Details

Time bar (total: 13.7s)

sample53.0ms

Algorithm
intervals
Results
10.0ms35×body2560valid
9.0ms185×body80valid
5.0ms23×body1280valid
5.0ms103×body80nan
4.0ms19×body640valid
1.0ms7×body160valid
1.0ms4×body320valid

simplify155.0ms

Counts
1 → 1
Iterations
IterNodes
done164
6164
5160
4153
3121
264
129
014

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.3b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ b (sqrt (fma (* (- a) c) 4.0 (* b b)))) (* 2.0 a))
0.6b
(fma (* (- a) c) 4.0 (* b b))
2.0b
(+ b (sqrt (fma (* (- a) c) 4.0 (* b b))))
22.7b
(sqrt (fma (* (- a) c) 4.0 (* b b)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity
9×add-sqr-sqrt add-cbrt-cube add-exp-log
8×add-cube-cbrt
6×add-log-exp
5×pow1
4×expm1-log1p-u times-frac log1p-expm1-u associate-/l*
3×fma-def sqrt-prod distribute-lft-out
2×cbrt-undiv flip3-+ div-exp flip-+ associate-/l/
1×+-commutative rem-sqrt-square clear-num associate-/r* sum-log frac-2neg sqrt-pow1 pow1/2 prod-exp cbrt-unprod fma-udef div-inv
Counts
4 → 69
Calls
4 calls:
20.0ms
(/ (+ b (sqrt (fma (* (- a) c) 4.0 (* b b)))) (* 2.0 a))
0.0ms
(fma (* (- a) c) 4.0 (* b b))
6.0ms
(+ b (sqrt (fma (* (- a) c) 4.0 (* b b))))
1.0ms
(sqrt (fma (* (- a) c) 4.0 (* b b)))

series435.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(/ (+ b (sqrt (fma (* (- a) c) 4.0 (* b b)))) (* 2.0 a))
77.0ms
(fma (* (- a) c) 4.0 (* b b))
113.0ms
(+ b (sqrt (fma (* (- a) c) 4.0 (* b b))))
115.0ms
(sqrt (fma (* (- a) c) 4.0 (* b b)))

simplify688.0ms

Counts
81 → 81
Iterations
IterNodes
done5000
21064
1303
0124

prune634.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.7b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 2.0 (+ b (sqrt (fma c (* (- a) 4.0) (* b b)))))
0.2b
(* (/ 2.0 (+ b (sqrt (fma c (* (- a) 4.0) (* b b))))) a)
2.0b
(+ b (sqrt (fma c (* (- a) 4.0) (* b b))))
22.7b
(sqrt (fma c (* (- a) 4.0) (* b b)))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
40×*-un-lft-identity
30×add-sqr-sqrt
25×times-frac
24×add-cube-cbrt
18×associate-*l*
11×add-cbrt-cube add-exp-log
8×distribute-lft-out
7×pow1
6×add-log-exp
4×expm1-log1p-u associate-/r* associate-/r/ log1p-expm1-u
3×fma-def flip3-+ associate-*r* sqrt-prod flip-+ associate-/l*
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
1×+-commutative rem-sqrt-square clear-num sum-log frac-2neg sqrt-pow1 pow1/2 pow-prod-down associate-*l/ *-commutative
Counts
4 → 106
Calls
4 calls:
13.0ms
(/ 2.0 (+ b (sqrt (fma c (* (- a) 4.0) (* b b)))))
36.0ms
(* (/ 2.0 (+ b (sqrt (fma c (* (- a) 4.0) (* b b))))) a)
11.0ms
(+ b (sqrt (fma c (* (- a) 4.0) (* b b))))
2.0ms
(sqrt (fma c (* (- a) 4.0) (* b b)))

series615.0ms

Counts
4 → 12
Calls
4 calls:
158.0ms
(/ 2.0 (+ b (sqrt (fma c (* (- a) 4.0) (* b b)))))
227.0ms
(* (/ 2.0 (+ b (sqrt (fma c (* (- a) 4.0) (* b b))))) a)
123.0ms
(+ b (sqrt (fma c (* (- a) 4.0) (* b b))))
107.0ms
(sqrt (fma c (* (- a) 4.0) (* b b)))

simplify976.0ms

Counts
118 → 118
Iterations
IterNodes
done5000
21729
1418
0171

prune865.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.6b

localize71.0ms

Local error

Found 4 expressions with local error:

