Details

sample22.0ms

Algorithm

intervals

Results

14.0ms

256×

body

valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	12
1	11	12
done	11	12

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.7b

localize10.0ms

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))
31.2b	(sqrt (+ (* re re) (* im im)))

rewrite19.0ms

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:

2.0ms	(+ (* re re) (* im im))
10.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
3.0ms	(sqrt (+ (* re re) (* im im)))

series252.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(+ (* re re) (* im im))
140.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.3s

Counts

83 → 83

Iterations

Useful iterations: 3 (365.0ms)

Iter	Nodes	Cost
0	125	1357
1	255	1281
2	681	1165
3	2076	1163
done	5000	1163

prune259.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 6.6b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.3b	(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
0.5b	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
31.2b	(sqrt (+ (* re re) (* im im)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

127×	`times-frac`
108×	`add-sqr-sqrt`
78×	`sqrt-prod`
67×	`*-un-lft-identity`
61×	`add-cube-cbrt` `log-pow`
53×	`pow1`
46×	`associate-r`
28×	`add-exp-log`
25×	`associate-l`
18×	`add-cbrt-cube`
16×	`sqrt-pow1` `pow1/2`
15×	`unswap-sqr`
9×	`div-exp`
8×	`prod-exp`
7×	`associate-/r*`
6×	`associate-/l*` `add-log-exp`
5×	`cbrt-undiv`
4×	`sqrt-div` `cbrt-unprod`
3×	`flip3-+` `flip-+` `div-inv`
2×	`log-div` `rec-exp` `1-exp` `div-sub`
1×	`+-commutative` `frac-times` `rem-sqrt-square` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `sum-log` `*-commutative`

Counts

4 → 205

Calls

4 calls:

2.0ms	(+ (* re re) (* im im))
40.0ms	(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
11.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series430.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(+ (* re re) (* im im))
144.0ms	(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
222.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.8s

Counts

217 → 217

Iterations

Useful iterations: 2 (459.0ms)

Iter	Nodes	Cost
0	247	4621
1	645	4244
2	1920	3647
done	5000	3647

prune512.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 6.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
0.5b	(cbrt (pow (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))) 3))
0.7b	(pow (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))) 3)
31.2b	(sqrt (+ (* re re) (* im im)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

210×	`times-frac`
139×	`log-pow`
127×	`sqrt-prod`
110×	`add-sqr-sqrt`
109×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
98×	`cbrt-prod`
92×	`unpow-prod-down` `cube-prod`
37×	`sqrt-pow1` `pow1/2`
9×	`add-exp-log` `add-cbrt-cube`
7×	`associate-/r*`
6×	`associate-/l*`
5×	`div-inv`
4×	`sqrt-div` `add-log-exp`
3×	`pow-unpow`
2×	`cbrt-undiv` `cube-div` `cube-mult` `log-div` `flip3-+` `unpow3` `div-sub` `div-exp` `pow-exp` `flip-+` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `cbrt-div` `pow-pow` `frac-2neg` `pow1/3` `clear-num` `rem-cbrt-cube`

Counts

4 → 304

Calls

4 calls:

15.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
12.0ms	(cbrt (pow (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))) 3))
11.0ms	(pow (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))) 3)
4.0ms	(sqrt (+ (* re re) (* im im)))

series851.0ms

Counts

4 → 12

Calls

4 calls:

221.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
223.0ms	(cbrt (pow (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))) 3))
368.0ms	(pow (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))) 3)
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.1s

Counts

316 → 316

Iterations

Useful iterations: 2 (592.0ms)

Iter	Nodes	Cost
0	272	8155
1	710	7041
2	2008	6363
done	5000	6363

prune610.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 6.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.3b	(* (/ 1 (sqrt (log 10.0))) (* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0)))))
0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0))))
31.2b	(sqrt (+ (* re re) (* im im)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-exp-log`
47×	`add-sqr-sqrt`
46×	`times-frac`
40×	`prod-exp`
36×	`*-un-lft-identity`
34×	`add-cube-cbrt`
31×	`associate-l`
30×	`add-cbrt-cube`
29×	`sqrt-prod`
26×	`associate-r`
20×	`pow1` `div-exp`
12×	`cbrt-unprod`
10×	`rec-exp` `1-exp`
9×	`log-pow`
6×	`cbrt-undiv` `add-log-exp`
5×	`associate-*r/` `unswap-sqr`
4×	`pow-prod-down`
3×	`un-div-inv`
2×	`frac-times` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `*-commutative` `flip-+` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `associate-*l/` `sum-log`

Counts

4 → 146

Calls

4 calls:

2.0ms	(+ (* re re) (* im im))
31.0ms	(* (/ 1 (sqrt (log 10.0))) (* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0)))))
16.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0))))
4.0ms	(sqrt (+ (* re re) (* im im)))

series445.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ (* re re) (* im im))
147.0ms	(* (/ 1 (sqrt (log 10.0))) (* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0)))))
226.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0))))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify3.2s

Counts

158 → 158

Iterations

Useful iterations: 3 (2.2s)

Iter	Nodes	Cost
0	214	3267
1	548	2774
2	1582	2055
3	4289	2051
done	5001	2051

prune359.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 6.4b

regimes1.1s

Accuracy

55.8% (10.9b remaining)

Error of 18.3b against oracle of 7.4b and baseline of 32.1b

bsearch135.0ms

Steps

Iters	Range		Point
6	7.459508686254044e+91	5.794156929029034e+92	5.673289848730013e+92
6	3.255384081654771e-138	3.751532506820157e-137	3.3295675416622e-138
8	-2.897696440015651e-243	-1.0192993546445385e-247	-2.2886800929856353e-244
5	-1.755535606339435e+108	-7.845778557459706e+107	-9.015088170629904e+107

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	101
1	49	101
done	49	101

end0.0ms

sample489.0ms

Algorithm

intervals

Results

350.0ms

8000×

body

valid