 → 80
Calls
4 calls:
93.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
44.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
16.0ms
(- (* b_2 b_2) (* a c))
22.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series428.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
123.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
70.0ms
(- (* b_2 b_2) (* a c))
130.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify673.0ms

Counts
92 → 92

prune384.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.5b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.6b
(- (* b_2 b_2) (* a c))
20.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite193.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
21×add-sqr-sqrt
13×add-exp-log add-cube-cbrt associate-*r*
11×times-frac
10×add-log-exp
9×add-cbrt-cube
7×pow1
5×associate-*l*
4×prod-exp distribute-lft-out
3×flip3-+ sqrt-prod flip-+ unswap-sqr
2×frac-times flip3-- distribute-rgt-neg-in sqrt-div div-exp associate-*l/ sum-log flip-- cbrt-unprod
1×cbrt-undiv +-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square rec-exp sqrt-pow1 pow1/2 diff-log 1-exp associate-*r/ pow-prod-down neg-log un-div-inv *-commutative div-inv
Counts
4 → 84
Calls
4 calls:
128.0ms
(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
28.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
12.0ms
(- (* b_2 b_2) (* a c))
19.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series383.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
134.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
58.0ms
(- (* b_2 b_2) (* a c))
88.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.0s

Counts
96 → 96

prune341.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.5b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.6b
(- (* b_2 b_2) (* a c))
20.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite190.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
123×add-sqr-sqrt
96×*-un-lft-identity
70×add-cube-cbrt
26×difference-of-squares
24×associate-/r*
16×sqrt-prod
15×add-exp-log
13×distribute-lft-out--
9×associate-/r/ add-cbrt-cube
8×add-log-exp
7×flip3-- div-exp flip--
6×pow1
5×div-inv
3×cbrt-undiv associate-/l*
2×sub-neg rec-exp sqrt-div diff-log 1-exp
1×rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 clear-num inv-pow
Counts
4 → 162
Calls
4 calls:
75.0ms
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
68.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
17.0ms
(- (* b_2 b_2) (* a c))
19.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series464.0ms

Counts
4 → 12
Calls
4 calls:
196.0ms
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
124.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
61.0ms
(- (* b_2 b_2) (* a c))
83.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.2s

Counts
174 → 174

prune440.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b_2 b_2) (* a c))
1.4b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.7b
(* (/ 1 a) (* a c))
20.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
26×add-exp-log
17×add-sqr-sqrt
16×*-un-lft-identity add-cbrt-cube
13×associate-*l*
12×add-cube-cbrt prod-exp
10×pow1 add-log-exp
9×times-frac
6×cbrt-unprod
4×div-exp sqrt-prod
3×flip3-- diff-log pow-prod-down flip--
2×cbrt-undiv sub-neg rec-exp sqrt-div 1-exp distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 pow1/2 associate-*r* neg-log associate-*l/ *-commutative div-inv
Counts
4 → 82
Calls
4 calls:
8.0ms
(- (* b_2 b_2) (* a c))
28.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
43.0ms
(* (/ 1 a) (* a c))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series254.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(- (* b_2 b_2) (* a c))
97.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
8.0ms
(* (/ 1 a) (* a c))
105.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.1s

Counts
94 → 94

prune321.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.1b

regimes420.0ms

Accuracy

96.1% (1.1b remaining)

Error of 6.5b against oracle of 5.4b and baseline of 34.3b

bsearch211.0ms

Steps
ItersRangePoint
4
9.936283634246925e+77
1.8488019868481542e+78
1.6082844052603056e+78
11
-1.0472779812871276e-269
-2.473343252086336e-295
-3.1400906193105714e-291
8
-6.990724105819741e+111
-2.6156774686163576e+108
-1.569310777886352e+111

simplify2.2s

end0.0ms

sample2.9s

Algorithm
intervals
Results
538.0ms117×body5120valid
518.0ms5805×body80valid
510.0ms1087×body2560valid
318.0ms936×body1280valid
283.0ms2994×body80nan
108.0ms443×body640valid
68.0ms211×body320valid
13.0ms113×body160valid