Details

Time bar (total: 4.8s)

sample21.0ms

Algorithm
intervals
Results
11.0ms256×body80valid

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0137
1157
2157
done157

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(log (sqrt (+ (* re re) (* im im))))
0.6b
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
31.7b
(sqrt (+ (* re re) (* im im)))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
25×log-pow
24×times-frac
23×pow1
19×add-sqr-sqrt
18×add-cube-cbrt *-un-lft-identity
7×sqrt-pow1 pow1/2
6×add-exp-log log-prod sqrt-div sqrt-prod associate-/l*
5×add-cbrt-cube
4×log-div associate-/r*
3×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u add-log-exp
2×div-sub
1×cbrt-undiv rem-sqrt-square frac-2neg div-exp rem-log-exp clear-num hypot-def div-inv
Counts
3 → 89
Calls
3 calls:
10.0ms
(log (sqrt (+ (* re re) (* im im))))
26.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
8.0ms
(sqrt (+ (* re re) (* im im)))

series225.0ms

Counts
3 → 9
Calls
3 calls:
56.0ms
(log (sqrt (+ (* re re) (* im im))))
132.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
37.0ms
(sqrt (+ (* re re) (* im im)))

simplify50.0ms

Counts
98 → 98
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
0244876
1610820
21463817
35001817
done5001817

prune245.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.3b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(log (* 1 (hypot re im)))
0.0b
(hypot re im)
0.6b
(/ (log (* 1 (hypot re im))) (log 10.0))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
27×pow1
20×times-frac
18×log-pow
14×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×add-exp-log
6×pow-prod-down
5×add-cbrt-cube associate-/l*
4×associate-/r*
3×expm1-log1p-u rem-log-exp log1p-expm1-u add-log-exp
2×prod-exp
1×cbrt-undiv log-prod hypot-udef frac-2neg 1-exp div-exp clear-num div-inv
Counts
3 → 68
Calls
3 calls:
6.0ms
(log (* 1 (hypot re im)))
0.0ms
(hypot re im)
20.0ms
(/ (log (* 1 (hypot re im))) (log 10.0))

series262.0ms

Counts
3 → 9
Calls
3 calls:
71.0ms
(log (* 1 (hypot re im)))
45.0ms
(hypot re im)
146.0ms
(/ (log (* 1 (hypot re im))) (log 10.0))

simplify446.0ms

Counts
77 → 77
Iterations

Useful iterations: 2 (10.0ms)

IterNodesCost
0138468
1339430
2874425
33748425
45001425
done5001425

prune197.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(log (* 1 (hypot re im)))
0.0b
(hypot re im)
0.3b
(* (/ 1 (sqrt (log 10.0))) (/ (log (* 1 (hypot re im))) (sqrt (log 10.0))))
0.5b
(/ (log (* 1 (hypot re im))) (sqrt (log 10.0)))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
113×times-frac
102×add-sqr-sqrt
68×pow1
67×sqrt-prod
62×*-un-lft-identity
56×add-cube-cbrt
46×log-pow
39×associate-*r*
32×add-exp-log
25×associate-*l*
18×add-cbrt-cube
17×pow-prod-down
15×unswap-sqr
10×prod-exp
9×div-exp
7×associate-/r*
5×cbrt-undiv associate-/l*
4×expm1-log1p-u cbrt-unprod log1p-expm1-u add-log-exp
3×1-exp rem-log-exp div-inv
2×rec-exp
1×frac-times log-prod hypot-udef frac-2neg associate-*r/ associate-*l/ clear-num *-commutative
Counts
4 → 191
Calls
4 calls:
6.0ms
(log (* 1 (hypot re im)))
0.0ms
(hypot re im)
61.0ms
(* (/ 1 (sqrt (log 10.0))) (/ (log (* 1 (hypot re im))) (sqrt (log 10.0))))
24.0ms
(/ (log (* 1 (hypot re im))) (sqrt (log 10.0)))

series488.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(log (* 1 (hypot re im)))
51.0ms
(hypot re im)
154.0ms
(* (/ 1 (sqrt (log 10.0))) (/ (log (* 1 (hypot re im))) (sqrt (log 10.0))))
217.0ms
(/ (log (* 1 (hypot re im))) (sqrt (log 10.0)))

simplify59.0ms

Counts
203 → 203
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
04712167
120511877
250011788
done50011788

prune411.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot re im)
0.0b
(log (pow (hypot re im) (/ 1 (sqrt (log 10.0)))))
0.3b
(* (/ 1 (sqrt (log 10.0))) (log (pow (hypot re im) (/ 1 (sqrt (log 10.0))))))
3.9b
(pow (hypot re im) (/ 1 (sqrt (log 10.0))))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
52×add-sqr-sqrt
46×times-frac
42×*-un-lft-identity
40×add-cube-cbrt
26×sqrt-prod
25×pow-unpow associate-*l*
21×log-prod
16×add-exp-log
13×pow1
12×unpow-prod-down
9×add-cbrt-cube
8×log-pow
7×distribute-rgt-in distribute-lft-in
5×unswap-sqr
4×expm1-log1p-u associate-*r* prod-exp log1p-expm1-u add-log-exp sqr-pow
3×rem-log-exp
2×pow-to-exp hypot-udef div-exp pow-exp cbrt-unprod div-inv
1×cbrt-undiv rec-exp pow-pow 1-exp pow-prod-down associate-*l/ *-commutative sqrt-pow2
Counts
4 → 138
Calls
4 calls:
0.0ms
(hypot re im)
3.0ms
(log (pow (hypot re im) (/ 1 (sqrt (log 10.0)))))
29.0ms
(* (/ 1 (sqrt (log 10.0))) (log (pow (hypot re im) (/ 1 (sqrt (log 10.0))))))
9.0ms
(pow (hypot re im) (/ 1 (sqrt (log 10.0))))

series1.1s

Counts
4 → 12
Calls
4 calls:
52.0ms
(hypot re im)
303.0ms
(log (pow (hypot re im) (/ 1 (sqrt (log 10.0)))))
355.0ms
(* (/ 1 (sqrt (log 10.0))) (log (pow (hypot re im) (/ 1 (sqrt (log 10.0))))))
348.0ms
(pow (hypot re im) (/ 1 (sqrt (log 10.0))))

simplify50.0ms

Counts
150 → 150
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
04571510
119801241
250021101
done50021101

prune350.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

regimes86.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01511
11511
done1511

end0.0ms

sample536.0ms

Algorithm
intervals
Results
349.0ms8000×body80valid