Details

Time bar (total: 7.3s)

sample40.0ms

Algorithm
intervals
Results
7.0ms34×body2560valid
7.0ms180×body80valid
5.0ms30×body1280valid
3.0ms85×body80nan
2.0ms16×body640valid
0.0ms4×body320valid
0.0ms1×body5120valid
0.0ms3×body160valid

simplify72.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
01417
12517
24616
38616
410816
511616
done11616

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 2.0 a))
0.6b
(- (* b b) (* 4.0 (* a c)))
1.4b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
24.3b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite164.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
27×*-un-lft-identity
21×add-cube-cbrt
19×prod-diff
18×sqrt-prod
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×fma-neg
6×times-frac associate-/l* difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×distribute-lft-out--
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/l/
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 106
Calls
4 calls:
90.0ms
(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 2.0 a))
9.0ms
(- (* b b) (* 4.0 (* a c)))
51.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
11.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series309.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 2.0 a))
46.0ms
(- (* b b) (* 4.0 (* a c)))
81.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
74.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify924.0ms

Counts
118 → 118
Iterations

Useful iterations: done (920.0ms)

IterNodesCost
01932476
14812169
214191861
done50001789

prune292.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
0.6b
(- (* b b) (* 4.0 (* a c)))
1.4b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
24.3b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite136.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt
60×times-frac
50×*-un-lft-identity
40×add-cube-cbrt
25×add-exp-log
20×sqrt-prod
19×prod-diff
13×add-cbrt-cube
12×div-exp associate-/r*
10×difference-of-squares
9×associate-/r/
8×add-log-exp
7×flip3-- fma-neg flip--
6×pow1
5×cbrt-undiv div-inv distribute-lft-out--
4×expm1-log1p-u log1p-expm1-u
3×rec-exp 1-exp prod-exp associate-/l*
2×sub-neg sqrt-div diff-log
1×rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 clear-num cbrt-unprod inv-pow
Counts
4 → 152
Calls
4 calls:
58.0ms
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
9.0ms
(- (* b b) (* 4.0 (* a c)))
51.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
12.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series345.0ms

Counts
4 → 12
Calls
4 calls:
143.0ms
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
45.0ms
(- (* b b) (* 4.0 (* a c)))
82.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
75.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify907.0ms

Counts
164 → 164
Iterations

Useful iterations: done (902.0ms)

IterNodesCost
02594025
15883484
216333082
done50002938

prune317.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (/ 1 2.0) a) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b))
0.6b
(- (pow b 2) (* 4.0 (* a c)))
1.4b
(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
24.3b
(sqrt (- (pow b 2) (* 4.0 (* a c))))

rewrite300.0ms

Algorithm
rewrite-expression-head
Rules
104×add-sqr-sqrt
88×*-un-lft-identity
83×add-cube-cbrt
71×times-frac
62×prod-diff
43×associate-*l*
35×sqrt-prod
20×distribute-rgt-in distribute-lft-in
19×add-exp-log
14×fma-neg
13×add-cbrt-cube
8×add-log-exp
7×pow1
6×unpow-prod-down div-exp associate-*r*
5×flip3-- prod-exp flip--
4×expm1-log1p-u sub-neg log1p-expm1-u div-inv difference-of-squares unswap-sqr
3×cbrt-undiv cbrt-unprod
2×frac-times sqrt-div diff-log associate-*r/ distribute-lft-out-- unpow2 sqr-pow
1×rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp pow-prod-down associate-*l/ *-commutative
Counts
4 → 205
Calls
4 calls:
177.0ms
(* (/ (/ 1 2.0) a) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b))
17.0ms
(- (pow b 2) (* 4.0 (* a c)))
80.0ms
(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
17.0ms
(sqrt (- (pow b 2) (* 4.0 (* a c))))

series347.0ms

Counts
4 → 12
Calls
4 calls:
147.0ms
(* (/ (/ 1 2.0) a) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b))
46.0ms
(- (pow b 2) (* 4.0 (* a c)))
81.0ms
(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
73.0ms
(sqrt (- (pow b 2) (* 4.0 (* a c))))

simplify1.1s

Counts
217 → 217
Iterations

Useful iterations: done (1.1s)

IterNodesCost
03365769
18304989
221864136
done50013815

prune462.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.1b

localize3.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune0.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 6.1b

regimes184.0ms

Accuracy

82.7% (4.9b remaining)

Error of 11.0b against oracle of 6.1b and baseline of 34.6b

bsearch90.0ms

Steps
ItersRangePoint
8
1.7227097696114035e-146
1.4073942755830443e-143
1.3880700472259379e-143
7
-4.0536724039500882e+121
-2.0347159842260902e+119
-1.5371152004560157e+121

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02940
13640
done3640

end0.0ms

sample1.2s

Algorithm
intervals
Results
235.0ms1092×body2560valid
222.0ms5865×body80valid
165.0ms916×body1280valid
109.0ms2944×body80nan
67.0ms460×body640valid
30.0ms116×body5120valid
22.0ms209×body320valid
7.0ms105×body160valid