Details

Time bar (total: 6.3s)

sample20.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize13.0ms

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))
31.6b
(sqrt (+ (* re re) (* im im)))

rewrite17.0ms

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:
4.0ms
(+ (* re re) (* im im))
7.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
4.0ms
(sqrt (+ (* re re) (* im im)))

series200.0ms

Counts
3 → 9
Calls
3 calls:
27.0ms
(+ (* re re) (* im im))
137.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
35.0ms
(sqrt (+ (* re re) (* im im)))

simplify86.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
0256741
1895697
22846694
35001694

prune242.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 7.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ (log (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im)))))) (log 10.0))
31.6b
(sqrt (+ (* re re) (* im im)))
31.6b
(sqrt (+ (* re re) (* im im)))
31.6b
(sqrt (+ (* re re) (* im im)))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
126×pow1
94×log-pow
72×times-frac
60×sqrt-div
54×cbrt-div
45×pow1/3 pow-prod-up
34×add-sqr-sqrt
31×add-cube-cbrt *-un-lft-identity
30×flip3-+ pow-plus flip-+
28×frac-times
26×log-div div-sub
25×pow-prod-down
18×associate-/l*
15×pow-sqr
14×associate-*l/
10×pow2
9×sqrt-prod
8×associate-*r/
6×add-exp-log add-cbrt-cube
5×pow3
4×associate-/r* add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
1×cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
4 → 177
Calls
4 calls:
27.0ms
(/ (log (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im)))))) (log 10.0))
4.0ms
(sqrt (+ (* re re) (* im im)))
4.0ms
(sqrt (+ (* re re) (* im im)))
4.0ms
(sqrt (+ (* re re) (* im im)))

series242.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(/ (log (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im)))))) (log 10.0))
34.0ms
(sqrt (+ (* re re) (* im im)))
34.0ms
(sqrt (+ (* re re) (* im im)))
39.0ms
(sqrt (+ (* re re) (* im im)))

simplify143.0ms

Algorithm
egg-herbie
Counts
189 → 189
Iterations

Useful iterations: 3 (117.0ms)

IterNodesCost
04803559
19553468
230163076
350033048

prune425.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 3 (/ (log 10.0) (log (cbrt (sqrt (+ (* re re) (* im im)))))))
0.6b
(cbrt (sqrt (+ (* re re) (* im im))))
0.6b
(/ (log 10.0) (log (cbrt (sqrt (+ (* re re) (* im im))))))
31.6b
(sqrt (+ (* re re) (* im im)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
172×times-frac
84×add-sqr-sqrt
83×add-cube-cbrt *-un-lft-identity
68×log-pow
52×pow1
29×associate-/r*
22×pow1/3
11×add-exp-log add-cbrt-cube
7×associate-/l*
6×cbrt-prod sqrt-prod div-inv
4×cbrt-undiv sqrt-div div-exp add-log-exp
2×cbrt-div frac-2neg flip3-+ clear-num flip-+
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/
Counts
4 → 186
Calls
4 calls:
11.0ms
(/ 3 (/ (log 10.0) (log (cbrt (sqrt (+ (* re re) (* im im)))))))
4.0ms
(cbrt (sqrt (+ (* re re) (* im im))))
4.0ms
(/ (log 10.0) (log (cbrt (sqrt (+ (* re re) (* im im))))))
4.0ms
(sqrt (+ (* re re) (* im im)))

series478.0ms

Counts
4 → 12
Calls
4 calls:
178.0ms
(/ 3 (/ (log 10.0) (log (cbrt (sqrt (+ (* re re) (* im im)))))))
91.0ms
(cbrt (sqrt (+ (* re re) (* im im))))
172.0ms
(/ (log 10.0) (log (cbrt (sqrt (+ (* re re) (* im im))))))
36.0ms
(sqrt (+ (* re re) (* im im)))

simplify87.0ms

Algorithm
egg-herbie
Counts
198 → 198
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
05572597
125272482
250022476

prune555.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 7.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* re re) (* im im))
0.3b
(/ (/ 1 (sqrt (log 10.0))) (/ (sqrt (log 10.0)) (log (sqrt (+ (* re re) (* im im))))))
0.5b
(/ (sqrt (log 10.0)) (log (sqrt (+ (* re re) (* im im)))))
31.6b
(sqrt (+ (* re re) (* im im)))

rewrite195.0ms

Algorithm
rewrite-expression-head
Rules
3271×times-frac
1219×sqrt-prod
1206×add-sqr-sqrt
1205×add-cube-cbrt *-un-lft-identity
874×log-pow
689×pow1
191×sqrt-pow1 pow1/2
75×div-inv
52×associate-/r*
32×associate-/l*
28×add-exp-log
18×add-cbrt-cube
17×div-exp
9×cbrt-undiv
6×add-log-exp
2×rec-exp frac-2neg flip3-+ sqrt-div 1-exp clear-num flip-+
1×+-commutative rem-sqrt-square sum-log associate-/r/ associate-/l/
Counts
4 → 1338
Calls
4 calls:
4.0ms
(+ (* re re) (* im im))
40.0ms
(/ (/ 1 (sqrt (log 10.0))) (/ (sqrt (log 10.0)) (log (sqrt (+ (* re re) (* im im))))))
5.0ms
(/ (sqrt (log 10.0)) (log (sqrt (+ (* re re) (* im im)))))
4.0ms
(sqrt (+ (* re re) (* im im)))

series402.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(+ (* re re) (* im im))
137.0ms
(/ (/ 1 (sqrt (log 10.0))) (/ (sqrt (log 10.0)) (log (sqrt (+ (* re re) (* im im))))))
189.0ms
(/ (sqrt (log 10.0)) (log (sqrt (+ (* re re) (* im im)))))
44.0ms
(sqrt (+ (* re re) (* im im)))

simplify280.0ms

Algorithm
egg-herbie
Counts
1350 → 1350
Iterations

Useful iterations: 1 (52.0ms)

IterNodesCost
0312330962
1500128693

prune1.3s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 7.0b

regimes788.0ms

Accuracy

56% (10.7b remaining)

Error of 18.4b against oracle of 7.7b and baseline of 32.0b

bsearch203.0ms

Steps
ItersRangePoint
5
1.3859668012923316e+39
5.407361050114019e+39
5.156219500915728e+39
6
1.2888602883193277e-191
1.0756529683068688e-190
1.3057340609530177e-191
9
3.7751008726876715e-235
1.6016645181124128e-228
1.1342785571534004e-228
9
-6.806283990879702e-262
-7.541756626495359e-267
-2.968956980813959e-266
4
-2.1257158676027876e-194
-1.276837797885082e-194
-1.3504253849915568e-194
9
-5.613835374986806e+74
-5.067726987112932e+69
-1.103215696956926e+72

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05569
15569

end0.0ms

sample492.0ms

Algorithm
intervals
Results
347.0ms8000×body80valid