Details

Time bar (total: 15.9s)

sample59.0ms

Algorithm
intervals
Results
10.0ms33×body2560valid
9.0ms35×body1280valid
9.0ms168×body80valid
5.0ms92×body80nan
3.0ms15×body640valid
2.0ms6×body5120valid
1.0ms9×body320valid
1.0ms8×body160valid

simplify153.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
01417
12517
24616
38616
410816
511616
done11616

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
1.2b
(- (* b b) (* (* 4.0 a) c))
2.0b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite257.0ms

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:
135.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
19.0ms
(- (* b b) (* (* 4.0 a) c))
83.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series420.0ms

Counts
4 → 12
Calls
4 calls:
160.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
61.0ms
(- (* b b) (* (* 4.0 a) c))
104.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
95.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts
118 → 118
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01952476
14802169
214411861
done50001789

prune513.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.4b

localize4.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify7.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune33.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.4b

localize29.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) a)
1.2b
(- (* b b) (* (* 4.0 a) c))
2.0b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite257.0ms

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:
138.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) a)
11.0ms
(- (* b b) (* (* 4.0 a) c))
80.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
24.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series881.0ms

Counts
4 → 12
Calls
4 calls:
149.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) a)
529.0ms
(- (* b b) (* (* 4.0 a) c))
127.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
77.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.8s

Counts
130 → 130
Iterations

Useful iterations: 3 (2.0s)

IterNodesCost
01992768
14662451
212552182
346272092
done50002092

prune554.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ a (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
1.2b
(- (* b b) (* (* 4.0 a) c))
2.0b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite149.0ms

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 associate-/r* add-cbrt-cube
5×pow1 distribute-lft-out--
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×associate-/l*
2×sub-neg sqrt-div diff-log associate-/r/
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv
Counts
4 → 117
Calls
4 calls:
55.0ms
(/ a (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
9.0ms
(- (* b b) (* (* 4.0 a) c))
65.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
16.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series481.0ms

Counts
4 → 12
Calls
4 calls:
243.0ms
(/ a (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
55.0ms
(- (* b b) (* (* 4.0 a) c))
97.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
86.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.7s

Counts
129 → 129
Iterations

Useful iterations: done (2.7s)

IterNodesCost
01922728
14122412
210792146
338512059
done50002058

prune492.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 7.3b

regimes300.0ms

Accuracy

87.3% (4.4b remaining)

Error of 10.0b against oracle of 5.6b and baseline of 40.0b

bsearch220.0ms

Steps
ItersRangePoint
10
7.858103861298114e-57
4.4245337053054734e-42
7.029337360841496e-56
10
-3.742210988141449e+103
-1.1204690717208776e+87
-8.301687926884189e+98

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02840
13540
done3540

end0.0ms

sample2.9s

Algorithm
intervals
Results
892.0ms1051×body2560valid
537.0ms5870×body80valid
357.0ms893×body1280valid
332.0ms2845×body80nan
203.0ms480×body640valid
43.0ms218×body320valid
43.0ms98×body5120valid
13.0ms108×body160valid