Details

Time bar (total: 5.1s)

sample19.0ms

Algorithm
intervals
Results
10.0ms256×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: 32.5b

localize13.0ms

Local error

Found 2 expressions with local error:

0.6b
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
29.9b
(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)))

series176.0ms

Counts
2 → 6
Calls
2 calls:
138.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
37.0ms
(sqrt (+ (* re re) (* im im)))

simplify124.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 4 (116.0ms)

IterNodesCost
0221664
1556631
21309628
34047628
45001627

prune188.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.8b

localize16.0ms

Local error

Found 3 expressions with local error:

0.3b
(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
0.5b
(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
31.1b
(log (+ (* re re) (* im im)))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
89×times-frac
82×add-sqr-sqrt
54×sqrt-prod
52×add-cube-cbrt *-un-lft-identity
33×pow1
32×associate-*r*
28×log-pow
25×associate-*l*
18×add-exp-log
17×add-cbrt-cube
9×unswap-sqr
7×associate-/r*
5×cbrt-undiv div-exp
4×log-div prod-exp cbrt-unprod associate-/l*
3×log-prod div-inv add-log-exp
2×flip3-+ div-sub flip-+
1×frac-times frac-2neg associate-*r/ rem-log-exp pow-prod-down associate-*l/ clear-num *-commutative
Counts
3 → 153
Calls
3 calls:
33.0ms
(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
10.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
3.0ms
(log (+ (* re re) (* im im)))

series384.0ms

Counts
3 → 9
Calls
3 calls:
142.0ms
(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
189.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
52.0ms
(log (+ (* re re) (* im im)))

simplify61.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
05282082
120651915
250011832

prune373.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.6b

localize14.0ms

Local error

Found 3 expressions with local error:

0.3b
(* (/ 1/2 (sqrt (log 10.0))) (* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
0.3b
(* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
31.1b
(log (+ (* re re) (* im im)))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
48×add-exp-log
46×times-frac
45×add-sqr-sqrt
35×*-un-lft-identity
33×add-cube-cbrt
29×associate-*l* add-cbrt-cube
26×associate-*r* sqrt-prod
22×prod-exp
18×pow1
12×cbrt-unprod
11×div-exp
8×log-pow
6×cbrt-undiv
5×associate-*r/ unswap-sqr
4×pow-prod-down
3×rec-exp log-prod 1-exp un-div-inv add-log-exp
2×frac-times log-div *-commutative div-inv
1×flip3-+ rem-log-exp associate-*l/ flip-+
Counts
3 → 122
Calls
3 calls:
32.0ms
(* (/ 1/2 (sqrt (log 10.0))) (* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
16.0ms
(* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
3.0ms
(log (+ (* re re) (* im im)))

series381.0ms

Counts
3 → 9
Calls
3 calls:
140.0ms
(* (/ 1/2 (sqrt (log 10.0))) (* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
193.0ms
(* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
49.0ms
(log (+ (* re re) (* im im)))

simplify57.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
05611520
124471274
250011227

prune288.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.6b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b
(log (pow (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0)))) (/ 1/2 (sqrt (log 10.0)))))
16.4b
(pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))
17.8b
(pow (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0)))) (/ 1/2 (sqrt (log 10.0))))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
50×pow-unpow
42×times-frac
37×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
24×sqrt-prod
23×unpow-prod-down
11×log-prod
10×pow1
9×add-exp-log pow-exp
7×log-pow
5×pow-to-exp rem-log-exp sqr-pow
3×add-cbrt-cube add-log-exp
2×pow-pow div-inv
Counts
3 → 108
Calls
3 calls:
9.0ms
(log (pow (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0)))) (/ 1/2 (sqrt (log 10.0)))))
9.0ms
(pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))
11.0ms
(pow (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0)))) (/ 1/2 (sqrt (log 10.0))))

series1.4s

Counts
3 → 9
Calls
3 calls:
505.0ms
(log (pow (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0)))) (/ 1/2 (sqrt (log 10.0)))))
327.0ms
(pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))
540.0ms
(pow (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0)))) (/ 1/2 (sqrt (log 10.0))))

simplify46.0ms

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
04391493
115751398
250021328

prune320.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 7.6b

regimes408.0ms

Accuracy

57.7% (10.5b remaining)

Error of 17.8b against oracle of 7.3b and baseline of 32.1b

bsearch158.0ms

Steps
ItersRangePoint
7
1.2064922412751594e+141
2.3676647091815954e+142
1.2454205315559948e+141
7
4.279018400982983e-187
7.948010818007005e-186
3.2705168987572832e-186
6
-3.287548568638134e-295
-2.0715907135994897e-296
-3.75379841200666e-296
8
-2.5337000025306127e+146
-9.056303434704759e+142
-9.16501881147336e+142

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05755
15755

end0.0ms

sample471.0ms

Algorithm
intervals
Results
334.0ms8000×body80valid