Details

sample52.0ms

Algorithm

intervals

Results

17.0ms	256×	body	80	valid
17.0ms	265×	body	80	nan

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	16
1	23	16

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
31.0b	(sqrt (+ (* re re) (* im im)))

rewrite26.0ms

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:

10.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
5.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
5.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series370.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
90.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
148.0ms	(* (log base) (log base))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify63.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	445	1361
1	1751	1236
2	5001	1205

prune459.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.6b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (log base) 2)
31.0b	(sqrt (+ (* re re) (* im im)))
31.0b	(sqrt (+ (* re re) (* im im)))
31.0b	(sqrt (+ (* re re) (* im im)))

rewrite17.0ms

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:

2.0ms	(pow (log base) 2)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
7.0ms	(sqrt (+ (* re re) (* im im)))

series256.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(pow (log base) 2)
39.0ms	(sqrt (+ (* re re) (* im im)))
35.0ms	(sqrt (+ (* re re) (* im im)))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify61.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (56.0ms)

Iter	Nodes	Cost
0	169	373
1	482	348
2	1597	348
3	5002	344

prune518.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 7.6b

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (- (pow 0.0 3)) 0.0) (pow (log base) 4)))
0.5b	(* (log base) (log base))
0.9b	(pow (log base) 4)
31.0b	(sqrt (+ (* re re) (* im im)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

13.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (- (pow 0.0 3)) 0.0) (pow (log base) 4)))
5.0ms	(* (log base) (log base))
2.0ms	(pow (log base) 4)
4.0ms	(sqrt (+ (* re re) (* im im)))

series472.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (- (pow 0.0 3)) 0.0) (pow (log base) 4)))
144.0ms	(* (log base) (log base))
164.0ms	(pow (log base) 4)
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify63.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	465	1176
1	1940	1064
2	5001	1045

prune498.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 7.5b

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt base)
0.5b	(cbrt base)
31.0b	(sqrt (+ (* re re) (* im im)))
32.2b	(log (+ (* re re) (* im im)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

1.0ms	(cbrt base)
1.0ms	(cbrt base)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(log (+ (* re re) (* im im)))

series432.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(cbrt base)
181.0ms	(cbrt base)
34.0ms	(sqrt (+ (* re re) (* im im)))
49.0ms	(log (+ (* re re) (* im im)))

simplify73.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 4 (68.0ms)

Iter	Nodes	Cost
0	167	300
1	354	275
2	818	271
3	2399	271
4	5001	270

prune313.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 7.5b

regimes327.0ms

Accuracy

59% (10.1b remaining)

Error of 17.5b against oracle of 7.4b and baseline of 32.0b

bsearch111.0ms

Steps

Iters	Range		Point
4	1.464110213656478e+115	2.1406716088450655e+115	2.029807406530831e+115
8	-6.222592740773542e+91	-3.608472222967844e+87	-6.531289779340832e+88

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	55
1	55	55

end0.0ms

sample1.4s

Algorithm

intervals

Results

547.0ms	8000×	body	80	valid
525.0ms	8197×	body	80	nan