Details

sample89.0ms

Algorithm

intervals

Results

30.0ms	289×	body	80	nan
25.0ms	256×	body	80	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (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))
32.5b	(sqrt (+ (* re re) (* im im)))

rewrite85.0ms

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:

15.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
43.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
15.0ms	(* (log base) (log base))
9.0ms	(sqrt (+ (* re re) (* im im)))

series473.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
104.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
232.0ms	(* (log base) (log base))
39.0ms	(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

prune699.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 10.5b

localize52.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (* (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)
32.5b	(sqrt (+ (* re re) (* im im)))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
15×	`sqrt-prod`
9×	`pow1`
8×	`add-exp-log` `unpow-prod-down`
6×	`pow-unpow` `associate-/r*` `add-cbrt-cube`
4×	`sqrt-div` `add-log-exp`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`pow-to-exp` `pow-pow` `pow-exp` `associate-/r/` `log-pow` `associate-/l/` `unpow2` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 96

Calls

4 calls:

67.0ms	(/ (+ (* (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)
3.0ms	(pow (log base) 2)
11.0ms	(sqrt (+ (* re re) (* im im)))

series652.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (pow (log base) 2) (* 0.0 0.0))))
251.0ms	(pow (log base) 2)
246.0ms	(pow (log base) 2)
66.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.5s

Counts

108 → 108

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	167	2516
1	366	2350
2	921	2199
3	2753	2173
done	5000	2169

prune735.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.2b

localize51.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.4b	(/ (+ (pow (log base) 2) (* 0.0 0.0)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
0.5b	(pow (log base) 2)
32.5b	(sqrt (+ (* re re) (* im im)))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
12×	`pow1`
9×	`add-exp-log` `times-frac`
8×	`add-cbrt-cube`
6×	`log-prod` `associate-l`
5×	`log-pow`
4×	`unpow-prod-down` `associate-r` `add-log-exp`
3×	`distribute-rgt-in` `pow-unpow` `distribute-lft-in` `flip3-+` `associate-/r` `sqrt-prod` `flip-+` `associate-/l`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `pow-pow` `frac-2neg` `div-exp` `pow-prod-down` `pow-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `unpow2` `unswap-sqr` `sqr-pow`

Counts

4 → 93

Calls

4 calls:

27.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
100.0ms	(/ (+ (pow (log base) 2) (* 0.0 0.0)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
6.0ms	(pow (log base) 2)
15.0ms	(sqrt (+ (* re re) (* im im)))

series561.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
230.0ms	(/ (+ (pow (log base) 2) (* 0.0 0.0)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
178.0ms	(pow (log base) 2)
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify3.5s

Counts

105 → 105

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	194	2235
1	438	2123
2	1249	1937
3	4242	1910
done	5001	1908

prune738.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 10.2b

localize63.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (log base) 2)
32.5b	(sqrt (+ (* re re) (* im im)))
32.5b	(sqrt (+ (* re re) (* im im)))
32.5b	(sqrt (+ (* re re) (* im im)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

6.0ms	(pow (log base) 2)
16.0ms	(sqrt (+ (* re re) (* im im)))
16.0ms	(sqrt (+ (* re re) (* im im)))
15.0ms	(sqrt (+ (* re re) (* im im)))

series377.0ms

Counts

4 → 12

Calls

4 calls:

210.0ms	(pow (log base) 2)
60.0ms	(sqrt (+ (* re re) (* im im)))
51.0ms	(sqrt (+ (* re re) (* im im)))
56.0ms	(sqrt (+ (* re re) (* im im)))

simplify4.8s

Counts

76 → 76

Iterations

Useful iterations: 4 (1.8s)

Iter	Nodes	Cost
0	74	788
1	165	683
2	360	618
3	981	597
4	4546	593
done	5001	593

prune495.0ms

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 10.2b

regimes638.0ms

Accuracy

58% (10.5b remaining)

Error of 17.3b against oracle of 6.9b and baseline of 31.8b

bsearch248.0ms

Steps

Iters	Range		Point
8	1.7093693165976804e+92	1.1883716721202888e+95	5.828695856258046e+93
9	-3.9469515639049987e+130	-3.0722031062910235e+124	-7.37256703577609e+124

simplify15.0ms

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	39	56
1	50	54
2	53	54
done	53	54

end0.0ms

sample2.3s

Algorithm

intervals

Results

816.0ms	8043×	body	80	nan
784.0ms	8000×	body	80	valid