Details

Time bar (total: 15.3s)

sample71.0ms

Algorithm
intervals
Results
21.0ms9×body5120valid
14.0ms198×body80valid
11.0ms28×body2560valid
3.0ms9×body1280valid
1.0ms6×body640valid
1.0ms6×body320valid

simplify28.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
012324
124219
230219
332219
done32219

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.7b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b
(hypot re im)
0.0b
(+ (hypot re im) re)
0.2b
(sqrt (* (+ (hypot re im) re) 2.0))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
6×pow1 *-un-lft-identity
5×add-log-exp
4×add-sqr-sqrt add-cube-cbrt
3×expm1-log1p-u fma-def add-cbrt-cube add-exp-log log1p-expm1-u
2×sqrt-pow1 flip3-+ sqrt-div associate-*l/ flip-+
1×+-commutative hypot-udef sum-log pow1/2 pow-prod-down sqrt-prod distribute-lft-out
Counts
3 → 42
Calls
3 calls:
0.0ms
(hypot re im)
8.0ms
(+ (hypot re im) re)
12.0ms
(sqrt (* (+ (hypot re im) re) 2.0))

series455.0ms

Counts
3 → 9
Calls
3 calls:
82.0ms
(hypot re im)
94.0ms
(+ (hypot re im) re)
279.0ms
(sqrt (* (+ (hypot re im) re) 2.0))

simplify2.5s

Counts
51 → 51
Iterations

Useful iterations: 3 (941.0ms)

IterNodesCost
0869505
11878133
26237923
338127803
done50007803

prune311.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ (hypot re im) re))
0.0b
(hypot re im)
0.0b
(+ (hypot re im) re)
0.3b
(* (sqrt (+ (hypot re im) re)) (sqrt 2.0))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
16×*-un-lft-identity
15×sqrt-prod
10×add-cube-cbrt
9×pow1
7×associate-*l*
6×add-cbrt-cube associate-*r* add-exp-log add-log-exp
4×expm1-log1p-u sqrt-div log1p-expm1-u unswap-sqr
3×fma-def sqrt-pow1 flip3-+ pow1/2 pow-prod-down flip-+ distribute-lft-out
2×associate-*l/
1×+-commutative rem-sqrt-square hypot-udef sum-log sqrt-unprod prod-exp *-commutative cbrt-unprod hypot-def
Counts
4 → 81
Calls
4 calls:
6.0ms
(sqrt (+ (hypot re im) re))
0.0ms
(hypot re im)
4.0ms
(+ (hypot re im) re)
32.0ms
(* (sqrt (+ (hypot re im) re)) (sqrt 2.0))

series634.0ms

Counts
4 → 12
Calls
4 calls:
207.0ms
(sqrt (+ (hypot re im) re))
64.0ms
(hypot re im)
85.0ms
(+ (hypot re im) re)
278.0ms
(* (sqrt (+ (hypot re im) re)) (sqrt 2.0))

simplify1.3s

Counts
93 → 93
Iterations

Useful iterations: done (1.3s)

IterNodesCost
013521792
130719266
2128518910
done500118710

prune512.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 11.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot re im)
0.0b
(+ (hypot re im) re)
0.2b
(* (sqrt (+ (hypot re im) re)) (sqrt (sqrt 2.0)))
0.2b
(* (* (sqrt (+ (hypot re im) re)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

rewrite127.0ms

Algorithm
rewrite-expression-head
Rules
31×sqrt-prod
25×add-sqr-sqrt
18×associate-*r*
17×*-un-lft-identity
16×pow1
13×add-cube-cbrt
11×add-cbrt-cube add-exp-log
10×pow-prod-down
8×associate-*l*
6×associate-*l/ add-log-exp unswap-sqr
5×sqrt-pow1 pow1/2
4×expm1-log1p-u sqrt-div prod-exp cbrt-unprod log1p-expm1-u
3×fma-def flip3-+ sqrt-unprod flip-+
2×*-commutative distribute-lft-out
1×+-commutative hypot-udef sum-log
Counts
4 → 98
Calls
4 calls:
0.0ms
(hypot re im)
8.0ms
(+ (hypot re im) re)
43.0ms
(* (sqrt (+ (hypot re im) re)) (sqrt (sqrt 2.0)))
70.0ms
(* (* (sqrt (+ (hypot re im) re)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series784.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(hypot re im)
88.0ms
(+ (hypot re im) re)
367.0ms
(* (sqrt (+ (hypot re im) re)) (sqrt (sqrt 2.0)))
262.0ms
(* (* (sqrt (+ (hypot re im) re)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify2.0s

Counts
110 → 110
Iterations

Useful iterations: done (1.9s)

IterNodesCost
015733069
139728234
2217527519
done500127339

prune662.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 11.2b

localize48.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot re im)
0.2b
(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (sqrt 2.0)))
0.3b
(* (* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
14.2b
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
30×sqrt-prod
24×add-sqr-sqrt
18×associate-*r*
16×pow1
12×*-un-lft-identity add-cube-cbrt
11×add-cbrt-cube add-exp-log
10×pow-prod-down
7×associate-*l*
6×unswap-sqr
5×sqrt-pow1 pow1/2
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×sqrt-unprod
2×*-commutative
1×hypot-udef fma-udef
Counts
4 → 86
Calls
4 calls:
0.0ms
(hypot re im)
17.0ms
(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (sqrt 2.0)))
38.0ms
(* (* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series1.1s

Counts
4 → 12
Calls
4 calls:
74.0ms
(hypot re im)
546.0ms
(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (sqrt 2.0)))
307.0ms
(* (* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
206.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify1.9s

Counts
98 → 98
Iterations

Useful iterations: done (1.9s)

IterNodesCost
015437633
138127541
2197526801
done500026481

prune525.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 11.2b

regimes216.0ms

Accuracy

0% (0.3b remaining)

Error of 13.0b against oracle of 12.7b and baseline of 13.0b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
09219
112219
done12219

end0.0ms

sample1.9s

Algorithm
intervals
Results
523.0ms286×body5120valid
496.0ms6072×body80valid
412.0ms694×body2560valid
165.0ms491×body1280valid
93.0ms253×body640valid
24.0ms136×body320valid
11.0ms68×body160valid