Details

Time bar (total: 11.2s)

sample278.0ms

Algorithm
intervals
Results
8.0ms37×body2560valid
7.0ms195×body80valid
5.0ms21×body1280valid
3.0ms81×body80nan
2.0ms19×body640valid
1.0ms3×body5120valid
0.0ms4×body320valid
0.0ms4×body160valid

simplify22.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
01013
11413
22212
32512
42712
52912
done2912

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.4b
(- (* b_2 b_2) (* a c))
1.2b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
20.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×*-un-lft-identity
18×times-frac
16×add-cube-cbrt
10×difference-of-squares
8×sqrt-prod add-log-exp
6×add-exp-log add-cbrt-cube associate-/l*
5×pow1 distribute-lft-out--
4×flip3-- flip--
3×associate-/r*
2×sub-neg sqrt-div diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub div-exp clear-num div-inv
Counts
4 → 84
Calls
4 calls:
36.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
3.0ms
(- (* b_2 b_2) (* a c))
19.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series270.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
33.0ms
(- (* b_2 b_2) (* a c))
72.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
75.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.6s

Counts
96 → 96
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01541624
13621526
29501426
326751422
done50011420

prune250.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.4b
(- (* b_2 b_2) (* a c))
1.2b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
20.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite59.0ms

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:
26.0ms
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
3.0ms
(- (* b_2 b_2) (* a c))
18.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series294.0ms

Counts
4 → 12
Calls
4 calls:
129.0ms
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
32.0ms
(- (* b_2 b_2) (* a c))
72.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
62.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.9s

Counts
174 → 174
Iterations

Useful iterations: 3 (927.0ms)

IterNodesCost
02583976
15693485
213393208
336763128
done50003128

prune254.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.4b
(- (* b_2 b_2) (* a c))
1.2b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
20.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite62.0ms

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:
26.0ms
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
3.0ms
(- (* b_2 b_2) (* a c))
21.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series293.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
33.0ms
(- (* b_2 b_2) (* a c))
72.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
63.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.9s

Counts
174 → 174
Iterations

Useful iterations: 3 (918.0ms)

IterNodesCost
02583976
15693485
213393208
336763128
done50003128

prune266.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.5b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 1 a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
0.4b
(- (* b_2 b_2) (* a c))
1.2b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
20.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
18×*-un-lft-identity
13×add-exp-log add-cube-cbrt associate-*l*
11×times-frac
9×add-cbrt-cube
8×add-log-exp
7×pow1
6×associate-*r*
5×flip3-- sqrt-prod flip--
4×sub-neg prod-exp difference-of-squares
3×unswap-sqr
2×distribute-rgt-in frac-times distribute-lft-in sqrt-div diff-log associate-*r/ div-exp cbrt-unprod distribute-lft-out--
1×cbrt-undiv rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp pow-prod-down associate-*l/ *-commutative div-inv
Counts
4 → 88
Calls
4 calls:
53.0ms
(* (/ 1 a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
3.0ms
(- (* b_2 b_2) (* a c))
18.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series283.0ms

Counts
4 → 12
Calls
4 calls:
121.0ms
(* (/ 1 a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
35.0ms
(- (* b_2 b_2) (* a c))
67.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
60.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.8s

Counts
100 → 100
Iterations

Useful iterations: 3 (933.0ms)

IterNodesCost
01621633
13991448
211331288
331581282
done50001282

prune212.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.5b

regimes167.0ms

Accuracy

83.4% (4.8b remaining)

Error of 10.4b against oracle of 5.6b and baseline of 34.3b

bsearch103.0ms

Steps
ItersRangePoint
10
3.056596725548563e-78
7.076105677608322e-63
3.446447862996811e-75
10
-1.852183237050365e+100
-1.9127319211193897e+86
-4.123103533644211e+95

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
02740
13438
done3438

end0.0ms

sample1.0s

Algorithm
intervals
Results
220.0ms1099×body2560valid
195.0ms5881×body80valid
141.0ms851×body1280valid
95.0ms2944×body80nan
62.0ms470×body640valid
26.0ms109×body5120valid
21.0ms219×body320valid
6.0ms98×body160valid