Details

sample41.0ms

Algorithm

intervals

Results

13.0ms	203×	body	80	valid
6.0ms	256×	pre	80	true
3.0ms	19×	body	640	valid
3.0ms	14×	body	1280	valid
2.0ms	10×	body	320	valid
1.0ms	10×	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

prune2.0ms

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: 23.4b

Counts

2 → 1

localize13.0ms

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))

2.5b

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

20.5b

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

rewrite67.0ms

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:

21.0ms

(/ (/ (* (+ 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)

13.0ms

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

series574.0ms

Counts

3 → 9

Calls

3 calls:

221.0ms

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

272.0ms

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

81.0ms

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

simplify102.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 1 (19.0ms)

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

prune336.0ms

Filtered

120 candidates to 89 candidates (74.2%)

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: 6.5b

Counts

121 → 12

localize13.0ms

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))))
2.5b	(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite75.0ms

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:

10.0ms	(/ (- 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))
19.0ms	(* (+ 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)

series656.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
231.0ms	(/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
80.0ms	(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
273.0ms	(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify102.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 1 (19.0ms)

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

prune345.0ms

Filtered

141 candidates to 101 candidates (71.6%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	132	9	141
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	138	15	153

Merged error: 6.5b

Counts

153 → 15

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))))
2.5b	(+ (log (exp (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)
3.7b	(log (exp (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 115

Calls

4 calls:

20.0ms	(/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
16.0ms	(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
20.0ms	(+ (log (exp (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)
12.0ms	(log (exp (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))

series819.0ms

Counts

4 → 12

Calls

4 calls:

226.0ms	(/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
80.0ms	(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
278.0ms	(+ (log (exp (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)
234.0ms	(log (exp (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))

simplify88.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	629	1596
1	3298	1439
2	5002	1439

prune346.0ms

Filtered

127 candidates to 95 candidates (74.8%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	127	15	142

Merged error: 6.5b

Counts

142 → 15

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
0.1b	(exp (log (+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)))
2.5b	(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
3.7b	(log (+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

31×	`*-un-lft-identity`
28×	`add-sqr-sqrt`
21×	`associate-r`
17×	`add-cube-cbrt`
16×	`times-frac`
10×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1` `log-prod`
6×	`flip3-+` `flip-+` `add-log-exp`
4×	`log-div` `exp-prod` `associate-l` `exp-sum` `distribute-lft-out`
3×	`distribute-lft-out--` `difference-of-squares`
2×	`frac-times` `exp-diff` `associate-*l/` `prod-exp` `associate-/r/` `log-pow` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `associate-r/` `div-exp` `rem-log-exp` `pow-prod-down` `sum-log` `-commutative` `div-inv` `rem-exp-log`

Counts

4 → 90

Calls

4 calls:

19.0ms	(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
22.0ms	(exp (log (+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)))
21.0ms	(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
21.0ms	(log (+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0))

series911.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
275.0ms	(exp (log (+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)))
275.0ms	(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
279.0ms	(log (+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0))

simplify69.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	539	1525
1	2481	1384
2	5001	1348

prune264.0ms

Filtered

102 candidates to 74 candidates (72.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	98	4	102
Fresh	7	6	13
Picked	1	0	1
Done	0	1	1
Total	106	11	117

Merged error: 4.2b

Counts

117 → 11

regimes221.0ms

Accuracy

2.4% (8.0b remaining)

Error of 12.3b against oracle of 4.3b and baseline of 12.5b

bsearch225.0ms

Steps

Iters	Range	Point
8	8.706013559962144e+248	1.185812019923002e+252	1.167289139801623e+252
8	1.7240522366403408e+224	2.3827083199484607e+227	7.964944561691012e+224
8	2.5314442159097765e+113	4.163133967814639e+117	4.094149957430972e+117

Iters

Range

Point

8.706013559962144e+248

1.185812019923002e+252

1.167289139801623e+252

1.7240522366403408e+224

2.3827083199484607e+227

7.964944561691012e+224

2.5314442159097765e+113

4.163133967814639e+117

4.094149957430972e+117

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	57
1	75	57

end0.0ms

sample959.0ms

Algorithm

intervals

Results

302.0ms	6333×	body	80	valid
168.0ms	8000×	pre	80	true
123.0ms	524×	body	1280	valid
109.0ms	588×	body	640	valid
51.0ms	361×	body	320	valid
18.0ms	194×	body	160	valid

Details

sample41.0ms

simplify54.0ms

prune2.0ms

localize13.0ms

rewrite67.0ms

series574.0ms

simplify102.0ms

prune336.0ms

localize13.0ms

rewrite75.0ms

series656.0ms

simplify102.0ms

prune345.0ms

localize17.0ms

rewrite72.0ms

series819.0ms

simplify88.0ms

prune346.0ms

localize16.0ms

rewrite86.0ms

series911.0ms

simplify69.0ms

prune264.0ms

regimes221.0ms

bsearch225.0ms

simplify2.0ms

end0.0ms

sample959.0ms

Profiling