Details

Time bar (total: 6.2s)

sample57.0ms

Algorithm
intervals
Results
12.0ms161×body160valid
10.0ms297×body80nan
10.0ms553×pre80true
4.0ms41×body320valid
2.0ms54×body80valid

simplify50.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
01417
12517
24516
38716
410616
511416
done11416

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
41.0b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
135×add-sqr-sqrt
108×*-un-lft-identity
82×add-cube-cbrt
28×sqrt-prod
26×difference-of-squares
22×associate-/l*
19×prod-diff
13×distribute-lft-out--
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×fma-neg
5×pow1 div-inv
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv flip3-- div-exp associate-/r* flip--
2×sub-neg sqrt-div diff-log div-sub
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l/
Counts
4 → 183
Calls
4 calls:
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms
(- (* b b) (* (* 4.0 a) c))
38.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
25.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

series310.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
44.0ms
(- (* b b) (* (* 4.0 a) c))
113.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
81.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

simplify999.0ms

Counts
195 → 195
Iterations

Useful iterations: done (992.0ms)

IterNodesCost
03214967
17804592
230174265
done50014264

prune508.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 4.8b

localize4.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify1.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000
done00

prune49.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 4.8b

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (* a c) b)
0.3b
(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
27×add-exp-log add-cbrt-cube
20×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
13×cbrt-undiv div-exp
8×associate-/l*
6×associate-/r* div-inv
5×prod-exp cbrt-unprod
2×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
1×associate-/l/
Counts
2 → 77
Calls
2 calls:
3.0ms
(/ (* a c) b)
10.0ms
(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)

series40.0ms

Counts
2 → 6
Calls
2 calls:
19.0ms
(/ (* a c) b)
21.0ms
(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)

simplify749.0ms

Counts
83 → 83
Iterations

Useful iterations: 2 (150.0ms)

IterNodesCost
01711200
14591154
22313992
done5000992

prune232.0ms

Pruning

30 alts after pruning (29 fresh and 1 done)

Merged error: 4.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(log1p (/ (* a c) b))
0.2b
(/ (* a c) b)
0.3b
(/ (/ (* -2.0 (expm1 (log1p (/ (* a c) b)))) 2.0) a)
0.3b
(expm1 (log1p (/ (* a c) b)))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
22×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×add-exp-log add-cbrt-cube
8×associate-/l*
7×cbrt-undiv div-exp
6×associate-/r* div-inv
5×expm1-log1p-u
4×pow1 log1p-expm1-u add-log-exp
2×frac-2neg prod-exp clear-num cbrt-unprod
1×log1p-udef expm1-log1p log1p-expm1 associate-/l/ expm1-udef
Counts
4 → 95
Calls
4 calls:
0.0ms
(log1p (/ (* a c) b))
3.0ms
(/ (* a c) b)
6.0ms
(/ (/ (* -2.0 (expm1 (log1p (/ (* a c) b)))) 2.0) a)
0.0ms
(expm1 (log1p (/ (* a c) b)))

series268.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(log1p (/ (* a c) b))
19.0ms
(/ (* a c) b)
91.0ms
(/ (/ (* -2.0 (expm1 (log1p (/ (* a c) b)))) 2.0) a)
97.0ms
(expm1 (log1p (/ (* a c) b)))

simplify661.0ms

Counts
107 → 107
Iterations

Useful iterations: done (658.0ms)

IterNodesCost
02061524
14891317
221531171
done50001168

prune225.0ms

Pruning

31 alts after pruning (30 fresh and 1 done)

Merged error: 4.7b

regimes356.0ms

Accuracy

13.7% (6.2b remaining)

Error of 11.2b against oracle of 5.0b and baseline of 12.1b

bsearch47.0ms

Steps
ItersRangePoint
6
0.00017659738910379716
0.0013183985859660308
0.00017936624356974993

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02238
12638
done2638

end0.0ms

sample1.5s

Algorithm
intervals
Results
349.0ms4850×body160valid
301.0ms16215×pre80true
282.0ms8215×body80nan
144.0ms1326×body320valid
66.0ms1824×body80valid