Details

Time bar (total: 13.5s)

sample85.0ms

Algorithm
intervals
Results
26.0ms273×body80valid
10.0ms103×body80nan

simplify197.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
02038
13838
27837
313637
416337
517537
617937
done17937

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.6b

localize112.0ms

Local error

Found 4 expressions with local error:

1.3b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite71.0ms

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-cbrt-cube sqrt-div add-exp-log
3×flip3-- flip--
2×neg-sub0 rem-sqrt-square sum-log distribute-rgt-neg-in sqrt-pow1 pow1/2 diff-log neg-log distribute-lft-out distribute-lft-out-- difference-of-squares
1×associate--l- +-commutative sub-neg flip3-+ associate-+l- flip-+
Counts
4 → 63
Calls
4 calls:
25.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
7.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series438.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
121.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
101.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
111.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify628.0ms

Counts
75 → 75
Iterations

Useful iterations: done (624.0ms)

IterNodesCost
01001330
12541186
210361089
done50001074

prune458.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.9b

localize153.0ms

Local error

Found 4 expressions with local error:

6.6b
(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.5b
(cbrt (- (* b b) (* (* 4.0 a) c)))
23.5b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
7×*-un-lft-identity add-cube-cbrt
6×cbrt-prod
5×pow1
4×cbrt-div add-cbrt-cube add-exp-log
3×flip3-- sqrt-prod flip--
2×sum-log pow1/3 sqrt-div
1×neg-sub0 +-commutative rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log associate-+l- flip-+
Counts
4 → 54
Calls
4 calls:
13.0ms
(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
7.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series480.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
91.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
124.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
137.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify711.0ms

Counts
66 → 66
Iterations

Useful iterations: done (707.0ms)

IterNodesCost
01461516
13781426
215351235
done50001203

prune582.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.9b

localize191.0ms

Local error

Found 4 expressions with local error:

23.5b
(cbrt (- (* b b) (* (* 4.0 a) c)))
23.5b
(cbrt (- (* b b) (* (* 4.0 a) c)))
23.5b
(cbrt (- (* b b) (* (* 4.0 a) c)))
23.5b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt cbrt-div *-un-lft-identity add-cube-cbrt
4×pow1 flip3-- add-cbrt-cube pow1/3 add-exp-log flip-- add-log-exp
Counts
4 → 52
Calls
4 calls:
9.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
10.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
10.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
10.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series570.0ms

Counts
4 → 12
Calls
4 calls:
153.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
147.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
160.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
110.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify2.4s

Counts
64 → 64
Iterations

Useful iterations: done (2.4s)

IterNodesCost
0651180
11611144
25811024
332551004
done5001964

prune787.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 7.9b

localize138.0ms

Local error

Found 4 expressions with local error:

1.3b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.5b
(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
6.0b
(/ (* a c) b)
22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
14×add-cbrt-cube add-exp-log
13×*-un-lft-identity
10×add-sqr-sqrt
9×add-cube-cbrt
8×add-log-exp
6×times-frac
5×pow1
4×cbrt-undiv associate-/r* div-exp associate-/l*
3×sqrt-prod
2×clear-num sum-log frac-2neg flip3-- sqrt-div prod-exp cbrt-unprod div-inv flip-- distribute-lft-out associate-/l/
1×neg-sub0 +-commutative rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 flip3-+ pow1/2 div-sub neg-log associate-+l- flip-+
Counts
4 → 75
Calls
4 calls:
25.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
45.0ms
(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
8.0ms
(/ (* a c) b)
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series368.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
126.0ms
(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
39.0ms
(/ (* a c) b)
85.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.3s

Counts
87 → 87
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01781385
15111293
226291127
done50011123

prune637.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.8b

regimes314.0ms

Accuracy

89.9% (1.5b remaining)

Error of 8.0b against oracle of 6.5b and baseline of 21.3b

bsearch268.0ms

Steps
ItersRangePoint
9
6.258218916731328e+93
1.8883840965187804e+99
3.911332892361616e+98
7
-1.2092396089946692e+59
-6.172175216823688e+56
-9.72071777755916e+58

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
050148
162148
done62148

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.6s8730×body80valid
287.0ms2931×body80nan