Details

Time bar (total: 20.0s)

sample348.0ms

Algorithm
intervals
Results
31.0ms52×body1280valid
23.0ms250×body80valid
21.0ms52×body640valid
5.0ms18×body320valid
2.0ms10×body160valid

simplify356.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
01937
13526
26325
39825
421525
588225
done500025

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* (pow (hypot x.re x.im) y.re) (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))) (exp (* (atan2 x.im x.re) y.im)))
0.6b
(* (atan2 x.im x.re) y.re)
1.5b
(* (atan2 x.im x.re) y.im)
33.8b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log add-sqr-sqrt
13×add-cbrt-cube
10×add-cube-cbrt *-un-lft-identity
8×pow1
6×associate-*r* associate-*l*
5×prod-exp
4×expm1-log1p-u div-exp log1p-expm1-u add-log-exp
3×times-frac associate-/r* cbrt-unprod
2×cbrt-undiv pow-prod-down *-commutative unswap-sqr
1×pow-to-exp cos-sum frac-2neg pow-exp clear-num fma-udef div-inv associate-/l*
Counts
4 → 75
Calls
4 calls:
5.0ms
(/ (* (pow (hypot x.re x.im) y.re) (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))) (exp (* (atan2 x.im x.re) y.im)))
3.0ms
(* (atan2 x.im x.re) y.re)
3.0ms
(* (atan2 x.im x.re) y.im)
3.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series521.0ms

Counts
4 → 12
Calls
4 calls:
323.0ms
(/ (* (pow (hypot x.re x.im) y.re) (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))) (exp (* (atan2 x.im x.re) y.im)))
16.0ms
(* (atan2 x.im x.re) y.re)
17.0ms
(* (atan2 x.im x.re) y.im)
165.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify1.8s

Counts
87 → 87
Iterations

Useful iterations: 3 (416.0ms)

IterNodesCost
01491444
13261414
210581207
346911200
done50001200

prune363.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.7b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b
(expm1 (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))))
0.6b
(* (atan2 x.im x.re) y.re)
1.5b
(* (atan2 x.im x.re) y.im)
33.8b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×associate-*r* associate-*l*
5×log1p-expm1-u
4×expm1-log1p-u add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×cos-sum expm1-log1p fma-udef expm1-udef
Counts
4 → 61
Calls
4 calls:
0.0ms
(expm1 (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))))
3.0ms
(* (atan2 x.im x.re) y.re)
3.0ms
(* (atan2 x.im x.re) y.im)
1.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series405.0ms

Counts
4 → 12
Calls
4 calls:
222.0ms
(expm1 (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))))
16.0ms
(* (atan2 x.im x.re) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)
150.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify4.6s

Counts
73 → 73
Iterations

Useful iterations: 3 (155.0ms)

IterNodesCost
0104761
1187747
2453656
3871652
41465652
53455652
done5000652

prune346.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.7b

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (atan2 x.im x.re) y.re)
0.8b
(pow (expm1 (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))) 3)
1.5b
(* (atan2 x.im x.re) y.im)
33.8b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
11×add-cube-cbrt *-un-lft-identity
9×pow1 add-exp-log add-cbrt-cube
6×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×unpow-prod-down pow-unpow cube-prod
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×cube-mult pow-to-exp cos-sum pow-pow unpow3 pow-exp fma-udef rem-cube-cbrt sqr-pow
Counts
4 → 75
Calls
4 calls:
3.0ms
(* (atan2 x.im x.re) y.re)
1.0ms
(pow (expm1 (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))) 3)
3.0ms
(* (atan2 x.im x.re) y.im)
1.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series710.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.re)
530.0ms
(pow (expm1 (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))) 3)
17.0ms
(* (atan2 x.im x.re) y.im)
147.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify2.8s

Counts
87 → 87
Iterations

Useful iterations: 3 (463.0ms)

IterNodesCost
01291145
12741082
2851943
33578935
done5000935

prune427.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.7b

localize31.0ms

Local error

Found 4 expressions with local error:

0.8b
(pow (expm1 (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))) 3)
1.0b
(log (exp (pow (expm1 (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))) 3)))
1.5b
(* (atan2 x.im x.re) y.im)
33.8b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity log-pow
12×exp-prod
8×pow1
7×add-exp-log add-cbrt-cube
6×unpow-prod-down cube-prod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow log-prod associate-*r* associate-*l*
2×cube-mult unpow3 sqr-pow
1×pow-to-exp cos-sum pow-pow rem-log-exp pow-prod-down pow-exp prod-exp *-commutative cbrt-unprod fma-udef rem-cube-cbrt unswap-sqr
Counts
4 → 81
Calls
4 calls:
1.0ms
(pow (expm1 (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))) 3)
6.0ms
(log (exp (pow (expm1 (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))) 3)))
3.0ms
(* (atan2 x.im x.re) y.im)
1.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series1.2s

Counts
4 → 12
Calls
4 calls:
522.0ms
(pow (expm1 (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))) 3)
531.0ms
(log (exp (pow (expm1 (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))) 3)))
17.0ms
(* (atan2 x.im x.re) y.im)
149.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify1.9s

Counts
93 → 93
Iterations

Useful iterations: 3 (438.0ms)

IterNodesCost
01421592
12681429
27741219
330351207
done50011207

prune458.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.7b

regimes314.0ms

Accuracy

38.6% (3.2b remaining)

Error of 7.0b against oracle of 3.8b and baseline of 9.0b

bsearch113.0ms

Steps
ItersRangePoint
9
-8.146676569045775e+55
-2.0266373448693503e+50
-1.6507641711952303e+52

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03164
13564
done3564

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.2s2039×body1280valid
691.0ms7988×body80valid
612.0ms1558×body640valid
178.0ms664×body320valid
51.0ms284×body160valid