Details

Time bar (total: 19.4s)

sample138.0ms

Algorithm
intervals
Results
18.0ms198×body80valid
12.0ms29×body1280valid
9.0ms17×body2560valid
6.0ms82×body80nan
5.0ms13×body640valid
2.0ms10×body320valid
2.0ms4×body5120valid
1.0ms10×body160valid

simplify101.0ms

Counts
1 → 1
Iterations
IterNodes
629
529
427
325
222
114
010

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
1.2b
(- (* b_2 b_2) (* a c))
2.9b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite209.0ms

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-cbrt-cube add-exp-log associate-/l*
5×pow1 distribute-lft-out--
4×flip3-- insert-posit16 flip--
3×associate-/r*
2×sub-neg sqrt-div diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-sub div-exp div-inv
Counts
4 → 88
Calls
4 calls:
103.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
13.0ms
(- (* b_2 b_2) (* a c))
73.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
18.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series376.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
55.0ms
(- (* b_2 b_2) (* a c))
91.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
104.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.1s

Counts
100 → 100
Iterations
IterNodes
32923
2999
1378
0158

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.3b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
1.2b
(- (* b_2 b_2) (* a c))
2.9b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite147.0ms

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×add-cbrt-cube associate-/r/
8×add-log-exp
7×flip3-- div-exp flip--
6×pow1
5×div-inv
4×insert-posit16
3×cbrt-undiv associate-/l*
2×rec-exp sub-neg sqrt-div diff-log 1-exp
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 pow-flip inv-pow
Counts
4 → 166
Calls
4 calls:
69.0ms
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
14.0ms
(- (* b_2 b_2) (* a c))
54.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series406.0ms

Counts
4 → 12
Calls
4 calls:
193.0ms
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
49.0ms
(- (* b_2 b_2) (* a c))
85.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
79.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.9s

Counts
178 → 178
Iterations
IterNodes
35649
21739
1624
0262

prune2.0s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.3b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
1.2b
(- (* b_2 b_2) (* a c))
2.9b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite132.0ms

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-cbrt-cube add-exp-log associate-/l*
5×pow1 distribute-lft-out--
4×flip3-- insert-posit16 flip--
3×associate-/r*
2×sub-neg sqrt-div diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-sub div-exp div-inv
Counts
4 → 88
Calls
4 calls:
65.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
7.0ms
(- (* b_2 b_2) (* a c))
45.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
13.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series399.0ms

Counts
4 → 12
Calls
4 calls:
156.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
59.0ms
(- (* b_2 b_2) (* a c))
99.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
84.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.0s

Counts
100 → 100
Iterations
IterNodes
32923
2999
1378
0158

prune1.0s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 6.3b

localize43.0ms

Local error

Found 4 expressions with local error:

2.9b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.9b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.2b
(sqrt (- (* b_2 b_2) (* a c)))
22.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite127.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×*-un-lft-identity
8×sqrt-prod add-log-exp
6×pow1 add-cube-cbrt
4×flip3-- add-cbrt-cube sqrt-div add-exp-log insert-posit16 flip-- difference-of-squares
2×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log distribute-lft-out--
Counts
4 → 64
Calls
4 calls:
56.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
56.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms
(sqrt (- (* b_2 b_2) (* a c)))
7.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series411.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
114.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
94.0ms
(sqrt (- (* b_2 b_2) (* a c)))
101.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.9s

Counts
76 → 76
Iterations
IterNodes
43644
31513
2537
1185
080

prune894.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 6.3b

regimes398.0ms

Accuracy

78% (6.1b remaining)

Error of 11.9b against oracle of 5.8b and baseline of 33.5b

bsearch341.0ms

Steps
ItersRangePoint
3
1.897422751335727e-16
2.3824489835354504e-16
1.922674299151799e-16
7
4.1266326978064226e-111
9.799836324706106e-110
4.664677641347216e-111
8
9.808312070140145e-191
3.260010576758525e-187
3.207624111695675e-187
10
-4.8388360275630777e+135
-9.113678877832951e+119
-1.3725796156555912e+127

simplify16.0ms

Iterations
IterNodes
251
151
038

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.1s882×body1280valid
850.0ms5930×body80valid
800.0ms1046×body2560valid
379.0ms2875×body80nan
361.0ms498×body640valid
101.0ms121×body5120valid
89.0ms116×body160valid
67.0ms200×body320valid