Details

Time bar (total: 21.7s)

sample89.0ms

Algorithm
intervals
Results
10.0ms190×body80valid
9.0ms36×body2560valid
6.0ms28×body1280valid
4.0ms92×body80nan
3.0ms16×body640valid
1.0ms7×body320valid
0.0ms1×body5120valid
0.0ms3×body160valid

simplify70.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
01013
11513
22312
33012
43212
53412
done3412

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.2b
(- (* b_2 b_2) (* a c))
1.1b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite220.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
40×*-un-lft-identity
30×add-cube-cbrt
20×sqrt-prod
19×prod-diff
18×times-frac
10×difference-of-squares
8×add-log-exp
7×fma-neg
6×add-exp-log add-cbrt-cube associate-/l*
5×pow1 distribute-lft-out--
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
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 → 118
Calls
4 calls:
124.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
9.0ms
(- (* b_2 b_2) (* a c))
65.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series428.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
69.0ms
(- (* b_2 b_2) (* a c))
103.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
109.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify3.4s

Counts
130 → 130
Iterations

Useful iterations: done (3.4s)

IterNodesCost
01952408
14532113
211071874
334021795
done50001785

prune522.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* b_2 b_2) (* a c))
0.2b
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
1.1b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite221.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
137×add-sqr-sqrt
110×*-un-lft-identity
84×add-cube-cbrt
28×sqrt-prod
26×difference-of-squares
24×associate-/r*
19×prod-diff
15×add-exp-log
13×distribute-lft-out--
9×associate-/r/ add-cbrt-cube
8×add-log-exp
7×flip3-- fma-neg div-exp flip--
6×pow1
5×div-inv
4×expm1-log1p-u log1p-expm1-u
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 → 196
Calls
4 calls:
15.0ms
(- (* b_2 b_2) (* a c))
92.0ms
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
86.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
18.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series442.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(- (* b_2 b_2) (* a c))
197.0ms
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
114.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
84.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify3.2s

Counts
208 → 208
Iterations

Useful iterations: 3 (1.7s)

IterNodesCost
02994764
16414074
214363649
342343500
done50003500

prune510.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
0.2b
(- (* b_2 b_2) (* a c))
1.1b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite295.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
32×*-un-lft-identity
27×add-cube-cbrt
19×prod-diff
17×sqrt-prod
13×add-exp-log associate-*r*
11×times-frac
9×add-cbrt-cube
8×add-log-exp
7×pow1 fma-neg
6×associate-*l*
5×flip3-- flip--
4×expm1-log1p-u prod-exp log1p-expm1-u difference-of-squares
3×unswap-sqr
2×frac-times sub-neg sqrt-div diff-log div-exp associate-*l/ cbrt-unprod distribute-lft-out--
1×cbrt-undiv rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp associate-*r/ pow-prod-down un-div-inv *-commutative div-inv
Counts
4 → 119
Calls
4 calls:
195.0ms
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
11.0ms
(- (* b_2 b_2) (* a c))
63.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
17.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series372.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
46.0ms
(- (* b_2 b_2) (* a c))
104.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
88.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify4.4s

Counts
131 → 131
Iterations

Useful iterations: done (4.4s)

IterNodesCost
02152391
15071990
213331701
345861622
done50001621

prune456.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* b_2 b_2) (* a c))) a)
0.2b
(- (* b_2 b_2) (* a c))
6.1b
(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
22.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite202.0ms

Algorithm
rewrite-expression-head
Rules
481×times-frac
378×add-sqr-sqrt
366×*-un-lft-identity
358×add-cube-cbrt
287×prod-diff
143×sqrt-prod
39×div-inv
23×fma-neg
8×add-log-exp
6×add-exp-log add-cbrt-cube associate-/l* difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- sqrt-div flip-- log1p-expm1-u distribute-lft-out--
3×associate-/r*
2×sub-neg diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square distribute-rgt-out-- frac-2neg sqrt-pow1 pow1/2 div-exp clear-num frac-sub sub-div
Counts
4 → 411
Calls
4 calls:
24.0ms
(/ (sqrt (- (* b_2 b_2) (* a c))) a)
10.0ms
(- (* b_2 b_2) (* a c))
91.0ms
(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series388.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(/ (sqrt (- (* b_2 b_2) (* a c))) a)
64.0ms
(- (* b_2 b_2) (* a c))
100.0ms
(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
89.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.3s

Counts
423 → 423
Iterations

Useful iterations: done (2.3s)

IterNodesCost
049718768
1109816536
2235213182
done500110638

prune712.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 4.6b

regimes270.0ms

Accuracy

84.4% (4.5b remaining)

Error of 9.8b against oracle of 5.3b and baseline of 34.2b

bsearch144.0ms

Steps
ItersRangePoint
11
1.5906747666251227e-34
6.100620313640196e-08
1.611450844781215e-34
9
-6.354265220965125e+156
-1.769171722317776e+149
-1.0084023741576003e+154

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02337
12637
done2637

end0.0ms

sample3.1s

Algorithm
intervals
Results
623.0ms5880×body80valid
617.0ms1077×body2560valid
595.0ms466×body640valid
362.0ms850×body1280valid
177.0ms2914×body80nan
49.0ms107×body5120valid
42.0ms212×body320valid
15.0ms123×body160valid