Details

sample20.0ms

Algorithm

intervals

Results

12.0ms

256×

body

valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	7
1	11	7

prune3.0ms

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: 30.1b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

0.6b	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
27.8b	(sqrt (+ (* re re) (* im im)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
24×	`times-frac`
22×	`log-pow`
20×	`pow1`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
8×	`sqrt-prod`
6×	`sqrt-pow1` `pow1/2` `associate-/l*`
5×	`distribute-lft-out`
4×	`add-exp-log` `sqrt-div` `associate-l` `associate-/r*` `add-cbrt-cube`
2×	`log-div` `flip3-+` `div-sub` `swap-sqr` `flip-+` `add-log-exp`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

2 → 68

Calls

2 calls:

25.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
16.0ms	(sqrt (+ (* re re) (* im im)))

series171.0ms

Counts

2 → 6

Calls

2 calls:

135.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify140.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 4 (133.0ms)

Iter	Nodes	Cost
0	224	683
1	584	650
2	1411	648
3	4802	648
4	5001	647

prune189.0ms

Filtered

74 candidates to 45 candidates (60.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	62	12	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	63	12	75

Merged error: 7.2b

Counts

75 → 12

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
0.5b	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
28.8b	(log (+ (* re re) (* im im)))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

210×	`associate-/r*`
182×	`frac-times`
170×	`sqrt-prod`
169×	`add-sqr-sqrt`
152×	`*-un-lft-identity`
139×	`add-cube-cbrt`
107×	`associate-/l*`
89×	`times-frac`
77×	`pow1`
72×	`log-pow`
32×	`associate-r`
31×	`clear-num`
30×	`frac-2neg`
29×	`associate-l`
18×	`add-exp-log`
17×	`add-cbrt-cube`
14×	`associate-*r/`
13×	`associate-*l/`
9×	`unswap-sqr`
8×	`log-prod`
5×	`cbrt-undiv` `div-exp` `distribute-lft-out`
4×	`log-div` `prod-exp` `cbrt-unprod`
3×	`un-div-inv` `div-inv` `add-log-exp`
2×	`flip3-+` `div-sub` `swap-sqr` `flip-+`
1×	`rem-log-exp` `pow-prod-down` `*-commutative`

Counts

3 → 367

Calls

3 calls:

32.0ms	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
24.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
17.0ms	(log (+ (* re re) (* im im)))

series379.0ms

Counts

3 → 9

Calls

3 calls:

141.0ms	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
185.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
52.0ms	(log (+ (* re re) (* im im)))

simplify66.0ms

Algorithm

egg-herbie

Counts

376 → 376

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1108	4963
1	5001	4456

prune591.0ms

Filtered

376 candidates to 155 candidates (41.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	365	11	376
Fresh	9	2	11
Picked	1	0	1
Done	0	0	0
Total	375	13	388

Merged error: 7.1b

Counts

388 → 13

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (* (sqrt (/ 1/2 (sqrt (log 10.0)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))))
0.3b	(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
0.5b	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
28.8b	(log (+ (* re re) (* im im)))

rewrite835.0ms

Algorithm

rewrite-expression-head

Rules

5694×	`sqrt-div`
5486×	`frac-times`
4543×	`associate-/r*`
2903×	`sqrt-prod`
2355×	`add-sqr-sqrt`
2188×	`associate-/l*`
2072×	`*-un-lft-identity`
2045×	`add-cube-cbrt`
929×	`pow1`
918×	`log-pow`
664×	`clear-num`
649×	`frac-2neg`
422×	`associate-*r/`
257×	`times-frac`
208×	`associate-*l/`
141×	`associate-r`
124×	`unswap-sqr`
88×	`associate-l`
45×	`un-div-inv`
21×	`add-exp-log`
20×	`add-cbrt-cube`
8×	`log-prod`
7×	`prod-exp` `cbrt-unprod`
6×	`div-inv`
5×	`distribute-lft-out`
4×	`log-div` `pow-prod-down` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `*-commutative`
2×	`flip3-+` `div-sub` `swap-sqr` `flip-+`
1×	`rem-log-exp`

Counts

4 → 3523

Calls

4 calls:

170.0ms	(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (* (sqrt (/ 1/2 (sqrt (log 10.0)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))))
35.0ms	(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
24.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
16.0ms	(log (+ (* re re) (* im im)))

series916.0ms

Counts

4 → 12

Calls

4 calls:

