Details

sample52.0ms

Algorithm

intervals

Results

18.0ms	256×	body	80	valid
17.0ms	252×	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

Filtered

1 candidates to 0 candidates (0.0%)

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: 34.7b

Counts

2 → 1

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)))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
32.1b	(sqrt (+ (* re re) (* im im)))

rewrite29.0ms

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)))
6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
5.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series381.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
93.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
152.0ms	(* (log base) (log base))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify64.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (47.0ms)

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

prune459.0ms

Filtered

122 candidates to 84 candidates (68.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	109	13	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	110	13	123

Merged error: 5.2b

Counts

123 → 13

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
32.1b	(sqrt (+ (* re re) (* im im)))

rewrite25.0ms

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:

6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
5.0ms	(* (log base) (log base))
5.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series431.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
151.0ms	(* (log base) (log base))
151.0ms	(* (log base) (log base))
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify155.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 3 (146.0ms)

Iter	Nodes	Cost
0	262	720
1	966	639
2	4681	599
3	5001	592

prune428.0ms

Filtered

127 candidates to 71 candidates (55.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	124	3	127
Fresh	0	12	12
Picked	1	0	1
Done	0	0	0
Total	125	15	140

Merged error: 5.1b

Counts

140 → 15

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
32.1b	(sqrt (+ (* re re) (* im im)))

rewrite28.0ms

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:

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

series438.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
154.0ms	(* (log base) (log base))
154.0ms	(* (log base) (log base))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify151.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 3 (142.0ms)

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

prune628.0ms

Filtered

127 candidates to 71 candidates (55.9%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	125	2	127
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	125	17	142

Merged error: 5.1b

Counts

142 → 17

localize34.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sqrt (+ (* re re) (* im im))))
32.1b	(sqrt (+ (* re re) (* im im)))
32.1b	(sqrt (+ (* re re) (* im im)))
32.1b	(sqrt (+ (* re re) (* im im)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

4.0ms	(cbrt (sqrt (+ (* re re) (* im im))))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
7.0ms	(sqrt (+ (* re re) (* im im)))

series199.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(cbrt (sqrt (+ (* re re) (* im im))))
38.0ms	(sqrt (+ (* re re) (* im im)))
35.0ms	(sqrt (+ (* re re) (* im im)))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify45.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (39.0ms)

Iter	Nodes	Cost
0	146	478
1	405	458
2	1153	456
3	5001	452

prune319.0ms

Filtered

73 candidates to 61 candidates (83.6%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	15	15
Picked	0	1	1
Done	0	1	1
Total	73	17	90

Merged error: 5.1b

Counts

90 → 17

regimes575.0ms

Accuracy

51% (12.0b remaining)

Error of 19.2b against oracle of 7.1b and baseline of 31.7b

bsearch383.0ms

Steps

Iters	Range		Point
9	1.7826190976464906e+97	3.4828836903185487e+103	2.4340519697292538e+101
7	1.4591964328985516e-103	2.8075661510406972e-101	1.4925855149012688e-103
6	2.789165867438981e-142	1.2564920093147229e-141	6.2141675390848365e-142
8	5.016844875046628e-209	2.7445170318229955e-206	1.9780598850161828e-206
10	-1.1713672228449014e-157	-6.544877159892713e-173	-7.2713402830638425e-171
6	-1.7575017886047935e+118	-2.3284542825231955e+117	-3.219075409315374e+117

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	76	91
1	76	91

end0.0ms

sample1.4s

Algorithm

intervals

Results

562.0ms	8000×	body	80	valid
534.0ms	8012×	body	80	nan