Details

sample29.0ms

Algorithm

intervals

Results

15.0ms

256×

body

valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	7
1	11	7

prune4.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 28.9b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.6b	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
26.7b	(sqrt (+ (* re re) (* im im)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

24×	`times-frac`
22×	`log-pow`
21×	`pow1`
17×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-pow1` `pow1/2` `associate-/l*`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`sqrt-div` `associate-/r*`
3×	`flip3-+` `sqrt-prod` `flip-+`
2×	`log-div` `div-sub`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 74

Calls

3 calls:

4.0ms	(+ (* re re) (* im im))
7.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
3.0ms	(sqrt (+ (* re re) (* im im)))

series34.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(+ (* re re) (* im im))
19.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
7.0ms	(sqrt (+ (* re re) (* im im)))

simplify87.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 3 (79.0ms)

Iter	Nodes	Cost
0	259	745
1	894	701
2	2872	696
3	5001	694

prune325.0ms

Filtered

83 candidates to 55 candidates (33.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	69	14	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	14	84

Merged error: 7.6b

Counts

84 → 14

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sqrt (+ (* re re) (* im im))))
26.7b	(sqrt (+ (* re re) (* im im)))
26.7b	(sqrt (+ (* re re) (* im im)))
26.7b	(sqrt (+ (* re re) (* im im)))

rewrite16.0ms

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

series39.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt (sqrt (+ (* re re) (* im im))))
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify52.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (43.0ms)

Iter	Nodes	Cost
0	176	496
1	464	476
2	1323	470
3	5001	457

prune490.0ms

Filtered

73 candidates to 60 candidates (17.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	72	1	73
Fresh	0	13	13
Picked	1	0	1
Done	0	0	0
Total	73	14	87

Merged error: 7.6b

Counts

87 → 14

localize22.0ms

Local error

Found 4 expressions with local error:

4.2b	(exp (log (cbrt (sqrt (+ (* re re) (* im im))))))
26.7b	(sqrt (+ (* re re) (* im im)))
26.7b	(sqrt (+ (* re re) (* im im)))
26.7b	(sqrt (+ (* re re) (* im im)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

6.0ms	(exp (log (cbrt (sqrt (+ (* re re) (* im im))))))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series38.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(exp (log (cbrt (sqrt (+ (* re re) (* im im))))))
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify50.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (43.0ms)

Iter	Nodes	Cost
0	221	562
1	527	539
2	1407	516
3	5001	493

prune611.0ms

Filtered

81 candidates to 64 candidates (21.0%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	80	1	81
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	80	15	95

Merged error: 7.6b

Counts

95 → 15

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (pow (/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0)) 3))
0.6b	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
0.7b	(pow (/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0)) 3)
26.7b	(sqrt (+ (* re re) (* im im)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

120×	`times-frac`
94×	`log-pow`
79×	`pow1`
64×	`add-sqr-sqrt`
63×	`add-cube-cbrt` `*-un-lft-identity`
62×	`cbrt-prod`
56×	`unpow-prod-down` `cube-prod`
22×	`sqrt-pow1` `pow1/2`
9×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
5×	`div-inv`
4×	`sqrt-div` `associate-/r*` `add-log-exp`
3×	`pow-unpow` `sqrt-prod`
2×	`cbrt-undiv` `cube-div` `cube-mult` `log-div` `flip3-+` `unpow3` `div-sub` `div-exp` `pow-exp` `flip-+` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `cbrt-div` `pow-pow` `frac-2neg` `pow1/3` `clear-num` `rem-cbrt-cube`

Counts

4 → 211

Calls

4 calls:

8.0ms	(cbrt (pow (/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0)) 3))
9.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
8.0ms	(pow (/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0)) 3)
4.0ms	(sqrt (+ (* re re) (* im im)))

series91.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(cbrt (pow (/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0)) 3))
22.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
44.0ms	(pow (/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0)) 3)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify74.0ms

Algorithm

egg-herbie

Counts

223 → 223

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	547	2589
1	2273	2460
2	5002	2436

prune667.0ms

Filtered

223 candidates to 96 candidates (57.0%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	213	10	223
Fresh	4	9	13
Picked	1	0	1
Done	0	1	1
Total	218	20	238

Merged error: 7.5b

Counts

238 → 20

regimes1.7s

Accuracy

57.4% (10.3b remaining)

Error of 17.7b against oracle of 7.4b and baseline of 31.7b

bsearch87.0ms

Steps

Iters	Range		Point
5	2.2866843337900248e+77	5.514542683406611e+77	4.325223030489154e+77
8	-3.719641692260901e+158	-1.2498419091925624e+154	-1.269258234578637e+154

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	34
1	38	34

end0.0ms

sample710.0ms

Algorithm

intervals

Results

488.0ms

8000×

body

valid

Details

sample29.0ms

simplify3.0ms

prune4.0ms

localize11.0ms

rewrite16.0ms

series34.0ms

simplify87.0ms

prune325.0ms

localize16.0ms

rewrite16.0ms

series39.0ms

simplify52.0ms

prune490.0ms

localize22.0ms

rewrite18.0ms

series38.0ms

simplify50.0ms

prune611.0ms

localize15.0ms

rewrite38.0ms

series91.0ms

simplify74.0ms

prune667.0ms

regimes1.7s

bsearch87.0ms

simplify1.0ms

end0.0ms

sample710.0ms

Profiling