Details

Time bar (total: 4.2s)

sample25.0ms

Algorithm
intervals
Results
12.0ms256×body80valid

simplify4.0ms

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: 32.1b

localize10.0ms

Local error

Found 2 expressions with local error:

0.6b
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
29.6b
(sqrt (+ (* re re) (* im im)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
22×log-pow
20×pow1
16×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
6×sqrt-pow1 pow1/2 associate-/l*
4×add-exp-log sqrt-div associate-/r* add-cbrt-cube
3×sqrt-prod
2×expm1-log1p-u log-div flip3-+ div-sub flip-+ log1p-expm1-u add-log-exp
1×cbrt-undiv rem-sqrt-square frac-2neg div-exp clear-num hypot-def div-inv
Counts
2 → 68
Calls
2 calls:
28.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
8.0ms
(sqrt (+ (* re re) (* im im)))

series207.0ms

Counts
2 → 6
Calls
2 calls:
172.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
35.0ms
(sqrt (+ (* re re) (* im im)))

simplify128.0ms

Counts
74 → 74
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
0232683
1597648
21428645
34416645
45001645
done5001645

prune182.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.3b

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
16×times-frac
12×pow1 add-sqr-sqrt add-cube-cbrt *-un-lft-identity
10×log-pow
4×add-exp-log associate-/r* add-cbrt-cube associate-/l*
2×expm1-log1p-u log1p-expm1-u add-log-exp
1×cbrt-undiv hypot-udef frac-2neg div-exp clear-num div-inv
Counts
2 → 48
Calls
2 calls:
0.0ms
(hypot re im)
7.0ms
(/ (log (hypot re im)) (log 10.0))

series193.0ms

Counts
2 → 6
Calls
2 calls:
46.0ms
(hypot re im)
146.0ms
(/ (log (hypot re im)) (log 10.0))

simplify56.0ms

Counts
54 → 54
Iterations

Useful iterations: 4 (53.0ms)

IterNodesCost
0129321
1302300
2694298
31942298
45002297
done5002297

prune277.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 3 expressions with local error:

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

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
99×times-frac
97×add-sqr-sqrt
59×sqrt-prod
57×*-un-lft-identity
51×add-cube-cbrt
32×pow1 associate-*r*
27×add-exp-log log-pow
25×associate-*l*
17×add-cbrt-cube
15×unswap-sqr
9×div-exp
8×prod-exp
7×associate-/r*
5×cbrt-undiv
4×cbrt-unprod associate-/l*
3×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
2×rec-exp 1-exp
1×frac-times hypot-udef frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
3 → 161
Calls
3 calls:
0.0ms
(hypot re im)
47.0ms
(* (/ 1 (sqrt (log 10.0))) (/ (log (hypot re im)) (sqrt (log 10.0))))
9.0ms
(/ (log (hypot re im)) (sqrt (log 10.0)))

series405.0ms

Counts
3 → 9
Calls
3 calls:
46.0ms
(hypot re im)
149.0ms
(* (/ 1 (sqrt (log 10.0))) (/ (log (hypot re im)) (sqrt (log 10.0))))
210.0ms
(/ (log (hypot re im)) (sqrt (log 10.0)))

simplify53.0ms

Counts
170 → 170
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
04631792
119941571
250011443
done50011443

prune331.0ms

Pruning

12 alts after pruning (11 fresh and 1 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))))

rewrite45.0ms

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)))))
30.0ms
(* (/ 1 (sqrt (log 10.0))) (log (pow (hypot re im) (/ 1 (sqrt (log 10.0))))))
6.0ms
(pow (hypot re im) (/ 1 (sqrt (log 10.0))))

series1.1s

Counts
4 → 12
Calls
4 calls:
46.0ms
(hypot re im)
308.0ms
(log (pow (hypot re im) (/ 1 (sqrt (log 10.0)))))
365.0ms
(* (/ 1 (sqrt (log 10.0))) (log (pow (hypot re im) (/ 1 (sqrt (log 10.0))))))
353.0ms
(pow (hypot re im) (/ 1 (sqrt (log 10.0))))

simplify57.0ms

Counts
150 → 150
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
04571510
119801241
250021101
done50021101

prune353.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

regimes72.0ms

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
01612
11612
done1612

end0.0ms

sample530.0ms

Algorithm
intervals
Results
334.0ms8000×body80valid