Details

sample48.0ms

Algorithm

intervals

Results

11.0ms	205×	body	80	valid
6.0ms	256×	pre	80	true
5.0ms	22×	body	640	valid
4.0ms	15×	body	1280	valid
1.0ms	8×	body	320	valid
1.0ms	6×	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

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: 22.7b

Counts

2 → 1

localize12.0ms

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))

1.5b

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

18.4b

(/ (* (+ 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:

19.0ms

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

31.0ms

(+ (/ (/ (* (+ 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)))

series164.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms

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

83.0ms

(+ (/ (/ (* (+ 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)))

simplify88.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 1 (16.0ms)

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

prune248.0ms

Filtered

120 candidates to 89 candidates (25.8%)

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: 4.6b

Counts

121 → 8

localize13.0ms

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)))
2.6b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
2.9b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite115.0ms

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:

19.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
9.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
39.0ms	(* (+ 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)

series196.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
14.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
61.0ms	(* (+ 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))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify71.0ms

Algorithm

egg-herbie

Counts

307 → 307

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1080	4781
1	5001	4605

prune585.0ms

Filtered

307 candidates to 200 candidates (34.9%)

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: 4.6b

Counts

315 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
2.6b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
2.9b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
2.9b	(log (exp (+ (* (+ 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

162×	`times-frac`
151×	`*-un-lft-identity`
116×	`add-sqr-sqrt`
90×	`associate-r`
75×	`add-cube-cbrt`
22×	`distribute-lft-out`
16×	`distribute-lft-out--` `difference-of-squares`
15×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r/`
9×	`flip3-+` `flip-+`
7×	`pow1`
6×	`div-inv` `add-log-exp`
5×	`associate-/l*`
4×	`cbrt-undiv` `log-prod` `div-exp` `associate-l` `log-pow`
3×	`exp-prod` `prod-exp` `associate-/r*` `cbrt-unprod` `unswap-sqr`
2×	`frac-times` `associate-*l/` `associate-/l/`
1×	`+-commutative` `flip3--` `frac-2neg` `div-sub` `associate-r/` `rem-log-exp` `exp-sum` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip--`

Counts

4 → 184

Calls

4 calls:

9.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
39.0ms	(* (+ 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)
25.0ms	(log (exp (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))

series246.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
65.0ms	(* (+ 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))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
84.0ms	(log (exp (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))

simplify49.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	922	2625
1	5001	2462

prune408.0ms

Filtered

196 candidates to 132 candidates (32.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	196	0	196
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	196	9	205

Merged error: 4.6b

Counts

205 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
0.1b	(pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3)
2.6b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
2.9b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

147×	`times-frac`
137×	`*-un-lft-identity`
102×	`add-sqr-sqrt`
90×	`associate-r`
69×	`add-cube-cbrt`
22×	`distribute-lft-out`
14×	`add-exp-log` `add-cbrt-cube`
12×	`cbrt-prod` `distribute-lft-out--` `difference-of-squares`
10×	`flip3-+` `associate-/r/` `flip-+`
7×	`pow1`
6×	`unpow-prod-down` `cube-prod` `add-log-exp`
5×	`div-inv`
4×	`cube-div` `associate-l`
3×	`cbrt-undiv` `pow-unpow` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`cube-mult` `frac-times` `cbrt-div` `unpow3` `associate-*l/` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `pow-pow` `pow1/3` `associate-r/` `pow-prod-down` `pow-exp` `sum-log` `-commutative` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 176

Calls

4 calls:

30.0ms	(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
26.0ms	(pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3)
39.0ms	(* (+ 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)

series445.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
221.0ms	(pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3)
61.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
82.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify53.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	973	3074
1	5001	2918

prune363.0ms

Filtered

188 candidates to 118 candidates (37.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	181	7	188
Fresh	5	2	7
Picked	1	0	1
Done	1	0	1
Total	188	9	197

Merged error: 4.6b

Counts

197 → 9

regimes373.0ms

Accuracy

16.9% (5.3b remaining)

Error of 11.2b against oracle of 6.0b and baseline of 12.3b

bsearch84.0ms

Steps

Iters	Range		Point
7	1.6557086241677143e+164	2.6633017381366873e+166	3.8590915361436717e+164
7	1.232128251842175e+109	2.9427459472680538e+110	1.521975336450981e+109
8	6.729357461929106e+84	8.30500387155405e+87	8.144745728199273e+87

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	72	88
1	72	88

end0.0ms

sample1.2s

Algorithm

intervals

Results

344.0ms	6361×	body	80	valid
162.0ms	8000×	pre	80	true
145.0ms	533×	body	1280	valid
124.0ms	576×	body	640	valid
55.0ms	337×	body	320	valid
21.0ms	193×	body	160	valid

Details

sample48.0ms

simplify50.0ms

prune4.0ms

localize12.0ms

rewrite67.0ms

series164.0ms

simplify88.0ms

prune248.0ms

localize13.0ms

rewrite115.0ms

series196.0ms

simplify71.0ms

prune585.0ms

localize16.0ms

rewrite109.0ms

series246.0ms

simplify49.0ms

prune408.0ms

localize15.0ms

rewrite129.0ms

series445.0ms

simplify53.0ms

prune363.0ms

regimes373.0ms

bsearch84.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling