Details

Time bar (total: 11.1s)

sample34.0ms

Algorithm
intervals
Results
15.0ms280×body80valid
4.0ms81×body80nan

simplify106.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (9.0ms)

IterNodesCost
02038
13838
27837
313637
415637
516537
616837
done16837

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.1b

localize118.0ms

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)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity
12×add-sqr-sqrt add-log-exp
7×sqrt-prod
6×pow1 add-cube-cbrt
4×add-exp-log sqrt-div add-cbrt-cube
3×flip3-- flip--
2×neg-sub0 rem-sqrt-square distribute-rgt-neg-in 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 → 63
Calls
4 calls:
12.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms
(+ (- 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)))

series304.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
79.0ms
(+ (- b) (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)))

simplify1.6s

Counts
75 → 75
Iterations

Useful iterations: 3 (593.0ms)

IterNodesCost
01001330
12461186
27661089
329201070
done50001070

prune286.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.0b

localize117.0ms

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
10×add-sqr-sqrt
9×sqrt-prod
8×add-log-exp
7×pow1 add-cube-cbrt *-un-lft-identity
6×sqrt-div
4×add-exp-log add-cbrt-cube
3×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip--
2×sum-log
1×+-commutative neg-sub0 associate-+l- flip3-+ neg-log flip-+
Counts
4 → 58
Calls
4 calls:
8.0ms
(+ (- 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)))

series288.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (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)))
68.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.5s

Counts
70 → 70
Iterations

Useful iterations: 3 (571.0ms)

IterNodesCost
0861428
12311014
2759938
32858926
done5000926

prune308.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.0b

localize121.0ms

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)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
7×add-cube-cbrt *-un-lft-identity
6×cbrt-prod
5×pow1
4×add-exp-log cbrt-div add-cbrt-cube
3×flip3-- sqrt-prod flip--
2×pow1/3 sqrt-div sum-log
1×+-commutative neg-sub0 associate-+l- rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 54
Calls
4 calls:
5.0ms
(+ (- 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)))

series347.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
96.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
98.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify2.4s

Counts
66 → 66
Iterations

Useful iterations: 3 (1.2s)

IterNodesCost
01461516
13701425
211991215
349381185
done50001185

prune353.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.0b

localize120.0ms

Local error

Found 4 expressions with local error:

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

rewrite16.0ms

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 rem-sqrt-square flip3-- sqrt-pow1 pow1/2 add-cbrt-cube flip-- add-log-exp
Counts
4 → 60
Calls
4 calls:
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)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series280.0ms

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

simplify1.2s

Counts
72 → 72
Iterations

Useful iterations: done (1.2s)

IterNodesCost
0521140
11301008
2434928
31651928
done5000924

prune341.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 7.0b

regimes192.0ms

Accuracy

91.5% (1.1b remaining)

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

bsearch186.0ms

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
040131
149131
done49131

end0.0ms

sample845.0ms

Algorithm
intervals
Results
452.0ms8720×body80valid
139.0ms2943×body80nan