Details

Time bar (total: 12.1s)

sample37.0ms

Algorithm
intervals
Results
14.0ms274×body80valid
5.0ms104×body80nan

simplify143.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (11.0ms)

IterNodesCost
02038
13938
27937
314237
417137
518137
618537
done18537

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.2b

localize82.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* (* 4.0 a) c))
1.2b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
11×add-sqr-sqrt
10×fma-def add-log-exp
9×add-cube-cbrt
6×pow1 sqrt-prod
4×add-exp-log expm1-log1p-u distribute-rgt-neg-in sqrt-div add-cbrt-cube log1p-expm1-u
3×distribute-lft-neg-in flip3-- flip--
2×rem-sqrt-square sqrt-pow1 pow1/2 sum-log distribute-lft-out
1×+-commutative neg-sub0 associate-+l- neg-mul-1 sub-neg flip3-+ fma-neg diff-log prod-diff neg-log flip-+
Counts
4 → 77
Calls
4 calls:
8.0ms
(- (* b b) (* (* 4.0 a) c))
22.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series271.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(- (* b b) (* (* 4.0 a) c))
81.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.7s

Counts
89 → 89
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01041247
12611114
29091017
335141006
done50001005

prune371.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.1b

localize84.0ms

Local error

Found 4 expressions with local error:

14.2b
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
23.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
10×fma-neg prod-diff
9×sqrt-prod
8×add-log-exp
7×pow1
6×distribute-lft-neg-in distribute-rgt-neg-in sqrt-div
4×add-exp-log expm1-log1p-u flip3-- add-cbrt-cube flip-- log1p-expm1-u
3×rem-sqrt-square sqrt-pow1 pow1/2
2×neg-mul-1 diff-log
1×associate--l- neg-sub0 sub-neg neg-log difference-of-squares
Counts
4 → 88
Calls
4 calls:
14.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series286.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
67.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.8s

Counts
100 → 100
Iterations

Useful iterations: done (1.8s)

IterNodesCost
01152639
12821649
28591574
333301538
done50001535

prune404.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.1b

localize88.0ms

Local error

Found 4 expressions with local error:

23.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
4×add-exp-log expm1-log1p-u rem-sqrt-square flip3-- sqrt-pow1 pow1/2 add-cbrt-cube flip-- log1p-expm1-u add-log-exp
Counts
4 → 68
Calls
4 calls:
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series283.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.9s

Counts
80 → 80
Iterations

Useful iterations: done (1.9s)

IterNodesCost
0541228
11391080
24471004
317101004
done50011000

prune395.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.1b

localize95.0ms

Local error

Found 4 expressions with local error:

23.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
4×add-exp-log expm1-log1p-u rem-sqrt-square flip3-- sqrt-pow1 pow1/2 add-cbrt-cube flip-- log1p-expm1-u add-log-exp
Counts
4 → 68
Calls
4 calls:
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series291.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.9s

Counts
80 → 80
Iterations

Useful iterations: done (1.9s)

IterNodesCost
0541228
11391080
24471004
317101004
done50011000

prune424.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.1b

regimes173.0ms

Accuracy

80.9% (2.4b remaining)

Error of 9.8b against oracle of 7.4b and baseline of 19.9b

bsearch129.0ms

Steps
ItersRangePoint
6
2.0335150395734557e+19
1.0746392320557105e+20
1.0610691325078738e+20
5
-130518226990374.3
-34802195229717.125
-128454993639955.03

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
046193
158193
done58193

end0.0ms

sample945.0ms

Algorithm
intervals
Results
457.0ms8685×body80valid
135.0ms2832×body80nan