Details

Time bar (total: 30.3s)

sample99.0ms

Algorithm
intervals
Results
17.0ms35×body1280valid
17.0ms31×body2560valid
16.0ms172×body80valid
8.0ms20×body640valid
7.0ms82×body80nan
3.0ms5×body5120valid
2.0ms7×body320valid
0.0ms3×body160valid

simplify474.0ms

Counts
1 → 1
Iterations
IterNodes
done105
7105
6104
5102
494
379
243
125
014

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.7b

localize144.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (- (sqrt (- (* b b) (* 4.0 (* c a)))) b) 2.0) a)
0.4b
(- (* b b) (* 4.0 (* c a)))
0.9b
(- (sqrt (- (* b b) (* 4.0 (* c a)))) b)
22.2b
(sqrt (- (* b b) (* 4.0 (* c a))))

rewrite539.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
135×add-sqr-sqrt
108×*-un-lft-identity
82×add-cube-cbrt
28×sqrt-prod
26×difference-of-squares
22×associate-/l*
19×prod-diff
13×distribute-lft-out--
9×add-cbrt-cube add-exp-log
8×add-log-exp
7×fma-neg
5×pow1 div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×cbrt-undiv associate-/r* flip3-- div-exp flip--
2×sub-neg sqrt-div diff-log div-sub
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 associate-/l/
Counts
4 → 187
Calls
4 calls:
272.0ms
(/ (/ (- (sqrt (- (* b b) (* 4.0 (* c a)))) b) 2.0) a)
41.0ms
(- (* b b) (* 4.0 (* c a)))
149.0ms
(- (sqrt (- (* b b) (* 4.0 (* c a)))) b)
44.0ms
(sqrt (- (* b b) (* 4.0 (* c a))))

series663.0ms

Counts
4 → 12
Calls
4 calls:
219.0ms
(/ (/ (- (sqrt (- (* b b) (* 4.0 (* c a)))) b) 2.0) a)
95.0ms
(- (* b b) (* 4.0 (* c a)))
171.0ms
(- (sqrt (- (* b b) (* 4.0 (* c a)))) b)
178.0ms
(sqrt (- (* b b) (* 4.0 (* c a))))

simplify4.8s

Counts
199 → 199
Iterations
IterNodes
done5003
22215
1797
0325

prune2.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.0b

localize126.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (- (sqrt (- (* b b) (* 4.0 (* c a)))) b) (/ (/ 1 2.0) a))
0.4b
(- (* b b) (* 4.0 (* c a)))
0.9b
(- (sqrt (- (* b b) (* 4.0 (* c a)))) b)
22.2b
(sqrt (- (* b b) (* 4.0 (* c a))))

rewrite661.0ms

Algorithm
rewrite-expression-head
Rules
76×add-sqr-sqrt
71×times-frac
60×*-un-lft-identity
55×add-cube-cbrt
43×associate-*r*
19×prod-diff add-exp-log
17×sqrt-prod
13×add-cbrt-cube
8×add-log-exp
7×pow1 fma-neg
6×div-exp associate-*l*
5×flip3-- prod-exp flip--
4×expm1-log1p-u insert-posit16 log1p-expm1-u div-inv difference-of-squares unswap-sqr
3×cbrt-undiv cbrt-unprod
2×frac-times sub-neg sqrt-div diff-log associate-*l/ distribute-lft-out--
1×rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp pow-prod-down associate-*r/ *-commutative
Counts
4 → 155
Calls
4 calls:
425.0ms
(* (- (sqrt (- (* b b) (* 4.0 (* c a)))) b) (/ (/ 1 2.0) a))
33.0ms
(- (* b b) (* 4.0 (* c a)))
148.0ms
(- (sqrt (- (* b b) (* 4.0 (* c a)))) b)
32.0ms
(sqrt (- (* b b) (* 4.0 (* c a))))

series589.0ms

Counts
4 → 12
Calls
4 calls:
208.0ms
(* (- (sqrt (- (* b b) (* 4.0 (* c a)))) b) (/ (/ 1 2.0) a))
82.0ms
(- (* b b) (* 4.0 (* c a)))
157.0ms
(- (sqrt (- (* b b) (* 4.0 (* c a)))) b)
142.0ms
(sqrt (- (* b b) (* 4.0 (* c a))))

simplify4.5s

Counts
167 → 167
Iterations
IterNodes
done5002
22346
1839
0310

prune1.8s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.8b

localize174.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* b b) (* 4.0 (* c a)))
22.2b
(sqrt (- (* b b) (* 4.0 (* c a))))
22.2b
(sqrt (- (* b b) (* 4.0 (* c a))))
24.2b
(fma (sqrt (sqrt (- (* b b) (* 4.0 (* c a))))) (sqrt (sqrt (- (* b b) (* 4.0 (* c a))))) (- b))

