Details

sample64.0ms

Algorithm

intervals

Results

25.0ms	256×	body	80	valid
21.0ms	252×	body	80	nan

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	16
1	44	16
2	56	16
3	74	16
4	80	16
5	80	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: 32.6b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.4b	(* (atan2 im re) (log base))
0.5b	(* (log base) (log base))
30.7b	(sqrt (+ (* re re) (* im im)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
23×	`add-cube-cbrt`
21×	`pow1`
12×	`log-prod`
10×	`add-exp-log` `add-cbrt-cube`
9×	`times-frac`
8×	`associate-r`
7×	`associate-l` `log-pow`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
4×	`add-log-exp`
3×	`associate-/r` `sqrt-prod` `associate-/l`
2×	`flip3-+` `sqrt-div` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `flip-+` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `pow2` `rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow-plus` `pow1/2` `div-sub` `div-exp` `clear-num` `pow-sqr` `pow-prod-up` `flip--` `div-inv`

Counts

4 → 108

Calls

4 calls:

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

series251.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
26.0ms	(* (atan2 im re) (log base))
150.0ms	(* (log base) (log base))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify63.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	444	1213
1	1816	1100
2	5001	1070

prune403.0ms

Filtered

120 candidates to 79 candidates (65.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	108	12	120
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	109	12	121

Merged error: 0.1b

Counts

121 → 12

localize6.0ms

Local error

Found 1 expressions with local error:

0.3b	(/ (atan2 im re) (log base))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

12×	`times-frac`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
4×	`associate-/r*` `log-pow`
3×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv` `add-log-exp`

Counts

1 → 31

Calls

1 calls:

4.0ms

(/ (atan2 im re) (log base))

series34.0ms

Counts

1 → 3

Calls

1 calls:

33.0ms

(/ (atan2 im re) (log base))

simplify55.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 4 (48.0ms)

Iter	Nodes	Cost
0	103	207
1	270	193
2	671	192
3	1907	190
4	5001	188

prune99.0ms

Filtered

34 candidates to 22 candidates (64.7%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	26	8	34
Fresh	4	7	11
Picked	0	1	1
Done	0	0	0
Total	30	16	46

Merged error: 0.0b

Counts

46 → 16

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ 1 (log base))
0.4b	(* (atan2 im re) (/ 1 (log base)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
26×	`times-frac`
21×	`*-un-lft-identity`
20×	`add-cube-cbrt`
16×	`associate-r`
15×	`add-exp-log`
12×	`pow1`
9×	`add-cbrt-cube`
7×	`log-pow`
4×	`div-exp` `prod-exp` `associate-/r*`
3×	`associate-l` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `1-exp` `cbrt-unprod` `div-inv` `add-log-exp`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

2 → 74

Calls

2 calls:

3.0ms	(/ 1 (log base))
8.0ms	(* (atan2 im re) (/ 1 (log base)))

series193.0ms

Counts

2 → 6

Calls

2 calls:

156.0ms	(/ 1 (log base))
36.0ms	(* (atan2 im re) (/ 1 (log base)))

simplify47.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 3 (42.0ms)

Iter	Nodes	Cost
0	206	403
1	829	345
2	2677	303
3	5002	296

prune136.0ms

Filtered

80 candidates to 38 candidates (47.5%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	77	3	80
Fresh	3	11	14
Picked	0	1	1
Done	0	1	1
Total	80	16	96

Merged error: 0.0b

Counts

96 → 16

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (pow (log base) 3))
0.4b	(* (atan2 im re) (cbrt (/ 1 (pow (log base) 3))))
0.6b	(cbrt (/ 1 (pow (log base) 3)))
0.7b	(pow (log base) 3)

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

134×	`times-frac`
106×	`add-sqr-sqrt`
101×	`cbrt-prod`
88×	`*-un-lft-identity`
84×	`add-cube-cbrt`
49×	`associate-r`
46×	`unpow-prod-down` `cube-prod`
29×	`pow1`
22×	`log-pow`
16×	`add-exp-log`
14×	`associate-/r*`
13×	`sqr-pow`
11×	`cube-mult` `unpow3`
10×	`unswap-sqr`
8×	`add-cbrt-cube`
6×	`div-exp`
4×	`pow-to-exp` `pow-exp` `add-log-exp`
3×	`rec-exp` `pow-unpow` `1-exp` `associate-l` `div-inv` `associate-/l*`
2×	`cbrt-div`
1×	`cbrt-undiv` `pow-flip` `pow-pow` `frac-2neg` `pow1/3` `associate-r/` `pow-prod-down` `prod-exp` `clear-num` `-commutative` `cbrt-unprod` `inv-pow` `rem-cube-cbrt`

Counts

4 → 235

Calls

4 calls:

10.0ms	(/ 1 (pow (log base) 3))
16.0ms	(* (atan2 im re) (cbrt (/ 1 (pow (log base) 3))))
6.0ms	(cbrt (/ 1 (pow (log base) 3)))
3.0ms	(pow (log base) 3)

series568.0ms

Counts

4 → 12

Calls

4 calls:

200.0ms	(/ 1 (pow (log base) 3))
33.0ms	(* (atan2 im re) (cbrt (/ 1 (pow (log base) 3))))
158.0ms	(cbrt (/ 1 (pow (log base) 3)))
178.0ms	(pow (log base) 3)

simplify56.0ms

Algorithm

egg-herbie

Counts

247 → 247

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	400	1694
1	1645	1321
2	5001	1292

prune307.0ms

Filtered

247 candidates to 96 candidates (38.9%)

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	243	4	247
Fresh	1	12	13
Picked	0	1	1
Done	1	1	2
Total	245	18	263

Merged error: 0.0b

Counts

263 → 18

regimes275.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	4
1	11	4

end0.0ms

sample1.8s

Algorithm

intervals

Results

706.0ms	8000×	body	80	valid
683.0ms	8227×	body	80	nan