Details

sample42.0ms

Algorithm

intervals

Results

11.0ms	202×	body	80	valid
6.0ms	256×	pre	80	true
6.0ms	21×	body	1280	valid
3.0ms	16×	body	640	valid
2.0ms	10×	body	320	valid
1.0ms	7×	body	160	valid

simplify44.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5446	29

prune14.0ms

Filtered

1 candidates to 1 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: 19.0b

Counts

2 → 2

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))
1.4b	(* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))
4.1b	(+ (* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))) 1.0)
18.2b	(/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 120

Calls

4 calls:

13.0ms	(* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))
24.0ms	(* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))
20.0ms	(+ (* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))) 1.0)
15.0ms	(/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))

series205.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))
64.0ms	(* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))
83.0ms	(+ (* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))) 1.0)
37.0ms	(/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))

simplify49.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5522	3306

prune263.0ms

Filtered

106 candidates to 132 candidates (-24.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	126	6	132
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	127	7	134

Merged error: 5.4b

Counts

134 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i))))
0.0b	(/ (- beta alpha) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))
0.1b	(* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))
1.9b	(+ (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) 1.0)

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

159×	`*-un-lft-identity`
86×	`times-frac`
80×	`add-sqr-sqrt`
51×	`distribute-lft-out`
46×	`add-cube-cbrt`
31×	`associate-r`
22×	`associate-l`
20×	`add-exp-log` `add-cbrt-cube`
11×	`distribute-lft-out--` `difference-of-squares`
9×	`associate-/r` `associate-/l`
8×	`associate-/r/`
6×	`pow1` `cbrt-undiv` `flip3-+` `div-exp` `flip-+` `add-log-exp`
4×	`prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `frac-times` `flip3--` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `sum-log` `*-commutative` `flip--`

Counts

4 → 180

Calls

4 calls:

8.0ms	(/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i))))
10.0ms	(/ (- beta alpha) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))
32.0ms	(* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))
20.0ms	(+ (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) 1.0)

series152.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i))))
19.0ms	(/ (- beta alpha) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))
62.0ms	(* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))
58.0ms	(+ (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) 1.0)

simplify64.0ms

Algorithm

egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5223	4158

prune276.0ms

Filtered

122 candidates to 192 candidates (-57.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	187	5	192
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	192	7	199

Merged error: 5.4b

Counts

199 → 7

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ beta (+ alpha (* 2.0 i))))
0.6b	(cbrt (+ beta (+ alpha (* 2.0 i))))
1.2b	(* (/ 1 (* (cbrt (+ beta (+ alpha (* 2.0 i)))) (cbrt (+ beta (+ alpha (* 2.0 i)))))) (* (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i))))) (/ (+ beta alpha) (cbrt (+ beta (+ alpha (* 2.0 i)))))))
9.5b	(+ (* (/ 1 (* (cbrt (+ beta (+ alpha (* 2.0 i)))) (cbrt (+ beta (+ alpha (* 2.0 i)))))) (* (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i))))) (/ (+ beta alpha) (cbrt (+ beta (+ alpha (* 2.0 i))))))) 1.0)

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

155×	`add-exp-log`
78×	`prod-exp`
57×	`add-cbrt-cube`
48×	`div-exp`
32×	`cbrt-unprod`
22×	`cbrt-undiv`
16×	`cbrt-div`
15×	`associate-l`
12×	`*-un-lft-identity`
10×	`rec-exp` `1-exp`
9×	`pow1` `frac-times` `flip3-+` `flip-+`
8×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `associate-/r/`
7×	`associate-*r/`
6×	`add-log-exp`
5×	`associate-*l/`
3×	`times-frac` `pow-prod-down`
2×	`pow1/3` `distribute-lft-out`
1×	`+-commutative` `associate-r` `sum-log` `*-commutative` `div-inv`

Counts

4 → 122

Calls

4 calls:

4.0ms	(cbrt (+ beta (+ alpha (* 2.0 i))))
5.0ms	(cbrt (+ beta (+ alpha (* 2.0 i))))
44.0ms	(* (/ 1 (* (cbrt (+ beta (+ alpha (* 2.0 i)))) (cbrt (+ beta (+ alpha (* 2.0 i)))))) (* (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i))))) (/ (+ beta alpha) (cbrt (+ beta (+ alpha (* 2.0 i)))))))
38.0ms	(+ (* (/ 1 (* (cbrt (+ beta (+ alpha (* 2.0 i)))) (cbrt (+ beta (+ alpha (* 2.0 i)))))) (* (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i))))) (/ (+ beta alpha) (cbrt (+ beta (+ alpha (* 2.0 i))))))) 1.0)

