Details

Time bar (total: 12.2s)

sample95.0ms

Algorithm
intervals
Results
31.0ms35×body1280valid
14.0ms33×body2560valid
12.0ms168×body80valid
6.0ms92×body80nan
4.0ms15×body640valid
3.0ms6×body5120valid
2.0ms9×body320valid
1.0ms8×body160valid

simplify130.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
01417
12517
24616
38616
410816
511616
done11616

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.6b

localize25.0ms

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))))

rewrite215.0ms

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:
131.0ms
(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 2.0 a))
10.0ms
(- (* b b) (* 4.0 (* a c)))
58.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
12.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series450.0ms

Counts
4 → 12
Calls
4 calls:
165.0ms
(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 2.0 a))
62.0ms
(- (* b b) (* 4.0 (* a c)))
127.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
96.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.5s

Counts
118 → 118
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01932476
14812169
214191861
done50001789

prune477.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.4b

localize13.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify1.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune31.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.4b

localize31.0ms

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))))

rewrite277.0ms

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:
124.0ms
(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 2.0 a))
14.0ms
(- (* b b) (* 4.0 (* a c)))
112.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
24.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series449.0ms

Counts
4 → 12
Calls
4 calls:
140.0ms
(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 2.0 a))
88.0ms
(- (* b b) (* 4.0 (* a c)))
123.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
97.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.4s

Counts
118 → 118
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01932476
14812169
214191861
done50001789

prune464.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 7.4b

localize34.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (* 2.0 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))))

rewrite157.0ms

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-/r* 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-/r/
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 prod-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
4 → 105
Calls
4 calls:
53.0ms
(/ (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
10.0ms
(- (* b b) (* 4.0 (* a c)))
71.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
17.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series650.0ms

Counts
4 → 12
Calls
4 calls:
333.0ms
(/ (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
67.0ms
(- (* b b) (* 4.0 (* a c)))
138.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
111.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.4s

Counts
117 → 117
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01842435
14402126
213111820
done50011750

prune418.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 7.4b

regimes294.0ms

Accuracy

87.3% (4.3b remaining)

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

bsearch231.0ms

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

simplify10.0ms

Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
02840
13638
done3638

end0.0ms

sample3.5s

Algorithm
intervals
Results
825.0ms2845×body80nan
600.0ms1051×body2560valid
586.0ms5870×body80valid
522.0ms893×body1280valid
235.0ms480×body640valid
56.0ms98×body5120valid
50.0ms218×body320valid
17.0ms108×body160valid