Details

sample101.0ms

Algorithm

intervals

Results

33.0ms	256×	body	80	valid
33.0ms	251×	body	80	nan

simplify16.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	28
1	23	28
done	23	28

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize79.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.4b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.5b	(* (log base) (log base))
30.6b	(sqrt (+ (* re re) (* im im)))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 110

Calls

4 calls:

16.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
70.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
21.0ms	(* (log base) (log base))
18.0ms	(sqrt (+ (* re re) (* im im)))

series539.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
120.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
235.0ms	(* (log base) (log base))
48.0ms	(sqrt (+ (* re re) (* im im)))

simplify3.2s

Counts

122 → 122

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	200	2451
1	442	2259
2	1344	2035
3	4400	1998
done	5000	1992

prune677.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 8.6b

localize41.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ 1 (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))))
0.5b	(pow (log base) 2)
0.5b	(pow (log base) 2)
30.6b	(sqrt (+ (* re re) (* im im)))

rewrite250.0ms

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` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 140

Calls

4 calls:

213.0ms	(* (/ 1 (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))))
3.0ms	(pow (log base) 2)
4.0ms	(pow (log base) 2)
18.0ms	(sqrt (+ (* re re) (* im im)))

series679.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(* (/ 1 (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))))
186.0ms	(pow (log base) 2)
265.0ms	(pow (log base) 2)
54.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.8s

Counts

152 → 152

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	235	5236
1	624	4886
2	2107	4095
done	5001	4080

prune905.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 8.6b

localize57.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (log base) 2)
0.5b	(cbrt (pow (log base) 6))
1.2b	(pow (log base) 6)
30.6b	(sqrt (+ (* re re) (* im im)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `unpow-prod-down`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1`
8×	`cbrt-prod`
6×	`add-exp-log` `pow-unpow`
4×	`add-cbrt-cube` `add-log-exp`
3×	`sqrt-prod` `log-pow` `sqr-pow`
2×	`pow-to-exp` `pow-pow` `sqrt-div` `pow-exp`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `flip-+` `unpow2`

Counts

4 → 68

Calls

4 calls:

5.0ms	(pow (log base) 2)
2.0ms	(cbrt (pow (log base) 6))
3.0ms	(pow (log base) 6)
9.0ms	(sqrt (+ (* re re) (* im im)))

series714.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(pow (log base) 2)
186.0ms	(cbrt (pow (log base) 6))
262.0ms	(pow (log base) 6)
59.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.2s

Counts

80 → 80

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	112	687
1	232	602
2	486	529
3	1753	467
done	5001	461

prune675.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 8.6b

localize44.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (+ (* (* 2 (log (cbrt base))) (log base)) (* (log (cbrt base)) (log base))) (* 0.0 0.0)))
0.6b	(cbrt base)
0.6b	(cbrt base)
30.6b	(sqrt (+ (* re re) (* im im)))

rewrite222.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`add-exp-log` `cbrt-prod` `add-cbrt-cube`
5×	`pow1`
4×	`add-log-exp`
3×	`flip3-+` `associate-/r` `sqrt-prod` `flip-+` `associate-/l`
2×	`pow1/3` `sqrt-div` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 68

Calls

4 calls:

210.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (+ (* (* 2 (log (cbrt base))) (log base)) (* (log (cbrt base)) (log base))) (* 0.0 0.0)))
1.0ms	(cbrt base)
1.0ms	(cbrt base)
8.0ms	(sqrt (+ (* re re) (* im im)))

series874.0ms

Counts

4 → 12

Calls

4 calls:

301.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (+ (* (* 2 (log (cbrt base))) (log base)) (* (log (cbrt base)) (log base))) (* 0.0 0.0)))
238.0ms	(cbrt base)
270.0ms	(cbrt base)
65.0ms	(sqrt (+ (* re re) (* im im)))

simplify3.6s

Counts

80 → 80

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	148	2200
1	369	2008
2	1172	1664
3	4679	1594
done	5001	1509

prune555.0ms

Pruning

20 alts after pruning (18 fresh and 2 done)

Merged error: 8.6b

regimes734.0ms

Accuracy

57.9% (10.2b remaining)

Error of 17.7b against oracle of 7.5b and baseline of 31.6b

bsearch364.0ms

Steps

Iters	Range		Point
8	1.4124772624905103e+51	5.988671907342664e+54	5.925540416458275e+52
10	-1.3239866454658551e+135	-8.146333316487294e+120	-1.477980765554153e+121

simplify10.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	45	66
1	58	64
2	61	64
done	61	64

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.9s	8000×	body	80	valid
1.5s	8157×	body	80	nan