Details

sample41.0ms

Algorithm

intervals

Results

10.0ms	197×	body	80	valid
6.0ms	25×	body	1280	valid
6.0ms	256×	pre	80	true
3.0ms	16×	body	640	valid
1.0ms	10×	body	320	valid
1.0ms	8×	body	160	valid

simplify54.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	31	14
1	103	14
2	454	14
3	2127	14
4	5001	14

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: 25.2b

Counts

2 → 1

localize18.0ms

Local error

Found 3 expressions with local error:

0.1b

(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))

2.1b

(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

21.8b

(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

54×	`times-frac`
47×	`*-un-lft-identity`
25×	`add-sqr-sqrt` `add-cube-cbrt`
17×	`add-exp-log` `add-cbrt-cube`
14×	`associate-/r/`
11×	`flip3-+` `flip-+` `distribute-lft-out`
10×	`associate-/l*`
9×	`associate-/l/`
7×	`cbrt-undiv` `div-exp` `associate-/r*` `div-inv`
5×	`add-log-exp`
4×	`frac-times`
3×	`pow1` `flip3--` `flip--`
2×	`frac-2neg` `associate-r/` `associate-l/` `prod-exp` `clear-num` `cbrt-unprod`
1×	`+-commutative` `sum-log`

Counts

3 → 111

Calls

3 calls:

20.0ms

(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))

29.0ms

(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

14.0ms

(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series598.0ms

Counts

3 → 9

Calls

3 calls:

228.0ms

(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))

288.0ms

(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

82.0ms

(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify96.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	681	1905
1	3622	1789
2	5001	1789

prune321.0ms

Filtered

120 candidates to 89 candidates (74.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	112	8	120
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	113	8	121

Merged error: 5.7b

Counts

121 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.1b	(/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b	(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
2.1b	(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

48×	`*-un-lft-identity`
45×	`add-sqr-sqrt`
35×	`times-frac`
26×	`add-cube-cbrt`
21×	`associate-r`
20×	`add-exp-log` `add-cbrt-cube`
8×	`flip3-+` `flip-+`
7×	`associate-/r*` `associate-/l/` `distribute-lft-out--` `difference-of-squares`
6×	`pow1` `cbrt-undiv` `div-exp` `associate-/r/` `associate-/l*` `add-log-exp`
4×	`frac-times` `associate-l` `associate-*l/` `prod-exp` `cbrt-unprod` `distribute-lft-out`
3×	`div-inv`
2×	`frac-2neg` `associate-*r/` `clear-num` `unswap-sqr`
1×	`+-commutative` `flip3--` `div-sub` `pow-prod-down` `sum-log` `*-commutative` `flip--`

Counts

4 → 129

Calls

4 calls:

9.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
20.0ms	(/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
17.0ms	(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
22.0ms	(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series678.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
234.0ms	(/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
76.0ms	(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
289.0ms	(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify95.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	657	1569
1	3554	1429
2	5002	1429

prune308.0ms

Filtered

141 candidates to 99 candidates (70.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	138	3	141
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	143	6	149

Merged error: 5.7b

Counts

149 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b	(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
2.1b	(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
2.1b	(log (exp (+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

34×	`*-un-lft-identity`
29×	`add-sqr-sqrt`
21×	`associate-r`
20×	`times-frac`
18×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
7×	`pow1` `flip3-+` `flip-+`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-exp` `log-pow` `associate-/l/` `distribute-lft-out`
4×	`frac-times` `log-prod` `exp-prod` `associate-l` `associate-l/` `prod-exp` `associate-/r` `associate-/r/` `cbrt-unprod`
3×	`distribute-lft-out--` `difference-of-squares`
2×	`associate-*r/` `div-inv` `unswap-sqr`
1×	`+-commutative` `frac-2neg` `rem-log-exp` `exp-sum` `pow-prod-down` `clear-num` `sum-log` `-commutative` `associate-/l`

Counts

4 → 106

Calls

4 calls:

22.0ms	(/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
20.0ms	(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
22.0ms	(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
25.0ms	(log (exp (+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)))

series897.0ms

Counts

4 → 12

Calls

4 calls:

237.0ms	(/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
81.0ms	(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
286.0ms	(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
292.0ms	(log (exp (+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)))

simplify88.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	618	1520
1	3353	1353
2	5002	1353

prune314.0ms

Filtered

118 candidates to 86 candidates (72.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	117	1	118
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	117	7	124

Merged error: 5.7b

Counts

124 → 7

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.1b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.7b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.5b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

321×	`times-frac`
290×	`*-un-lft-identity`
211×	`add-sqr-sqrt`
140×	`add-cube-cbrt`
90×	`associate-r`
44×	`distribute-lft-out`
31×	`distribute-lft-out--` `difference-of-squares`
26×	`associate-/l*`
24×	`associate-/r/`
20×	`add-exp-log` `add-cbrt-cube`
15×	`flip3-+` `flip-+`
12×	`div-inv`
7×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`pow1` `add-log-exp`
4×	`associate-l`
3×	`div-sub` `prod-exp` `cbrt-unprod` `associate-/l/` `unswap-sqr`
2×	`frac-times` `frac-2neg` `associate-*l/` `clear-num`
1×	`+-commutative` `flip3--` `associate-r/` `pow-prod-down` `sum-log` `-commutative` `flip--`

Counts

4 → 295

Calls

4 calls:

9.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
24.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
40.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
28.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series780.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
168.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
239.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
295.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify73.0ms

Algorithm

egg-herbie

Counts

307 → 307

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1080	4781
1	5001	4605

prune649.0ms

Filtered

307 candidates to 202 candidates (65.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	304	3	307
Fresh	1	4	5
Picked	1	0	1
Done	1	0	1
Total	307	7	314

Merged error: 5.7b

Counts

314 → 7

regimes152.0ms

Accuracy

12.4% (5.9b remaining)

Error of 11.7b against oracle of 5.8b and baseline of 12.5b

bsearch82.0ms

Steps

Iters	Range		Point
9	2.2870422288415107e+104	2.377004156358407e+112	6.494704746219284e+109

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	46
1	50	46

end0.0ms

sample1.0s

Algorithm

intervals

Results

313.0ms	6332×	body	80	valid
172.0ms	8000×	pre	80	true
133.0ms	520×	body	1280	valid
112.0ms	581×	body	640	valid
53.0ms	369×	body	320	valid
19.0ms	198×	body	160	valid

Details

sample41.0ms

simplify54.0ms

prune3.0ms

localize18.0ms

rewrite69.0ms

series598.0ms

simplify96.0ms

prune321.0ms

localize18.0ms

rewrite73.0ms

series678.0ms

simplify95.0ms

prune308.0ms

localize17.0ms

rewrite92.0ms

series897.0ms

simplify88.0ms

prune314.0ms

localize20.0ms

rewrite121.0ms

series780.0ms

simplify73.0ms

prune649.0ms

regimes152.0ms

bsearch82.0ms

simplify2.0ms

end0.0ms

sample1.0s

Profiling