Details

sample1.1s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 46.875%

Guaranteed chance to sample good point: 88.149127%

Results

24.0ms	256×	body	80	valid
1.0ms	15×	body	80	nan

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	16
1	23	16

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 31.3b

Counts

2 → 1

localize20.0ms

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))
29.2b	(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:

9.0ms	(/ (+ (* (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))
4.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series68.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
20.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
14.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify58.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	457	1397
1	1716	1276
2	5001	1225

prune217.0ms

Filtered

80 candidates to 122 candidates (-52.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	107	15	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	108	15	123

Merged error: 6.8b

Counts

123 → 15

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.6b	(cbrt base)
0.6b	(cbrt base)
29.2b	(sqrt (+ (* re re) (* im im)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1`
6×	`add-exp-log` `cbrt-prod` `log-prod` `associate-l` `add-cbrt-cube`
4×	`associate-r` `log-pow` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `sqrt-prod`
2×	`sqrt-pow1` `pow1/2` `pow1/3` `sqrt-div`
1×	`rem-sqrt-square` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 65

Calls

4 calls:

5.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
1.0ms	(cbrt base)
1.0ms	(cbrt base)
4.0ms	(sqrt (+ (* re re) (* im im)))

series71.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
21.0ms	(cbrt base)
21.0ms	(cbrt base)
7.0ms	(sqrt (+ (* re re) (* im im)))

simplify55.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	244	528
1	664	483
2	1904	432
3	5001	430

prune149.0ms

Filtered

55 candidates to 77 candidates (-40.0%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	74	3	77
Fresh	2	12	14
Picked	1	0	1
Done	0	0	0
Total	77	15	92

Merged error: 6.8b

Counts

92 → 15

localize32.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.6b	(cbrt base)
5.0b	(pow base 1/3)
29.2b	(sqrt (+ (* re re) (* im im)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
7×	`add-exp-log`
6×	`log-prod` `associate-l` `add-cbrt-cube`
4×	`associate-r` `log-pow` `add-log-exp`
3×	`cbrt-prod` `distribute-rgt-in` `unpow-prod-down` `pow-unpow` `distribute-lft-in` `sqrt-prod`
2×	`sqrt-pow1` `pow1/2` `sqrt-div`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `flip3-+` `unpow1/3` `pow1/3` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr` `sqr-pow`

Counts

4 → 72

Calls

4 calls:

7.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
1.0ms	(cbrt base)
2.0ms	(pow base 1/3)
4.0ms	(sqrt (+ (* re re) (* im im)))

series67.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
21.0ms	(cbrt base)
20.0ms	(pow base 1/3)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify110.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	293	532
1	929	478
2	3454	425
3	5002	425

prune193.0ms

Filtered

59 candidates to 84 candidates (-42.4%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	82	17	99

Merged error: 6.8b

Counts

99 → 17

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.4b	(/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
0.5b	(* (log base) (log base))
29.2b	(sqrt (+ (* re re) (* im im)))

rewrite27.0ms

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:

6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
9.0ms	(/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
5.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series87.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
43.0ms	(/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
17.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify63.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	464	1397
1	1754	1281
2	5002	1229

prune129.0ms

Filtered

80 candidates to 122 candidates (-52.5%)

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	118	4	122
Fresh	3	12	15
Picked	0	1	1
Done	0	1	1
Total	121	18	139

Merged error: 6.7b

Counts

139 → 18

regimes917.0ms

Accuracy

57% (10.7b remaining)

Error of 18.1b against oracle of 7.4b and baseline of 32.2b

bsearch249.0ms

Steps

Iters	Range		Point
8	7.01218380693315e+118	7.120551162457117e+121	1.8113364370543335e+121
7	2.0831718752067583e-197	1.800435656663127e-195	4.95235580437785e-197
8	-1.3249784860297623e-288	-3.99878949250107e-291	-1.2969982966567066e-289
9	-1.5031676884716056e+122	-1.5435092841151765e+116	-1.3516761864616795e+121

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	68	64
1	78	64
2	78	64

end0.0ms

sample2.2s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 46.875%

Guaranteed chance to sample good point: 88.149127%

Results

778.0ms	8000×	body	80	valid
44.0ms	500×	body	80	nan

Details

sample1.1s

simplify3.0ms

prune4.0ms

localize20.0ms

rewrite26.0ms

series68.0ms

simplify58.0ms

prune217.0ms

localize25.0ms

rewrite13.0ms

series71.0ms

simplify55.0ms

prune149.0ms

localize32.0ms

rewrite16.0ms

series67.0ms

simplify110.0ms

prune193.0ms

localize20.0ms

rewrite27.0ms

series87.0ms

simplify63.0ms

prune129.0ms

regimes917.0ms

bsearch249.0ms

simplify2.0ms

end0.0ms

sample2.2s

Profiling