Details

sample55.0ms

Algorithm

intervals

Results

20.0ms	266×	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

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: 31.9b

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))
29.6b	(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)))

series390.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(/ (+ (* (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))
41.0ms	(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

prune606.0ms

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: 6.6b

Counts

123 → 13

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))
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite22.0ms

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)))

series432.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
153.0ms	(* (log base) (log base))
149.0ms	(* (log base) (log base))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify155.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 3 (142.0ms)

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

prune466.0ms

Filtered

127 candidates to 71 candidates (55.9%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	124	3	127
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	124	16	140

Merged error: 6.5b

Counts

140 → 16

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
0.9b	(pow (log base) 4)
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
4.0ms	(* (log base) (log base))
2.0ms	(pow (log base) 4)
4.0ms	(sqrt (+ (* re re) (* im im)))

series460.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
155.0ms	(* (log base) (log base))
171.0ms	(pow (log base) 4)
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify43.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	319	642
1	1269	568
2	5002	539

prune463.0ms

Filtered

109 candidates to 66 candidates (60.6%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	105	4	109
Fresh	2	12	14
Picked	1	0	1
Done	0	1	1
Total	108	17	125

Merged error: 6.5b

Counts

125 → 17

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(cbrt base)
0.5b	(cbrt base)
29.6b	(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)))

series489.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
178.0ms	(cbrt base)
179.0ms	(cbrt base)
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify55.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 3 (44.0ms)

Iter	Nodes	Cost
0	225	495
1	626	452
2	1627	429
3	5001	422

prune347.0ms

Filtered

77 candidates to 58 candidates (75.3%)

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	73	4	77
Fresh	3	12	15
Picked	0	1	1
Done	0	1	1
Total	76	18	94

Merged error: 6.5b

Counts

94 → 18

regimes491.0ms

Accuracy

55.2% (11.1b remaining)

Error of 18.7b against oracle of 7.5b and baseline of 32.4b

bsearch260.0ms

Steps

Iters	Range		Point
6	2157434815204663.0	13141120828988944.0	8121789251388552.0
8	7.613724523315994e-199	4.58538657554641e-194	6.1019822211320945e-198
7	-8.758535608358512e-222	-1.1508617725285748e-223	-3.970425082207529e-222
8	-2.930375697785199e+121	-7.490667611783549e+116	-8.428333082377683e+116

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	68	99
1	72	99
2	75	99
3	75	99

end0.0ms

sample1.4s

Algorithm

intervals

Results

535.0ms	8000×	body	80	valid
519.0ms	8146×	body	80	nan