Details

Time bar (total: 6.2s)

sample20.0ms

Algorithm
intervals
Results
12.0ms256×body80valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0117
1117

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize14.0ms

Local error

Found 2 expressions with local error:

0.6b
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
26.6b
(sqrt (+ (* re re) (* im im)))

rewrite17.0ms

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×log-div flip3-+ div-sub flip-+ add-log-exp
1×cbrt-undiv rem-sqrt-square frac-2neg div-exp clear-num div-inv
Counts
2 → 63
Calls
2 calls:
11.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
4.0ms
(sqrt (+ (* re re) (* im im)))

series183.0ms

Counts
2 → 6
Calls
2 calls:
145.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
38.0ms
(sqrt (+ (* re re) (* im im)))

simplify124.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 4 (117.0ms)

IterNodesCost
0221664
1556631
21309628
34047628
45001627

prune200.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 7.2b

localize17.0ms

Local error

Found 3 expressions with local error:

0.2b
(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
0.5b
(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
26.6b
(sqrt (+ (* re re) (* im im)))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
127×times-frac
107×add-sqr-sqrt
78×sqrt-prod
66×*-un-lft-identity
61×log-pow
60×add-cube-cbrt
52×pow1
46×associate-*r*
27×add-exp-log
25×associate-*l*
17×add-cbrt-cube
16×sqrt-pow1 pow1/2
15×unswap-sqr
9×div-exp
8×prod-exp
7×associate-/r*
6×associate-/l*
5×cbrt-undiv
4×sqrt-div cbrt-unprod
3×div-inv add-log-exp
2×log-div rec-exp flip3-+ 1-exp div-sub flip-+
1×frac-times rem-sqrt-square frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
3 → 194
Calls
3 calls:
42.0ms
(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
12.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
4.0ms
(sqrt (+ (* re re) (* im im)))

series399.0ms

Counts
3 → 9
Calls
3 calls:
149.0ms
(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
213.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
36.0ms
(sqrt (+ (* re re) (* im im)))

simplify67.0ms

Algorithm
egg-herbie
Counts
203 → 203
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
06132721
124602427
250012325

prune433.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
0.2b
(* (/ 1 (sqrt (log 10.0))) (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))))
3.7b
(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
26.6b
(sqrt (+ (* re re) (* im im)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
58×add-sqr-sqrt
47×*-un-lft-identity
46×times-frac
45×add-cube-cbrt
41×sqrt-prod
30×log-prod
25×pow-unpow associate-*l*
24×unpow-prod-down
16×add-exp-log
15×pow1
10×distribute-rgt-in distribute-lft-in
9×add-cbrt-cube
8×log-pow
5×unswap-sqr
4×associate-*r* prod-exp add-log-exp sqr-pow
3×pow-pow rem-log-exp
2×pow-to-exp sqrt-pow1 pow1/2 sqrt-div div-exp pow-exp cbrt-unprod div-inv
1×cbrt-undiv rem-sqrt-square rec-exp flip3-+ 1-exp pow-prod-down associate-*l/ *-commutative sqrt-pow2 flip-+
Counts
4 → 151
Calls
4 calls:
6.0ms
(log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
28.0ms
(* (/ 1 (sqrt (log 10.0))) (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))))
7.0ms
(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
4.0ms
(sqrt (+ (* re re) (* im im)))

series1.1s

Counts
4 → 12
Calls
4 calls:
319.0ms
(log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
374.0ms
(* (/ 1 (sqrt (log 10.0))) (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))))
360.0ms
(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
37.0ms
(sqrt (+ (* re re) (* im im)))

simplify61.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
05582294
123431898
250021749

prune444.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.0b

localize21.0ms

Local error

Found 4 expressions with local error:

2.8b
(pow (sqrt (sqrt (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0))))
2.8b
(pow (sqrt (sqrt (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0))))
26.6b
(sqrt (+ (* re re) (* im im)))
26.6b
(sqrt (+ (* re re) (* im im)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
50×pow-unpow
48×sqrt-prod
42×add-sqr-sqrt times-frac
40×add-cube-cbrt *-un-lft-identity
18×pow1 unpow-prod-down
10×pow-pow sqrt-pow1
6×add-exp-log pow1/2 log-pow
4×sqrt-div add-cbrt-cube add-log-exp
2×pow-to-exp rem-sqrt-square flip3-+ pow-exp sqrt-pow2 flip-+ div-inv sqr-pow
Counts
4 → 130
Calls
4 calls:
11.0ms
(pow (sqrt (sqrt (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0))))
8.0ms
(pow (sqrt (sqrt (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0))))
3.0ms
(sqrt (+ (* re re) (* im im)))
4.0ms
(sqrt (+ (* re re) (* im im)))

series858.0ms

Counts
4 → 12
Calls
4 calls:
391.0ms
(pow (sqrt (sqrt (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0))))
394.0ms
(pow (sqrt (sqrt (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0))))
36.0ms
(sqrt (+ (* re re) (* im im)))
37.0ms
(sqrt (+ (* re re) (* im im)))

simplify75.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 2 (23.0ms)

IterNodesCost
03321410
110371316
232791250
350011250

prune510.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 7.0b

regimes887.0ms

Accuracy

59.5% (10.0b remaining)

Error of 17.3b against oracle of 7.4b and baseline of 32.0b

bsearch113.0ms

Steps
ItersRangePoint
10
3.070645734072953e+74
1.5848411429422667e+86
1.3249567362868981e+86
5
-2.408561575053933e+131
-6.201413291767227e+130
-6.33723413031495e+130

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04245
14245

end0.0ms

sample506.0ms

Algorithm
intervals
Results
362.0ms8000×body80valid