Details

sample88.0ms

Algorithm

intervals

Results

30.0ms	254×	body	80	nan
30.0ms	256×	body	80	valid

simplify30.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	23
1	23
0	18

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.9b

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (* (atan2 im re) 0.0) (* (log (sqrt (+ (* re re) (* im im)))) (log base))) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.6b	(* (log base) (log base))
27.5b	(sqrt (+ (* re re) (* im im)))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
23×	`pow1` `add-cube-cbrt`
12×	`log-prod`
10×	`add-cbrt-cube` `associate-l` `add-exp-log` `log-pow`
9×	`times-frac`
8×	`associate-r`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
4×	`add-log-exp`
3×	`associate-/r` `flip3-+` `sqrt-prod` `flip-+` `associate-/l`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `unswap-sqr` `associate-/l/`
1×	`pow2` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `pow-plus` `div-exp` `pow-sqr` `pow-prod-up` `div-inv`

Counts

4 → 110

Calls

4 calls:

40.0ms	(/ (+ (* (atan2 im re) 0.0) (* (log (sqrt (+ (* re re) (* im im)))) (log base))) (+ (* (log base) (log base)) (* 0.0 0.0)))
20.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
12.0ms	(* (log base) (log base))
10.0ms	(sqrt (+ (* re re) (* im im)))

series534.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(/ (+ (* (atan2 im re) 0.0) (* (log (sqrt (+ (* re re) (* im im)))) (log base))) (+ (* (log base) (log base)) (* 0.0 0.0)))
128.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
218.0ms	(* (log base) (log base))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.7s

Counts

122 → 122

Iterations

Iter	Nodes
done	5000
2	2867
1	515
0	205

prune883.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.3b

localize46.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ 1 (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))))
0.6b	(pow (log base) 2)
0.6b	(pow (log base) 2)
27.5b	(sqrt (+ (* re re) (* im im)))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

82×	`add-sqr-sqrt`
58×	`times-frac`
41×	`*-un-lft-identity`
35×	`add-cube-cbrt`
32×	`sqrt-prod`
28×	`add-exp-log`
24×	`associate-r` `associate-l`
16×	`add-cbrt-cube`
15×	`unswap-sqr`
11×	`pow1`
8×	`unpow-prod-down` `div-exp` `prod-exp`
6×	`pow-unpow` `sqrt-div`
4×	`cbrt-undiv` `associate-/r/` `cbrt-unprod` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`pow-to-exp` `rec-exp` `pow-pow` `1-exp` `pow-exp` `log-pow` `div-inv` `unpow2` `sqr-pow`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 140

Calls

4 calls:

108.0ms	(* (/ 1 (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))))
8.0ms	(pow (log base) 2)
2.0ms	(pow (log base) 2)
8.0ms	(sqrt (+ (* re re) (* im im)))

series631.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(* (/ 1 (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))))
232.0ms	(pow (log base) 2)
170.0ms	(pow (log base) 2)
41.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.9s

Counts

152 → 152

Iterations

Iter	Nodes
done	5000
2	4825
1	732
0	235

prune1.1s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.3b

localize73.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.6b	(cbrt base)
0.6b	(cbrt base)
27.5b	(sqrt (+ (* re re) (* im im)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`*-un-lft-identity` `add-cube-cbrt`
10×	`pow1`
6×	`cbrt-prod` `log-prod` `add-cbrt-cube` `associate-l` `add-exp-log`
4×	`associate-r` `log-pow` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `sqrt-prod`
2×	`sqrt-pow1` `pow1/2` `pow1/3` `sqrt-div`
1×	`rem-sqrt-square` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 65

Calls

4 calls:

11.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
1.0ms	(cbrt base)
1.0ms	(cbrt base)
7.0ms	(sqrt (+ (* re re) (* im im)))

series615.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
212.0ms	(cbrt base)
256.0ms	(cbrt base)
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.5s

Counts

77 → 77

Iterations

Iter	Nodes
done	5001
3	3856
2	771
1	245
0	116

prune745.0ms

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 0.3b

localize61.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (- (pow (log base) 4) (* 0.0 (pow 0.0 3))))
0.6b	(* (log base) (log base))
1.0b	(pow (log base) 4)
27.5b	(sqrt (+ (* re re) (* im im)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
21×	`add-cube-cbrt`
20×	`pow1`
9×	`times-frac` `add-exp-log`
8×	`add-cbrt-cube`
7×	`log-pow`
6×	`log-prod` `swap-sqr`
4×	`unpow-prod-down` `associate-r` `associate-l` `add-log-exp`
3×	`distribute-rgt-in` `pow-unpow` `associate-/r` `distribute-lft-in` `sqrt-prod` `associate-/l`
2×	`flip3-+` `sqrt-div` `associate-/r/` `flip-+` `associate-/l/`
1×	`pow2` `pow-to-exp` `cbrt-undiv` `rem-sqrt-square` `clear-num` `pow-pow` `frac-2neg` `sqrt-pow1` `pow-plus` `flip3--` `pow1/2` `div-exp` `pow-prod-down` `pow-exp` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `div-inv` `flip--` `unswap-sqr` `sqr-pow`

Counts

4 → 100

Calls

4 calls:

46.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (- (pow (log base) 4) (* 0.0 (pow 0.0 3))))
8.0ms	(* (log base) (log base))
2.0ms	(pow (log base) 4)
11.0ms	(sqrt (+ (* re re) (* im im)))

series627.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (- (pow (log base) 4) (* 0.0 (pow 0.0 3))))
173.0ms	(* (log base) (log base))
259.0ms	(pow (log base) 4)
52.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.6s

Counts

112 → 112

Iterations

Iter	Nodes
done	5001
2	3222
1	534
0	195

prune778.0ms

Pruning

21 alts after pruning (18 fresh and 3 done)

Merged error: 0.2b

regimes945.0ms

Accuracy

46.7% (17.0b remaining)

Error of 17.3b against oracle of 0.3b and baseline of 32.1b

bsearch503.0ms

Steps

Iters	Range		Point
8	1.1343483352271129e+117	3.6725649236991024e+120	2.1241250770989713e+117
7	1.6787310578533334e-237	2.057721147430021e-235	5.548497518142956e-237
1	-8.04405113032372e-293	-7.507777451466672e-293	-7.909982710609458e-293
6	-8.050065361169878e-260	-1.37436077313223e-260	-2.8376772879678723e-260
10	-1.3110312091667196e-160	-1.3554673749956964e-176	-4.758264364879206e-176
7	-6.0648428765404965e+87	-1.1825419614466222e+86	-5.80271682570903e+87

simplify14.0ms

Iterations

Iter	Nodes
done	99
3	99
2	97
1	88
0	69

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.7s	8000×	body	80	valid
1.1s	7946×	body	80	nan