Details

sample99.0ms

Algorithm

intervals

Results

32.0ms	253×	body	80	nan
32.0ms	256×	body	80	valid

simplify134.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	18	28
1	31	22
2	52	22
3	68	22
4	88	22
5	100	22
6	104	22
done	104	22

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize20.0ms

Local error

Found 3 expressions with local error:

0.3b	(* (atan2 im re) (log base))
0.3b	(/ (- (* (atan2 im re) (log base)) (* 0.0 (log (hypot re im)))) (fma (log base) (log base) (* 0.0 0.0)))
0.5b	(fma (log base) (log base) (* 0.0 0.0))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `log-prod`
4×	`associate-r`
3×	`distribute-rgt-in` `expm1-log1p-u` `distribute-lft-in` `associate-l` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `log-pow` `*-commutative` `flip--` `cbrt-unprod` `fma-udef` `div-inv` `unswap-sqr`

Counts

3 → 69

Calls

3 calls:

15.0ms	(* (atan2 im re) (log base))
32.0ms	(/ (- (* (atan2 im re) (log base)) (* 0.0 (log (hypot re im)))) (fma (log base) (log base) (* 0.0 0.0)))
0.0ms	(fma (log base) (log base) (* 0.0 0.0))

series519.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(* (atan2 im re) (log base))
90.0ms	(/ (- (* (atan2 im re) (log base)) (* 0.0 (log (hypot re im)))) (fma (log base) (log base) (* 0.0 0.0)))
394.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify2.5s

Counts

78 → 78

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	141	1568
1	291	1534
2	902	1349
3	3191	1290
done	5001	1289

prune406.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 1 expressions with local error:

0.3b	(/ (atan2 im re) (- (log base)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
26×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
16×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
12×	`associate-/r*`
9×	`pow1`
8×	`log-pow`
4×	`neg-mul-1`
3×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
1×	`cbrt-undiv` `expm1-log1p-u` `frac-2neg` `div-exp` `clear-num` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 65

Calls

1 calls:

15.0ms

(/ (atan2 im re) (- (log base)))

series66.0ms

Counts

1 → 3

Calls

1 calls:

66.0ms

(/ (atan2 im re) (- (log base)))

simplify4.1s

Counts

68 → 68

Iterations

Useful iterations: done (4.1s)

Iter	Nodes	Cost
0	108	903
1	186	857
2	396	831
3	777	823
4	1638	823
done	5000	820

prune257.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (atan2 im re) (/ -1 (log base)))
0.3b	(/ -1 (log base))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt` `times-frac`
20×	`add-cube-cbrt` `*-un-lft-identity`
16×	`associate-r`
11×	`pow1`
9×	`add-exp-log` `add-cbrt-cube`
7×	`log-pow`
4×	`associate-/r*`
3×	`associate-l` `associate-/l*`
2×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp` `unswap-sqr`
1×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

2 → 70

Calls

2 calls:

31.0ms	(* (atan2 im re) (/ -1 (log base)))
9.0ms	(/ -1 (log base))

series330.0ms

Counts

2 → 6

Calls

2 calls:

66.0ms	(* (atan2 im re) (/ -1 (log base)))
265.0ms	(/ -1 (log base))

simplify5.0s

Counts

76 → 76

Iterations

Useful iterations: done (5.0s)

Iter	Nodes	Cost
0	103	741
1	205	670
2	666	612
3	2011	604
done	5000	600

prune290.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (fma 0.0 0.0 (pow (log base) 2)))
0.3b	(* (- (* (atan2 im re) (log base)) (* 0.0 (log (hypot re im)))) (/ 1 (fma 0.0 0.0 (pow (log base) 2))))
0.3b	(* (atan2 im re) (log base))
0.5b	(pow (log base) 2)

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
26×	`add-cube-cbrt`
20×	`add-exp-log` `times-frac`
17×	`associate-r`
13×	`add-cbrt-cube`
12×	`pow1`
6×	`log-prod` `associate-l`
5×	`prod-exp`
4×	`expm1-log1p-u` `unpow-prod-down` `div-exp` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`distribute-rgt-in` `pow-unpow` `distribute-lft-in` `associate-/r` `cbrt-unprod` `associate-/l`
2×	`cbrt-undiv` `frac-times` `rec-exp` `flip3--` `1-exp` `pow-prod-down` `associate-l/` `log-pow` `-commutative` `flip--` `div-inv`
1×	`pow-to-exp` `pow-flip` `pow-pow` `frac-2neg` `associate-*r/` `pow-exp` `clear-num` `un-div-inv` `unpow2` `inv-pow` `sqr-pow`

Counts

4 → 123

Calls

4 calls:

6.0ms	(/ 1 (fma 0.0 0.0 (pow (log base) 2)))
36.0ms	(* (- (* (atan2 im re) (log base)) (* 0.0 (log (hypot re im)))) (/ 1 (fma 0.0 0.0 (pow (log base) 2))))
9.0ms	(* (atan2 im re) (log base))
3.0ms	(pow (log base) 2)

series660.0ms

Counts

4 → 12

Calls

4 calls:

301.0ms	(/ 1 (fma 0.0 0.0 (pow (log base) 2)))
97.0ms	(* (- (* (atan2 im re) (log base)) (* 0.0 (log (hypot re im)))) (/ 1 (fma 0.0 0.0 (pow (log base) 2))))
45.0ms	(* (atan2 im re) (log base))
216.0ms	(pow (log base) 2)

simplify1.4s

Counts

135 → 135

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	207	2291
1	439	2080
2	1297	1804
done	5000	1790

prune563.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0b

regimes292.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	8
1	10	8
done	10	8

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.7s	8000×	body	80	valid
1.3s	7718×	body	80	nan