223.0ms	(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (* (sqrt (/ 1/2 (sqrt (log 10.0)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))))
461.0ms	(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
179.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
53.0ms	(log (+ (* re re) (* im im)))

simplify696.0ms

Algorithm

egg-herbie

Counts

3535 → 3535

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5001	85306

prune6.7s

Filtered

3535 candidates to 1290 candidates (36.5%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	3526	9	3535
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	3532	16	3548

Merged error: 6.9b

Counts

3548 → 16

localize26.0ms

Local error

Found 3 expressions with local error:

0.3b

(/ (* (* (fabs (cbrt 1/2)) (sqrt 1)) (/ (log (+ (* re re) (* im im))) (sqrt 1))) (* (sqrt (/ (sqrt (log 10.0)) (cbrt 1/2))) (* (sqrt (/ (sqrt (log 10.0)) 1/2)) (sqrt (log 10.0)))))

0.5b

(* (* (fabs (cbrt 1/2)) (sqrt 1)) (/ (log (+ (* re re) (* im im))) (sqrt 1)))

28.8b

(log (+ (* re re) (* im im)))

rewrite2.5s

Algorithm

rewrite-expression-head

Rules

30611×	`add-sqr-sqrt`
24493×	`times-frac`
22630×	`sqrt-prod`
12268×	`unswap-sqr`
9057×	`associate-r`
8323×	`associate-l`
7861×	`*-un-lft-identity`
6425×	`add-cube-cbrt`
2655×	`cbrt-prod`
1662×	`pow1`
1654×	`log-pow`
450×	`*-commutative`
445×	`sqrt-div`
303×	`associate-/r*`
295×	`associate-/l*`
293×	`div-inv`
237×	`associate-*l/` `associate-/r/`
208×	`frac-times`
85×	`add-exp-log`
84×	`add-cbrt-cube`
39×	`associate-*r/` `prod-exp` `cbrt-unprod`
36×	`clear-num`
34×	`frac-2neg`
23×	`cbrt-undiv` `div-exp`
16×	`associate-/l/`
8×	`log-prod`
6×	`un-div-inv`
5×	`distribute-lft-out`
3×	`pow-prod-down` `add-log-exp`
2×	`log-div` `swap-sqr`
1×	`flip3-+` `rem-log-exp` `flip-+`

Counts

3 → 10925

Calls

3 calls:

362.0ms

(/ (* (* (fabs (cbrt 1/2)) (sqrt 1)) (/ (log (+ (* re re) (* im im))) (sqrt 1))) (* (sqrt (/ (sqrt (log 10.0)) (cbrt 1/2))) (* (sqrt (/ (sqrt (log 10.0)) 1/2)) (sqrt (log 10.0)))))

27.0ms

(* (* (fabs (cbrt 1/2)) (sqrt 1)) (/ (log (+ (* re re) (* im im))) (sqrt 1)))

21.0ms

(log (+ (* re re) (* im im)))

series514.0ms

Counts

3 → 9

Calls

3 calls:

381.0ms

(/ (* (* (fabs (cbrt 1/2)) (sqrt 1)) (/ (log (+ (* re re) (* im im))) (sqrt 1))) (* (sqrt (/ (sqrt (log 10.0)) (cbrt 1/2))) (* (sqrt (/ (sqrt (log 10.0)) 1/2)) (sqrt (log 10.0)))))

85.0ms

(* (* (fabs (cbrt 1/2)) (sqrt 1)) (/ (log (+ (* re re) (* im im))) (sqrt 1)))

47.0ms

(log (+ (* re re) (* im im)))

simplify3.9s

Algorithm

egg-herbie

Counts

10934 → 10934

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	6591	504001

prune30.0s

Filtered

10934 candidates to 4145 candidates (37.9%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	10929	5	10934
Fresh	4	11	15
Picked	1	0	1
Done	0	0	0
Total	10934	16	10950

Merged error: 6.9b

Counts

10950 → 16

regimes497.0ms

Accuracy

59.5% (9.9b remaining)

Error of 17.2b against oracle of 7.2b and baseline of 31.8b

bsearch123.0ms

Steps

Iters	Range		Point
9	1.441855190865374e+102	1.6710656672296886e+109	8.215111750981571e+102
6	-3.245969229886643e+141	-4.4689590379865175e+140	-4.555058156204304e+140

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	70	62
1	70	62

end0.0ms

sample511.0ms

Algorithm

intervals

Results

363.0ms

8000×

body

valid