Details

sample56.0ms

Algorithm

intervals

Results

18.0ms	251×	body	80	nan
17.0ms	256×	body	80	valid

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: 29.1b

localize23.0ms

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)))
0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
27.0b	(sqrt (+ (* re re) (* im im)))

rewrite72.0ms

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:

38.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
13.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
9.0ms	(* (log base) (log base))
8.0ms	(sqrt (+ (* re re) (* im im)))

series362.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
87.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
146.0ms	(* (log base) (log base))
34.0ms	(sqrt (+ (* re re) (* im im)))

simplify57.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (45.0ms)

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

prune446.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 7.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
27.0b	(sqrt (+ (* re re) (* im im)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

36×	`pow1`
28×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
21×	`add-cube-cbrt`
18×	`log-prod`
16×	`log-pow`
14×	`associate-l`
12×	`swap-sqr` `associate-r`
10×	`add-exp-log` `add-cbrt-cube`
9×	`distribute-rgt-in` `distribute-lft-in`
4×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `sqrt-prod` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`pow2` `sqrt-pow1` `pow-plus` `pow1/2` `sqrt-div` `pow-sqr` `pow-prod-up`
1×	`rem-sqrt-square` `flip3-+` `flip-+`

Counts

4 → 115

Calls

4 calls:

16.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
9.0ms	(* (log base) (log base))
9.0ms	(* (log base) (log base))
7.0ms	(sqrt (+ (* re re) (* im im)))

series417.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
148.0ms	(* (log base) (log base))
148.0ms	(* (log base) (log base))
34.0ms	(sqrt (+ (* re re) (* im im)))

simplify149.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 3 (141.0ms)

Iter	Nodes	Cost
0	262	719
1	966	639
2	4681	599
3	5001	592

prune423.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 7.3b

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
27.9b	(cbrt (+ (* re re) (* im im)))
27.9b	(cbrt (+ (* re re) (* im im)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

30×	`pow1`
22×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`add-cube-cbrt`
12×	`log-prod` `swap-sqr` `log-pow`
8×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
6×	`cbrt-prod` `distribute-rgt-in` `distribute-lft-in`
4×	`cbrt-div` `add-log-exp`
2×	`pow2` `flip3-+` `pow-plus` `pow1/3` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 98

Calls

4 calls:

9.0ms	(* (log base) (log base))
9.0ms	(* (log base) (log base))
4.0ms	(cbrt (+ (* re re) (* im im)))
5.0ms	(cbrt (+ (* re re) (* im im)))

series609.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(* (log base) (log base))
288.0ms	(* (log base) (log base))
90.0ms	(cbrt (+ (* re re) (* im im)))
89.0ms	(cbrt (+ (* re re) (* im im)))

simplify116.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 3 (109.0ms)

Iter	Nodes	Cost
0	216	548
1	792	486
2	3678	458
3	5001	442

prune443.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.3b

localize36.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
27.9b	(cbrt (+ (* re re) (* im im)))
30.3b	(pow (+ (* re re) (* im im)) 1/3)

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

31×	`pow1`
23×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
12×	`log-prod` `swap-sqr` `log-pow`
9×	`add-exp-log`
8×	`associate-r` `associate-l` `add-cbrt-cube`
6×	`distribute-rgt-in` `distribute-lft-in`
4×	`add-log-exp`
3×	`cbrt-prod` `unpow-prod-down` `pow-unpow`
2×	`pow2` `cbrt-div` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
1×	`pow-to-exp` `pow-pow` `flip3-+` `unpow1/3` `pow1/3` `pow-exp` `flip-+` `sqr-pow`

Counts

4 → 103

Calls

4 calls:

9.0ms	(* (log base) (log base))
9.0ms	(* (log base) (log base))
4.0ms	(cbrt (+ (* re re) (* im im)))
10.0ms	(pow (+ (* re re) (* im im)) 1/3)

series463.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(* (log base) (log base))
144.0ms	(* (log base) (log base))
86.0ms	(cbrt (+ (* re re) (* im im)))
88.0ms	(pow (+ (* re re) (* im im)) 1/3)

simplify38.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	266	539
1	1053	465
2	5001	439

prune446.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 7.3b

regimes421.0ms

Accuracy

58.1% (10.3b remaining)

Error of 17.8b against oracle of 7.4b and baseline of 32.1b

bsearch130.0ms

Steps

Iters	Range		Point
6	2.5905013689292844e+113	3.2749400383224745e+114	1.5707996749315065e+114
8	-1.4124068688051116e+103	-6.158636249166368e+99	-3.2770454727845497e+100

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	57
1	56	57

end0.0ms

sample1.6s

Algorithm

intervals

Results

551.0ms	8000×	body	80	valid
544.0ms	7772×	body	80	nan