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 *-un-lft-identity add-cube-cbrt sqrt-prod add-log-exp
4×expm1-log1p-u add-cbrt-cube sqrt-div add-exp-log insert-posit16 log1p-expm1-u
3×flip3-- flip--
2×rem-sqrt-square sqrt-pow1 pow1/2
1×sub-neg fma-neg diff-log prod-diff fma-udef
Counts
4 → 64
Calls
4 calls:
45.0ms
(- (* b b) (* 4.0 (* c a)))
32.0ms
(sqrt (- (* b b) (* 4.0 (* c a))))
43.0ms
(sqrt (- (* b b) (* 4.0 (* c a))))
2.0ms
(fma (sqrt (sqrt (- (* b b) (* 4.0 (* c a))))) (sqrt (sqrt (- (* b b) (* 4.0 (* c a))))) (- b))

series639.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (* b b) (* 4.0 (* c a)))
172.0ms
(sqrt (- (* b b) (* 4.0 (* c a))))
156.0ms
(sqrt (- (* b b) (* 4.0 (* c a))))
233.0ms
(fma (sqrt (sqrt (- (* b b) (* 4.0 (* c a))))) (sqrt (sqrt (- (* b b) (* 4.0 (* c a))))) (- b))

simplify3.7s

Counts
76 → 76
Iterations
IterNodes
done5000
32669
2671
1211
091

prune898.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.7b

localize137.0ms

Local error

Found 4 expressions with local error:

1.0b
(+ (sqrt (- (* b b) (* 4.0 (* c a)))) b)
13.8b
(/ (- (- (* b b) (* b b)) (* 4.0 (* c a))) (* a 2.0))
18.5b
(- (* b b) (* b b))
22.2b
(sqrt (- (* b b) (* 4.0 (* c a))))

rewrite351.0ms

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity
10×add-sqr-sqrt
9×add-cbrt-cube add-exp-log add-cube-cbrt
8×add-log-exp
6×fma-def sqrt-prod
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×times-frac flip3-- flip-- associate-/l*
2×cbrt-undiv sqrt-div div-exp associate-/l/
1×+-commutative rem-sqrt-square clear-num associate-/r* sum-log sub-neg frac-2neg sqrt-pow1 flip3-+ distribute-rgt-out-- pow1/2 +-inverses fma-neg diff-log div-sub prod-diff prod-exp cbrt-unprod flip-+ div-inv distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 87
Calls
4 calls:
81.0ms
(+ (sqrt (- (* b b) (* 4.0 (* c a)))) b)
213.0ms
(/ (- (- (* b b) (* b b)) (* 4.0 (* c a))) (* a 2.0))
24.0ms
(- (* b b) (* b b))
29.0ms
(sqrt (- (* b b) (* 4.0 (* c a))))

series265.0ms

Counts
4 → 12
Calls
4 calls:
129.0ms
(+ (sqrt (- (* b b) (* 4.0 (* c a)))) b)
18.0ms
(/ (- (- (* b b) (* b b)) (* 4.0 (* c a))) (* a 2.0))
2.0ms
(- (* b b) (* b b))
115.0ms
(sqrt (- (* b b) (* 4.0 (* c a))))

simplify2.5s

Counts
99 → 99
Iterations
IterNodes
done5000
21236
1413
0161

prune923.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.7b

regimes569.0ms

Accuracy

96.5% (0.8b remaining)

Error of 6.3b against oracle of 5.4b and baseline of 29.6b

bsearch313.0ms

Steps
ItersRangePoint
10
3.302865865338161e+140
2.8302951796802603e+150
5.413497103300552e+144
8
-8.876584595808978e-254
-3.147576329037351e-256
-6.459611810046018e-256
7
-8.18523145413159e+143
-2.8208844788355687e+142
-3.0775171197265305e+143

simplify21.0ms

Iterations
IterNodes
done44
144
035

end0.0ms

sample3.2s

Algorithm
intervals
Results
996.0ms2913×body80nan
593.0ms1056×body2560valid
512.0ms5744×body80valid
419.0ms978×body1280valid
126.0ms454×body640valid
98.0ms138×body5120valid
80.0ms257×body320valid
16.0ms119×body160valid