Details

Time bar (total: 10.2s)

sample35.0ms

Algorithm
intervals
Results
15.0ms280×body80valid
4.0ms81×body80nan

simplify107.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
02038
13938
27937
314337
416937
517837
618137
done18137

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.1b

localize114.0ms

Local error

Found 4 expressions with local error:

0.9b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.1b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
58×*-un-lft-identity
56×add-sqr-sqrt
50×add-cube-cbrt
37×sqrt-prod
26×distribute-rgt-neg-in
24×distribute-lft-neg-in
12×add-log-exp
10×fma-def fma-neg
8×neg-mul-1
6×pow1
4×add-exp-log expm1-log1p-u sqrt-div add-cbrt-cube log1p-expm1-u
3×flip3-- flip--
2×neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 diff-log neg-log sum-log distribute-lft-out distribute-lft-out-- difference-of-squares
1×+-commutative associate--l- associate-+l- sub-neg flip3-+ flip-+
Counts
4 → 151
Calls
4 calls:
16.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series296.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
77.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.2s

Counts
163 → 163
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01796238
14074208
211713343
done50003240

prune434.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.0b

localize114.0ms

Local error

Found 4 expressions with local error:

7.5b
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
21.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
10×add-cube-cbrt fma-def *-un-lft-identity
9×sqrt-prod
8×add-log-exp
7×pow1
6×sqrt-div
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×distribute-lft-neg-in rem-sqrt-square flip3-- distribute-rgt-neg-in sqrt-pow1 pow1/2 flip--
2×sum-log
1×+-commutative neg-sub0 associate-+l- neg-mul-1 flip3-+ neg-log flip-+
Counts
4 → 76
Calls
4 calls:
6.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series295.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts
88 → 88
Iterations

Useful iterations: 3 (684.0ms)

IterNodesCost
0901548
12471095
28301019
332751007
done50001007

prune394.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.0b

localize123.0ms

Local error

Found 4 expressions with local error:

21.9b
(cbrt (- (* b b) (* (* 4.0 a) c)))
21.9b
(cbrt (- (* b b) (* (* 4.0 a) c)))
21.9b
(cbrt (- (* b b) (* (* 4.0 a) c)))
23.9b
(fma (sqrt (cbrt (- (* b b) (* (* 4.0 a) c)))) (- (fabs (cbrt (- (* b b) (* (* 4.0 a) c))))) (- b))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×cbrt-div
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×flip3-- pow1/3 flip--
1×fma-udef
Counts
4 → 55
Calls
4 calls:
2.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
2.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
2.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
0.0ms
(fma (sqrt (cbrt (- (* b b) (* (* 4.0 a) c)))) (- (fabs (cbrt (- (* b b) (* (* 4.0 a) c))))) (- b))

series379.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
97.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
94.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
92.0ms
(fma (sqrt (cbrt (- (* b b) (* (* 4.0 a) c)))) (- (fabs (cbrt (- (* b b) (* (* 4.0 a) c))))) (- b))

simplify1.3s

Counts
67 → 67
Iterations

Useful iterations: 3 (421.0ms)

IterNodesCost
01121401
12701350
28161181
329561141
done50011141

prune472.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.0b

localize117.0ms

Local error

Found 4 expressions with local error:

7.5b
(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
21.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.9b
(cbrt (- (* b b) (* (* 4.0 a) c)))
21.9b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×add-cube-cbrt fma-def *-un-lft-identity
8×add-log-exp
6×cbrt-prod
5×pow1
4×add-exp-log expm1-log1p-u cbrt-div add-cbrt-cube log1p-expm1-u
3×distribute-lft-neg-in flip3-- distribute-rgt-neg-in sqrt-prod flip--
2×pow1/3 sqrt-div sum-log
1×+-commutative neg-sub0 associate-+l- neg-mul-1 rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 72
Calls
4 calls:
6.0ms
(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
2.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
2.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series351.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
98.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
99.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts
84 → 84
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01521636
13921532
213001322
done50001296

prune463.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.0b

regimes206.0ms

Accuracy

91.5% (1.1b remaining)

Error of 8.7b against oracle of 7.6b and baseline of 20.2b

bsearch176.0ms

Steps
ItersRangePoint
10
1.1889782913455773e+76
6.845935134449847e+90
1.4299971857112076e+88
7
-1.9127319211193897e+86
-3.881068201361415e+84
-1.885822949172535e+86

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
042131
152131
done52131

end0.0ms

sample870.0ms

Algorithm
intervals
Results
471.0ms8720×body80valid
145.0ms2943×body80nan