Details

Time bar (total: 16.1s)

sample53.0ms

Algorithm
intervals
Results
12.0ms256×pre80true
11.0ms256×body80valid

simplify73.0ms

Counts
1 → 1
Iterations
IterNodes
done117
5117
4113
376
241
118
07

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 1 expressions with local error:

0.1b
(* (+ (+ b c) d) a)

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
8×*-un-lft-identity
5×add-sqr-sqrt associate-*l*
3×pow1 add-cbrt-cube associate-*r* add-exp-log add-cube-cbrt distribute-lft-out
2×associate-*l/
1×expm1-log1p-u flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ log1p-expm1-u add-log-exp unswap-sqr
Counts
1 → 24
Calls
1 calls:
106.0ms
(* (+ (+ b c) d) a)

series46.0ms

Counts
1 → 3
Calls
1 calls:
46.0ms
(* (+ (+ b c) d) a)

simplify603.0ms

Counts
27 → 27
Iterations
IterNodes
done5000
2692
1134
051

prune121.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ (+ c d) b))
0.0b
(sqrt (+ (+ b c) d))
0.2b
(* (sqrt (+ (+ c d) b)) a)
0.3b
(* (sqrt (+ (+ b c) d)) (* (sqrt (+ (+ c d) b)) a))

rewrite386.0ms

Algorithm
rewrite-expression-head
Rules
31×*-un-lft-identity
21×add-sqr-sqrt sqrt-prod
18×sqrt-div
16×associate-*l*
13×pow1
12×distribute-lft-out
11×add-cbrt-cube add-exp-log add-cube-cbrt
10×associate-*l/
9×flip3-+ flip-+
4×expm1-log1p-u frac-times associate-*r* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ *-commutative hypot-def unswap-sqr
Counts
4 → 101
Calls
4 calls:
54.0ms
(sqrt (+ (+ c d) b))
51.0ms
(sqrt (+ (+ b c) d))
94.0ms
(* (sqrt (+ (+ c d) b)) a)
184.0ms
(* (sqrt (+ (+ b c) d)) (* (sqrt (+ (+ c d) b)) a))

series469.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(sqrt (+ (+ c d) b))
72.0ms
(sqrt (+ (+ b c) d))
129.0ms
(* (sqrt (+ (+ c d) b)) a)
201.0ms
(* (sqrt (+ (+ b c) d)) (* (sqrt (+ (+ c d) b)) a))

simplify1.3s

Counts
113 → 113
Iterations
IterNodes
done5000
22149
1494
0188

prune678.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot (sqrt (+ c d)) (sqrt b))
0.0b
(sqrt (+ (+ b c) d))
0.2b
(* (hypot (sqrt (+ c d)) (sqrt b)) a)
0.3b
(* (sqrt (+ (+ b c) d)) (* (hypot (sqrt (+ c d)) (sqrt b)) a))

rewrite155.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
14×add-sqr-sqrt
12×pow1
11×add-cbrt-cube associate-*l* add-exp-log
10×sqrt-prod
9×add-cube-cbrt
6×distribute-lft-out
4×expm1-log1p-u sqrt-div associate-*r* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u add-log-exp
2×flip3-+ associate-*l/ *-commutative flip-+
1×rem-sqrt-square hypot-udef sqrt-pow1 pow1/2 hypot-def unswap-sqr
Counts
4 → 77
Calls
4 calls:
0.0ms
(hypot (sqrt (+ c d)) (sqrt b))
31.0ms
(sqrt (+ (+ b c) d))
10.0ms
(* (hypot (sqrt (+ c d)) (sqrt b)) a)
109.0ms
(* (sqrt (+ (+ b c) d)) (* (hypot (sqrt (+ c d)) (sqrt b)) a))

series1.5s

Counts
4 → 12
Calls
4 calls:
337.0ms
(hypot (sqrt (+ c d)) (sqrt b))
68.0ms
(sqrt (+ (+ b c) d))
368.0ms
(* (hypot (sqrt (+ c d)) (sqrt b)) a)
701.0ms
(* (sqrt (+ (+ b c) d)) (* (hypot (sqrt (+ c d)) (sqrt b)) a))

simplify1.1s

Counts
89 → 89
Iterations
IterNodes
done5001
21886
1473
0181

prune627.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.2b
(* a (sqrt (+ (+ d b) c)))
0.3b
(* (hypot (sqrt (+ c d)) (sqrt b)) (* a (sqrt (+ (+ d b) c))))
0.3b
(* (hypot (sqrt (+ c d)) (sqrt b)) (* a (sqrt (+ (+ d b) c))))
0.5b
(* (sqrt (* (hypot (sqrt (+ c d)) (sqrt b)) (* a (sqrt (+ (+ d b) c))))) (sqrt (* (hypot (sqrt (+ c d)) (sqrt b)) (* a (sqrt (+ (+ d b) c))))))

rewrite712.0ms

Algorithm
rewrite-expression-head
Rules
143×pow1
78×pow-prod-down
60×sqrt-pow1
36×associate-*r/
30×sqrt-div
19×add-sqr-sqrt
18×*-un-lft-identity add-cbrt-cube add-exp-log
17×pow-prod-up
14×associate-*r*
13×associate-*l* add-cube-cbrt
12×pow1/2
11×pow-sqr
10×sqrt-prod
9×flip3-+ flip-+
8×prod-exp cbrt-unprod
4×expm1-log1p-u frac-times swap-sqr *-commutative log1p-expm1-u add-log-exp
3×distribute-lft-out unswap-sqr
2×associate-*l/
1×pow2 rem-square-sqrt pow-plus sqrt-unprod
Counts
4 → 148
Calls
4 calls:
72.0ms
(* a (sqrt (+ (+ d b) c)))
76.0ms
(* (hypot (sqrt (+ c d)) (sqrt b)) (* a (sqrt (+ (+ d b) c))))
81.0ms
(* (hypot (sqrt (+ c d)) (sqrt b)) (* a (sqrt (+ (+ d b) c))))
476.0ms
(* (sqrt (* (hypot (sqrt (+ c d)) (sqrt b)) (* a (sqrt (+ (+ d b) c))))) (sqrt (* (hypot (sqrt (+ c d)) (sqrt b)) (* a (sqrt (+ (+ d b) c))))))

series3.7s

Counts
4 → 12
Calls
4 calls:
106.0ms
(* a (sqrt (+ (+ d b) c)))
736.0ms
(* (hypot (sqrt (+ c d)) (sqrt b)) (* a (sqrt (+ (+ d b) c))))
659.0ms
(* (hypot (sqrt (+ c d)) (sqrt b)) (* a (sqrt (+ (+ d b) c))))
2.2s
(* (sqrt (* (hypot (sqrt (+ c d)) (sqrt b)) (* a (sqrt (+ (+ d b) c))))) (sqrt (* (hypot (sqrt (+ c d)) (sqrt b)) (* a (sqrt (+ (+ d b) c))))))

simplify1.1s

Counts
160 → 160
Iterations
IterNodes
done5001
22139
1498
0196

prune1.1s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes472.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done10
110
07

end0.0ms

sample1.6s

Algorithm
intervals
Results
346.0ms8000×body80valid
287.0ms8000×pre80true