series218.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(cbrt (+ beta (+ alpha (* 2.0 i))))
43.0ms	(cbrt (+ beta (+ alpha (* 2.0 i))))
68.0ms	(* (/ 1 (* (cbrt (+ beta (+ alpha (* 2.0 i)))) (cbrt (+ beta (+ alpha (* 2.0 i)))))) (* (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i))))) (/ (+ beta alpha) (cbrt (+ beta (+ alpha (* 2.0 i)))))))
65.0ms	(+ (* (/ 1 (* (cbrt (+ beta (+ alpha (* 2.0 i)))) (cbrt (+ beta (+ alpha (* 2.0 i)))))) (* (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i))))) (/ (+ beta alpha) (cbrt (+ beta (+ alpha (* 2.0 i))))))) 1.0)

simplify107.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	4985	3347
1	4985	3347

prune225.0ms

Filtered

73 candidates to 134 candidates (-83.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	133	1	134
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	135	6	141

Merged error: 5.4b

Counts

141 → 6

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- beta alpha))
0.6b	(cbrt (- beta alpha))
1.4b	(* (+ alpha beta) (* (* (cbrt (- beta alpha)) (/ (cbrt (- beta alpha)) (+ beta (+ alpha (* 2.0 i))))) (/ (cbrt (- beta alpha)) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))))
9.7b	(+ (* (+ alpha beta) (* (* (cbrt (- beta alpha)) (/ (cbrt (- beta alpha)) (+ beta (+ alpha (* 2.0 i))))) (/ (cbrt (- beta alpha)) (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))) 1.0)

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

49×	`frac-times`
33×	`add-exp-log`
29×	`associate-*l/`
28×	`cbrt-div`
24×	`add-cbrt-cube`
20×	`associate-*r/`
17×	`prod-exp` `cbrt-unprod`
14×	`flip3--` `flip--`
13×	`pow1` `*-un-lft-identity` `flip3-+` `flip-+`
11×	`add-sqr-sqrt`
10×	`cbrt-prod`
7×	`add-cube-cbrt`
6×	`pow-prod-down` `add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`associate-l`
2×	`pow1/3` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `associate-r` `sum-log` `*-commutative` `distribute-lft-out`

Counts

4 → 106

Calls

4 calls:

3.0ms	(cbrt (- beta alpha))
3.0ms	(cbrt (- beta alpha))
34.0ms	(* (+ alpha beta) (* (* (cbrt (- beta alpha)) (/ (cbrt (- beta alpha)) (+ beta (+ alpha (* 2.0 i))))) (/ (cbrt (- beta alpha)) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))))
39.0ms	(+ (* (+ alpha beta) (* (* (cbrt (- beta alpha)) (/ (cbrt (- beta alpha)) (+ beta (+ alpha (* 2.0 i))))) (/ (cbrt (- beta alpha)) (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))) 1.0)

series201.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(cbrt (- beta alpha))
26.0ms	(cbrt (- beta alpha))
66.0ms	(* (+ alpha beta) (* (* (cbrt (- beta alpha)) (/ (cbrt (- beta alpha)) (+ beta (+ alpha (* 2.0 i))))) (/ (cbrt (- beta alpha)) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))))
83.0ms	(+ (* (+ alpha beta) (* (* (cbrt (- beta alpha)) (/ (cbrt (- beta alpha)) (+ beta (+ alpha (* 2.0 i))))) (/ (cbrt (- beta alpha)) (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))) 1.0)

simplify62.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5258	3032

prune172.0ms

Filtered

92 candidates to 118 candidates (-28.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	116	2	118
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	117	7	124

Merged error: 5.4b

Counts

124 → 7

regimes270.0ms

Accuracy

10.5% (5.6b remaining)

Error of 11.2b against oracle of 5.6b and baseline of 11.9b

bsearch9.0ms

Steps

Iters	Range		Point
2	2.0156345825010526e+114	2.194543879169686e+114	2.1721802170861066e+114

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	63	51
1	63	51

end0.0ms

sample1.2s

Algorithm

intervals

Results

350.0ms	6420×	body	80	valid
171.0ms	8000×	pre	80	true
136.0ms	494×	body	1280	valid
120.0ms	546×	body	640	valid
55.0ms	344×	body	320	valid
21.0ms	196×	body	160	valid

Details

sample42.0ms

simplify44.0ms

prune14.0ms

localize15.0ms

rewrite76.0ms

series205.0ms

simplify49.0ms

prune263.0ms

localize15.0ms

rewrite77.0ms

series152.0ms

simplify64.0ms

prune276.0ms

localize24.0ms

rewrite97.0ms

series218.0ms

simplify107.0ms

prune225.0ms

localize20.0ms

rewrite84.0ms

series201.0ms

simplify62.0ms

prune172.0ms

regimes270.0ms

bsearch9.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling