Details

Time bar (total: 10.2s)

sample137.0ms

Algorithm
intervals
Results
40.0ms281×body80nan
23.0ms137×body160valid
21.0ms537×pre80true
16.0ms58×body320valid
5.0ms61×body80valid

simplify113.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
01417
12517
24616
38616
410816
511616
done11616

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.1b
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
37.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

rewrite186.0ms

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:
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(- (* b b) (* (* 4.0 a) c))
101.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
59.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

series442.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
79.0ms
(- (* b b) (* (* 4.0 a) c))
155.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
98.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

simplify1.2s

Counts
118 → 118
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01952476
14802169
214441861
done50011789

prune461.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 5.1b

localize4.0ms

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

prune68.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 5.1b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
39×add-exp-log add-cbrt-cube
14×cbrt-undiv div-exp
13×prod-exp cbrt-unprod
4×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac associate-/r*
2×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u div-inv associate-/l* add-log-exp
1×associate-*r/ associate-/l/
Counts
2 → 55
Calls
2 calls:
14.0ms
(/ (* a c) b)
24.0ms
(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))

series59.0ms

Counts
2 → 6
Calls
2 calls:
26.0ms
(/ (* a c) b)
33.0ms
(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))

simplify977.0ms

Counts
61 → 61
Iterations

Useful iterations: 2 (320.0ms)

IterNodesCost
0111818
1314787
21621559
done5001559

prune200.0ms

Pruning

27 alts after pruning (26 fresh and 1 done)

Merged error: 5.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(log1p (/ (* a c) b))
0.2b
(/ (* a c) b)
0.2b
(/ (* -2.0 (expm1 (log1p (/ (* a c) b)))) (* 2.0 a))
0.3b
(expm1 (log1p (/ (* a c) b)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
21×add-exp-log add-cbrt-cube
6×cbrt-undiv add-sqr-sqrt add-cube-cbrt *-un-lft-identity div-exp
5×expm1-log1p-u prod-exp cbrt-unprod
4×pow1 times-frac associate-/r* log1p-expm1-u add-log-exp
2×frac-2neg clear-num div-inv associate-/l*
1×log1p-udef expm1-log1p log1p-expm1 expm1-udef
Counts
4 → 68
Calls
4 calls:
0.0ms
(log1p (/ (* a c) b))
10.0ms
(/ (* a c) b)
18.0ms
(/ (* -2.0 (expm1 (log1p (/ (* a c) b)))) (* 2.0 a))
0.0ms
(expm1 (log1p (/ (* a c) b)))

series406.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(log1p (/ (* a c) b))
24.0ms
(/ (* a c) b)
122.0ms
(/ (* -2.0 (expm1 (log1p (/ (* a c) b)))) (* 2.0 a))
171.0ms
(expm1 (log1p (/ (* a c) b)))

simplify972.0ms

Counts
80 → 80
Iterations

Useful iterations: done (969.0ms)

IterNodesCost
0146972
1351851
21524683
done5000673

prune287.0ms

Pruning

27 alts after pruning (26 fresh and 1 done)

Merged error: 5.1b

regimes435.0ms

Accuracy

11.3% (6.1b remaining)

Error of 11.1b against oracle of 5.0b and baseline of 11.9b

bsearch86.0ms

Steps
ItersRangePoint
5
6.650147488704243e-06
1.5219671990751255e-05
6.724747266396374e-06

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02438
13138
done3138

end0.0ms

sample4.0s

Algorithm
intervals
Results
1.2s8422×body80nan
864.0ms4894×body160valid
761.0ms16422×pre80true
485.0ms1329×body320valid
147.0ms1777×body80valid