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

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×*-un-lft-identity
9×sqrt-prod
8×add-cube-cbrt
7×pow1
6×add-log-exp
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u
3×rem-sqrt-square fma-def sqrt-pow1 pow1/2
1×+-commutative sum-log flip3-+ flip-+ distribute-lft-out
Counts
4 → 62
Calls
4 calls:
11.0ms
(+ b (sqrt (fma (* (- a) c) 4.0 (* b b))))
2.0ms
(sqrt (fma (* (- a) c) 4.0 (* b b)))
2.0ms
(sqrt (fma (* (- a) c) 4.0 (* b b)))
3.0ms
(sqrt (fma c (* (- a) 4.0) (* b b)))

series455.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(+ b (sqrt (fma (* (- a) c) 4.0 (* b b))))
108.0ms
(sqrt (fma (* (- a) c) 4.0 (* b b)))
122.0ms
(sqrt (fma (* (- a) c) 4.0 (* b b)))
115.0ms
(sqrt (fma c (* (- a) 4.0) (* b b)))

simplify1.4s

Counts
74 → 74
Iterations
IterNodes
done5001
32799
2525
1165
078

prune854.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 5.5b

localize36.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt b)
0.6b
(fma (* (- a) c) 4.0 (* b b))
21.0b
(fma (* (cbrt b) (cbrt b)) (cbrt b) (sqrt (fma (* (- a) c) 4.0 (* b b))))
22.7b
(sqrt (fma (* (- a) c) 4.0 (* b b)))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt
6×*-un-lft-identity add-cube-cbrt
5×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
3×cbrt-prod sqrt-prod
2×fma-udef
1×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 48
Calls
4 calls:
1.0ms
(cbrt b)
0.0ms
(fma (* (- a) c) 4.0 (* b b))
0.0ms
(fma (* (cbrt b) (cbrt b)) (cbrt b) (sqrt (fma (* (- a) c) 4.0 (* b b))))
1.0ms
(sqrt (fma (* (- a) c) 4.0 (* b b)))

series692.0ms

Counts
4 → 12
Calls
4 calls:
287.0ms
(cbrt b)
99.0ms
(fma (* (- a) c) 4.0 (* b b))
180.0ms
(fma (* (cbrt b) (cbrt b)) (cbrt b) (sqrt (fma (* (- a) c) 4.0 (* b b))))
124.0ms
(sqrt (fma (* (- a) c) 4.0 (* b b)))

simplify841.0ms

Counts
60 → 60
Iterations
IterNodes
done5000
31453
2397
1148
083

prune373.0ms

Pruning

15 alts after pruning (12 fresh and 3 done)

Merged error: 5.5b

regimes523.0ms

Accuracy

81.8% (5.3b remaining)

Error of 10.8b against oracle of 5.5b and baseline of 34.5b

bsearch152.0ms

Steps
ItersRangePoint
9
6.258218916731328e+93
1.8883840965187804e+99
2.9380396584045826e+94
5
-1.0485618335166142e-22
-4.7809817903638944e-23
-7.668263498157484e-23

simplify11.0ms

Iterations
IterNodes
done58
358
257
151
034

end0.0ms

sample3.7s

Algorithm
intervals
Results
1.4s5781×body80valid
594.0ms1114×body2560valid
433.0ms2931×body80nan
354.0ms884×body1280valid
181.0ms464×body640valid
134.0ms250×body320valid
61.0ms110×body5120valid
21.0ms127×body160valid