Details

Time bar (total: 5.8s)

sample19.0ms

Algorithm
intervals
Results
11.0ms256×body80valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0117
1117

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.7b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* re re) (* im im))
0.6b
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
31.0b
(sqrt (+ (* re re) (* im im)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
22×log-pow
21×pow1
17×add-sqr-sqrt
16×add-cube-cbrt *-un-lft-identity
6×sqrt-pow1 pow1/2 associate-/l*
5×add-exp-log add-cbrt-cube add-log-exp
4×sqrt-div associate-/r*
3×flip3-+ sqrt-prod flip-+
2×log-div div-sub
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg div-exp clear-num sum-log div-inv
Counts
3 → 74
Calls
3 calls:
2.0ms
(+ (* re re) (* im im))
10.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
3.0ms
(sqrt (+ (* re re) (* im im)))

series338.0ms

Counts
3 → 9
Calls
3 calls:
166.0ms
(+ (* re re) (* im im))
132.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
40.0ms
(sqrt (+ (* re re) (* im im)))

simplify89.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
0256741
1895697
22846694
35001694

prune230.0ms

Filtered
83 candidates to 55 candidates (66.3%)
Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* re re) (* im im))
0.3b
(* (/ 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)))
31.0b
(sqrt (+ (* re re) (* im im)))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
127×times-frac
108×add-sqr-sqrt
78×sqrt-prod
67×*-un-lft-identity
61×add-cube-cbrt log-pow
53×pow1
46×associate-*r*
28×add-exp-log
25×associate-*l*
18×add-cbrt-cube
16×sqrt-pow1 pow1/2
15×unswap-sqr
9×div-exp
8×prod-exp
7×associate-/r*
6×associate-/l* add-log-exp
5×cbrt-undiv
4×sqrt-div cbrt-unprod
3×flip3-+ flip-+ div-inv
2×log-div rec-exp 1-exp div-sub
1×+-commutative frac-times rem-sqrt-square frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num sum-log *-commutative
Counts
4 → 205
Calls
4 calls:
2.0ms
(+ (* re re) (* im im))
40.0ms
(* (/ 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
4 → 12
Calls
4 calls:
27.0ms
(+ (* re re) (* im im))
136.0ms
(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
197.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
39.0ms
(sqrt (+ (* re re) (* im im)))

simplify79.0ms

Algorithm
egg-herbie
Counts
217 → 217
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
06482798
128782493
250022395

prune461.0ms

Filtered
217 candidates to 111 candidates (51.2%)
Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 6.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* re re) (* im im))
0.3b
(* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0))))
0.3b
(* (/ 1 (sqrt (log 10.0))) (* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0)))))
31.0b
(sqrt (+ (* re re) (* im im)))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
78×add-exp-log
47×add-sqr-sqrt
46×times-frac
40×prod-exp
36×*-un-lft-identity
34×add-cube-cbrt
31×associate-*l*
30×add-cbrt-cube
29×sqrt-prod
26×associate-*r*
20×pow1 div-exp
12×cbrt-unprod
10×rec-exp 1-exp
9×log-pow
6×cbrt-undiv add-log-exp
5×associate-*r/ unswap-sqr
4×pow-prod-down
3×un-div-inv
2×frac-times sqrt-pow1 flip3-+ pow1/2 sqrt-div *-commutative flip-+ div-inv
1×+-commutative rem-sqrt-square associate-*l/ sum-log
Counts
4 → 146
Calls
4 calls:
2.0ms
(+ (* re re) (* im im))
17.0ms
(* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0))))
30.0ms
(* (/ 1 (sqrt (log 10.0))) (* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0)))))
3.0ms
(sqrt (+ (* re re) (* im im)))

series403.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(+ (* re re) (* im im))
200.0ms
(* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0))))
137.0ms
(* (/ 1 (sqrt (log 10.0))) (* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0)))))
36.0ms
(sqrt (+ (* re re) (* im im)))

simplify61.0ms

Algorithm
egg-herbie
Counts
158 → 158
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
05721845
126851498
250011322

prune362.0ms

Filtered
158 candidates to 85 candidates (53.8%)
Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 6.8b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
0.3b
(* (/ 1 (sqrt (log 10.0))) (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))))
3.8b
(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
31.0b
(sqrt (+ (* re re) (* im im)))

rewrite48.0ms

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:
5.0ms
(log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
24.0ms
(* (/ 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)))

series1.0s

Counts
4 → 12
Calls
4 calls:
297.0ms
(log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
347.0ms
(* (/ 1 (sqrt (log 10.0))) (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))))
332.0ms
(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
37.0ms
(sqrt (+ (* re re) (* im im)))

simplify64.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
05582291
123431895
250011744

prune383.0ms

Filtered
163 candidates to 97 candidates (59.5%)
Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 6.8b

regimes989.0ms

Accuracy

57.5% (10.5b remaining)

Error of 17.8b against oracle of 7.3b and baseline of 32.0b

bsearch152.0ms

Steps
ItersRangePoint
9
5.867938426223691e+51
3.818311493425968e+58
3.762993852863067e+58
3
9.576244268311426e-216
1.116991590181558e-215
9.675848745405435e-216
8
-5.3907007133187425e-267
-6.8214408651225445e-270
-5.04942056547374e-269
8
-5.097960459803195e-05
-1.4117940793321767e-07
-5.047378760356491e-05

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05971
15971

end0.0ms

sample476.0ms

Algorithm
intervals
Results
340.0ms8000×body80valid