Details

Time bar (total: 10.4s)

sample35.0ms

Algorithm
intervals
Results
14.0ms277×body80valid
4.0ms94×body80nan

simplify98.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
02038
13838
27837
313637
415637
516537
616837
done16837

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.5b

localize120.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* (* 4.0 a) c))
2.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
26.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
26.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×*-un-lft-identity add-log-exp
7×sqrt-prod
6×pow1 add-cube-cbrt
4×add-exp-log flip3-- sqrt-div add-cbrt-cube flip--
3×diff-log
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 distribute-rgt-neg-in neg-log
Counts
4 → 60
Calls
4 calls:
2.0ms
(- (* b b) (* (* 4.0 a) c))
12.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series267.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(- (* b b) (* (* 4.0 a) c))
74.0ms
(- (- 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)))

simplify1.7s

Counts
72 → 72
Iterations

Useful iterations: 3 (558.0ms)

IterNodesCost
0971211
12281091
27651009
33087998
done5000998

prune287.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.6b

localize120.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* (* 4.0 a) c))
4.0b
(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
4.8b
(/ (* a c) b)
26.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
17×*-un-lft-identity
14×add-exp-log add-sqr-sqrt add-cbrt-cube
9×add-cube-cbrt times-frac
7×associate-/l*
6×add-log-exp
5×pow1
4×cbrt-undiv div-exp associate-/r* distribute-lft-out--
3×flip3-- sqrt-prod flip--
2×distribute-rgt-neg-in frac-2neg sqrt-div prod-exp clear-num cbrt-unprod div-inv associate-/l/ difference-of-squares
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log div-sub
Counts
4 → 78
Calls
4 calls:
2.0ms
(- (* b b) (* (* 4.0 a) c))
27.0ms
(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
3.0ms
(/ (* a c) b)
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series199.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(- (* b b) (* (* 4.0 a) c))
61.0ms
(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
19.0ms
(/ (* a c) b)
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify752.0ms

Counts
90 → 90
Iterations

Useful iterations: 2 (151.0ms)

IterNodesCost
01661417
14251349
216481173
done50001173

prune339.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.5b

localize121.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* 2.0 c) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
0.6b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
0.8b
(- (* b b) (* (* 4.0 a) c))
26.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
13×*-un-lft-identity
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×add-cube-cbrt
6×times-frac associate-/r* sqrt-prod difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-lft-out--
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/r/
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 prod-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
4 → 71
Calls
4 calls:
20.0ms
(/ (* 2.0 c) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
17.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
2.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series407.0ms

Counts
4 → 12
Calls
4 calls:
199.0ms
(/ (* 2.0 c) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
83.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
50.0ms
(- (* b b) (* (* 4.0 a) c))
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.9s

Counts
83 → 83
Iterations

Useful iterations: 3 (905.0ms)

IterNodesCost
01451551
13491445
211681291
346561287
done50001287

prune305.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.3b

localize119.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* 2.0 c) (/ 1 (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
0.6b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
0.8b
(- (* b b) (* (* 4.0 a) c))
26.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
26×add-exp-log
24×associate-*r*
23×*-un-lft-identity
18×times-frac
16×add-cbrt-cube
15×add-cube-cbrt
12×prod-exp
10×pow1
8×add-log-exp difference-of-squares
7×sqrt-prod
6×cbrt-unprod
4×flip3-- div-exp flip-- distribute-lft-out--
3×pow-prod-down
2×cbrt-undiv sub-neg rec-exp sqrt-div diff-log 1-exp associate-/r/
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ associate-*l* un-div-inv *-commutative div-inv
Counts
4 → 91
Calls
4 calls:
43.0ms
(* (* 2.0 c) (/ 1 (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
17.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
2.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series409.0ms

Counts
4 → 12
Calls
4 calls:
202.0ms
(* (* 2.0 c) (/ 1 (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
83.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
47.0ms
(- (* b b) (* (* 4.0 a) c))
77.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.5s

Counts
103 → 103
Iterations

Useful iterations: 2 (322.0ms)

IterNodesCost
01831968
14941761
217091489
done50001489

prune314.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.3b

regimes248.0ms

Accuracy

89.3% (1.5b remaining)

Error of 7.9b against oracle of 6.3b and baseline of 20.7b

bsearch180.0ms

Steps
ItersRangePoint
9
2.944023772201993e+37
9.447687191993962e+42
9.148614558474486e+42
8
-6.10058349091927e+155
-9.408528429616011e+151
-1.3696490745623736e+154

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
046124
155124
done55124

end0.0ms

sample882.0ms

Algorithm
intervals
Results
463.0ms8731×body80valid
134.0ms2868×body80nan