Details

sample45.0ms

Algorithm

intervals

Results

9.0ms	197×	body	80	valid
6.0ms	256×	pre	80	true
5.0ms	20×	body	1280	valid
3.0ms	17×	body	640	valid
2.0ms	13×	body	320	valid
1.0ms	9×	body	160	valid

simplify50.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune5.0ms

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: 25.0b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ alpha beta) (* 2.0 i))
0.1b	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
2.7b	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
21.0b	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 124

Calls

4 calls:

6.0ms	(+ (+ alpha beta) (* 2.0 i))
19.0ms	(/ (/ (* (+ 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)
17.0ms	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series173.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (+ alpha beta) (* 2.0 i))
63.0ms	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
87.0ms	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
18.0ms	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify101.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	701	1981
1	3980	1865
2	5002	1865

prune1.2s

Filtered

136 candidates to 101 candidates (25.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	128	8	136
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	129	8	137

Merged error: 6.5b

Counts

137 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.0b	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
1.7b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.9b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite109.0ms

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:

22.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
9.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
37.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
25.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series206.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
15.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
66.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
86.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify75.0ms

Algorithm

egg-herbie

Counts

307 → 307

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1080	4781
1	5001	4605

prune4.8s

Filtered

307 candidates to 199 candidates (35.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	301	6	307
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	306	9	315

Merged error: 6.5b

Counts

315 → 9

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.6b	(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.7b	(* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
6.4b	(+ (* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-exp-log`
39×	`add-cbrt-cube`
28×	`prod-exp` `cbrt-unprod`
27×	`cbrt-undiv` `div-exp`
13×	`*-un-lft-identity`
9×	`pow1` `frac-times`
8×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `flip3-+` `flip-+`
6×	`associate-*r/` `add-log-exp`
5×	`associate-*l/`
4×	`cbrt-div` `associate-l`
3×	`pow-prod-down` `distribute-lft-out`
2×	`pow1/3`
1×	`+-commutative` `associate-r` `sum-log` `*-commutative`

Counts

4 → 91

Calls

4 calls:

7.0ms	(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
6.0ms	(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
64.0ms	(* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
67.0ms	(+ (* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

series226.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
41.0ms	(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
64.0ms	(* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
83.0ms	(+ (* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

simplify96.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	804	3182
1	3484	2530
2	5002	2456

prune612.0ms

Filtered

103 candidates to 60 candidates (41.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	101	2	103
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	105	7	112

Merged error: 6.5b

Counts

112 → 7

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.6b	(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.7b	(* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
6.4b	(+ (* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-exp-log`
39×	`add-cbrt-cube`
28×	`prod-exp` `cbrt-unprod`
27×	`cbrt-undiv` `div-exp`
13×	`*-un-lft-identity`
9×	`pow1` `frac-times`
8×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `flip3-+` `flip-+`
6×	`associate-*r/` `add-log-exp`
5×	`associate-*l/`
4×	`cbrt-div` `associate-l`
3×	`pow-prod-down` `distribute-lft-out`
2×	`pow1/3`
1×	`+-commutative` `associate-r` `sum-log` `*-commutative`

Counts

4 → 91

Calls

4 calls:

7.0ms	(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
9.0ms	(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
66.0ms	(* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
69.0ms	(+ (* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

series226.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
40.0ms	(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
63.0ms	(* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
84.0ms	(+ (* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

simplify98.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	804	3182
1	3484	2530
2	5002	2456

prune940.0ms

Filtered

103 candidates to 61 candidates (40.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	99	4	103
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	102	8	110

Merged error: 6.5b

Counts

110 → 8

regimes355.0ms

Accuracy

12.3% (5.8b remaining)

Error of 11.9b against oracle of 6.2b and baseline of 12.7b

bsearch203.0ms

Steps

Iters	Range	Point
2	3.2153089248349697e+218	3.5148850389118494e+218	3.2527559390945796e+218
6	3.364823383576486e+101	4.3160686888801615e+102	3.4463023309256304e+101
9	3.4185557256365097e+69	3.633460336150937e+78	3.5792191086999877e+78

Iters

Range

Point

3.2153089248349697e+218

3.5148850389118494e+218

3.2527559390945796e+218

3.364823383576486e+101

4.3160686888801615e+102

3.4463023309256304e+101

3.4185557256365097e+69

3.633460336150937e+78

3.5792191086999877e+78

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	69	122
1	72	61
2	75	61
3	75	61

end0.0ms

sample1.1s

Algorithm

intervals

Results

305.0ms	6316×	body	80	valid
165.0ms	8000×	pre	80	true
134.0ms	554×	body	1280	valid
110.0ms	554×	body	640	valid
53.0ms	379×	body	320	valid
21.0ms	197×	body	160	valid

Details

sample45.0ms

simplify50.0ms

prune5.0ms

localize13.0ms

rewrite76.0ms

series173.0ms

simplify101.0ms

prune1.2s

localize16.0ms

rewrite109.0ms

series206.0ms

simplify75.0ms

prune4.8s

localize24.0ms

rewrite150.0ms

series226.0ms

simplify96.0ms

prune612.0ms

localize28.0ms

rewrite155.0ms

series226.0ms

simplify98.0ms

prune940.0ms

regimes355.0ms

bsearch203.0ms

simplify3.0ms

end0.0ms

sample1.1s

Profiling