Details

sample36.0ms

Algorithm

intervals

Results

8.0ms	210×	body	80	valid
4.0ms	256×	pre	80	true
3.0ms	14×	body	1280	valid
3.0ms	16×	body	640	valid
1.0ms	10×	body	320	valid
0.0ms	6×	body	160	valid

simplify53.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	14
1	107	14
2	479	14
3	2315	14
4	5002	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: 23.0b

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))

2.0b

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

19.3b

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

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

102×	`times-frac`
83×	`*-un-lft-identity`
43×	`add-sqr-sqrt` `add-cube-cbrt`
42×	`fma-def`
24×	`associate-/r/`
20×	`distribute-lft-out`
17×	`add-exp-log` `add-cbrt-cube`
16×	`flip3-+` `flip-+`
12×	`div-inv`
10×	`associate-/l*`
9×	`associate-/l/`
7×	`cbrt-undiv` `div-exp` `associate-/r*`
5×	`add-log-exp`
4×	`frac-times`
3×	`pow1` `expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
2×	`frac-2neg` `associate-r/` `associate-l/` `prod-exp` `clear-num` `cbrt-unprod`
1×	`+-commutative` `sum-log`

Counts

3 → 159

Calls

3 calls:

20.0ms

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

36.0ms

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

15.0ms

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

series585.0ms

Counts

3 → 9

Calls

3 calls:

229.0ms

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

275.0ms

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

simplify99.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	701	1971
1	3740	1800
2	5001	1782

prune479.0ms

Filtered

168 candidates to 131 candidates (78.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	162	6	168
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	163	6	169

Merged error: 4.4b

Counts

169 → 6

localize19.0ms

Local error

Found 3 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))

10.8b

(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

174×	`times-frac`
162×	`*-un-lft-identity`
118×	`add-sqr-sqrt`
80×	`add-cube-cbrt`
26×	`associate-/l*`
22×	`distribute-lft-out`
19×	`distribute-lft-out--` `difference-of-squares`
14×	`associate-/r/`
10×	`add-exp-log` `add-cbrt-cube`
7×	`flip3-+` `associate-/r*` `flip-+` `div-inv`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `div-sub` `log1p-expm1-u` `associate-/l/` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`flip3--` `flip--` `fma-udef`

Counts

3 → 181

Calls

3 calls:

10.0ms

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

20.0ms

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

1.0ms

(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series502.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms

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

161.0ms

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

264.0ms

(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify97.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	727	3112
1	3259	2892
2	5002	2876

prune509.0ms

Filtered

190 candidates to 135 candidates (71.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	187	3	190
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	189	7	196

Merged error: 4.4b

Counts

196 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.3b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.4b	(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
10.8b	(fma (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

490×	`times-frac`
410×	`*-un-lft-identity`
284×	`add-sqr-sqrt`
228×	`add-cube-cbrt`
156×	`sqrt-prod`
63×	`distribute-lft-out`
42×	`associate-/l*`
28×	`distribute-lft-out--` `difference-of-squares`
22×	`associate-/r/`
19×	`div-inv`
18×	`add-exp-log`
17×	`associate-/r*`
16×	`add-cbrt-cube`
11×	`flip3-+` `flip-+`
9×	`div-exp`
7×	`cbrt-undiv`
4×	`pow1` `expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `associate-/l/` `add-log-exp`
3×	`frac-2neg` `div-sub` `clear-num`
1×	`flip3--` `1-exp` `flip--` `fma-udef`

Counts

4 → 402

Calls

4 calls:

11.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
27.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
17.0ms	(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
1.0ms	(fma (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series820.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
366.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
136.0ms	(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
241.0ms	(fma (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify102.0ms

Algorithm

egg-herbie

Counts

414 → 414

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1283	7520
1	5002	6956

prune842.0ms

Filtered

414 candidates to 212 candidates (51.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	410	4	414
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	411	10	421

Merged error: 4.4b

Counts

421 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.2b	(exp (log (fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)))
3.0b	(log (fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0))
10.8b	(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

159×	`times-frac`
148×	`*-un-lft-identity`
104×	`add-sqr-sqrt`
74×	`add-cube-cbrt`
22×	`distribute-lft-out`
21×	`associate-/l*`
15×	`distribute-lft-out--` `difference-of-squares`
12×	`associate-/r/`
10×	`add-exp-log`
9×	`add-cbrt-cube`
6×	`pow1` `log-prod` `flip3-+` `flip-+` `div-inv`
4×	`expm1-log1p-u` `exp-prod` `associate-/r*` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `exp-sum`
2×	`div-sub` `log-pow`
1×	`frac-2neg` `rem-log-exp` `clear-num` `fma-udef` `rem-exp-log` `associate-/l/`

Counts

4 → 170

Calls

4 calls:

20.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
2.0ms	(exp (log (fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)))
1.0ms	(log (fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0))
1.0ms	(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series951.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
269.0ms	(exp (log (fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)))
264.0ms	(log (fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0))
263.0ms	(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify103.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	784	3403
1	3366	3119
2	5001	3055

prune537.0ms

Filtered

182 candidates to 129 candidates (70.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	179	3	182
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	183	9	192

Merged error: 2.4b

Counts

192 → 9

regimes194.0ms

Accuracy

14.8% (7.5b remaining)

Error of 11.5b against oracle of 4.0b and baseline of 12.8b

bsearch46.0ms

Steps

Iters	Range		Point
5	8.588642662975345e+117	2.204604034550096e+118	2.1607929032396156e+118

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	28
1	45	28
2	45	28

end0.0ms

sample847.0ms

Algorithm

intervals

Results

253.0ms	6331×	body	80	valid
124.0ms	8000×	pre	80	true
112.0ms	513×	body	1280	valid
96.0ms	585×	body	640	valid
44.0ms	365×	body	320	valid
17.0ms	206×	body	160	valid