Details

sample41.0ms

Algorithm

intervals

Results

12.0ms	197×	body	80	valid
6.0ms	256×	pre	80	true
4.0ms	17×	body	1280	valid
4.0ms	20×	body	640	valid
2.0ms	13×	body	320	valid
1.0ms	9×	body	160	valid

simplify54.0ms

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

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: 26.5b

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))

2.3b

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

22.1b

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

rewrite69.0ms

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:

22.0ms

(/ (/ (* (+ 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)

13.0ms

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

series581.0ms

Counts

3 → 9

Calls

3 calls:

224.0ms

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

273.0ms

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

84.0ms

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

simplify100.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 1 (17.0ms)

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: 7.1b

Counts

121 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
0.3b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.4b	(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
6.1b	(+ (* (/ (+ alpha beta) (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)

rewrite220.0ms

Algorithm

rewrite-expression-head

Rules

603×	`times-frac`
484×	`*-un-lft-identity`
408×	`add-sqr-sqrt`
260×	`add-cube-cbrt`
219×	`sqrt-prod`
153×	`associate-r`
67×	`distribute-lft-out`
45×	`distribute-lft-out--` `difference-of-squares`
38×	`associate-/r/`
34×	`associate-l`
32×	`add-exp-log` `add-cbrt-cube`
25×	`associate-/l*`
21×	`flip3-+` `flip-+`
19×	`div-inv`
15×	`unswap-sqr`
14×	`associate-/r*`
13×	`cbrt-undiv` `div-exp`
8×	`sqrt-div`
6×	`pow1` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`associate-/l/`
2×	`frac-2neg` `div-sub` `clear-num`
1×	`+-commutative` `frac-times` `associate-r/` `pow-prod-down` `associate-l/` `sum-log` `*-commutative`

Counts

4 → 485

Calls

4 calls:

110.0ms	(* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
21.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
13.0ms	(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
42.0ms	(+ (* (/ (+ alpha beta) (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)

series867.0ms

Counts

4 → 12

Calls

4 calls:

227.0ms	(* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
224.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
135.0ms	(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
281.0ms	(+ (* (/ (+ alpha beta) (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)

simplify131.0ms

Algorithm

egg-herbie

Counts

497 → 497

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	1727	10548
1	5001	10067

prune1.0s

Filtered

497 candidates to 254 candidates (51.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	492	5	497
Fresh	7	4	11
Picked	1	0	1
Done	0	0	0
Total	500	9	509

Merged error: 7.1b

Counts

509 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
0.3b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.4b	(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
6.1b	(+ (* (/ (+ alpha beta) (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)

rewrite224.0ms

Algorithm

rewrite-expression-head

Rules

603×	`times-frac`
484×	`*-un-lft-identity`
408×	`add-sqr-sqrt`
260×	`add-cube-cbrt`
219×	`sqrt-prod`
153×	`associate-r`
67×	`distribute-lft-out`
45×	`distribute-lft-out--` `difference-of-squares`
38×	`associate-/r/`
34×	`associate-l`
32×	`add-exp-log` `add-cbrt-cube`
25×	`associate-/l*`
21×	`flip3-+` `flip-+`
19×	`div-inv`
15×	`unswap-sqr`
14×	`associate-/r*`
13×	`cbrt-undiv` `div-exp`
8×	`sqrt-div`
6×	`pow1` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`associate-/l/`
2×	`frac-2neg` `div-sub` `clear-num`
1×	`+-commutative` `frac-times` `associate-r/` `pow-prod-down` `associate-l/` `sum-log` `*-commutative`

Counts

4 → 485

Calls

4 calls:

111.0ms	(* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
22.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
13.0ms	(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
43.0ms	(+ (* (/ (+ alpha beta) (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)

series1.1s

Counts

4 → 12

Calls

4 calls:

224.0ms	(* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
431.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
141.0ms	(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
279.0ms	(+ (* (/ (+ alpha beta) (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)

simplify131.0ms

Algorithm

egg-herbie

Counts

497 → 497

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	1727	10548
1	5001	10067

prune1.2s

Filtered

497 candidates to 256 candidates (51.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	489	8	497
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	495	11	506

Merged error: 7.1b

Counts

506 → 11

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.4b	(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
6.1b	(+ (* (/ (+ alpha beta) (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)
6.2b	(log (exp (+ (* (/ (+ alpha beta) (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)))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

295×	`times-frac`
258×	`*-un-lft-identity`
188×	`add-sqr-sqrt`
140×	`add-cube-cbrt`
108×	`sqrt-prod`
35×	`distribute-lft-out`
25×	`associate-/l*`
24×	`distribute-lft-out--` `difference-of-squares`
20×	`associate-/r/`
14×	`associate-/r*`
12×	`flip3-+` `flip-+`
11×	`add-exp-log` `add-cbrt-cube`
10×	`div-inv`
6×	`add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `log-prod` `sqrt-div` `div-exp` `log-pow`
3×	`exp-prod` `associate-/l/`
2×	`frac-2neg` `div-sub` `clear-num`
1×	`+-commutative` `rem-log-exp` `exp-sum` `sum-log`

Counts

4 → 275

Calls

4 calls:

22.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
17.0ms	(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
39.0ms	(+ (* (/ (+ alpha beta) (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)
42.0ms	(log (exp (+ (* (/ (+ alpha beta) (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)))

series885.0ms

Counts

4 → 12

Calls

4 calls:

219.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
135.0ms	(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
264.0ms	(+ (* (/ (+ alpha beta) (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)
267.0ms	(log (exp (+ (* (/ (+ alpha beta) (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)))

simplify134.0ms

Algorithm

egg-herbie

Counts

287 → 287

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1063	5948
1	4521	5605
2	5001	5605

prune834.0ms

Filtered

287 candidates to 161 candidates (56.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	285	2	287
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	286	12	298

Merged error: 7.1b

Counts

298 → 12

regimes349.0ms

Accuracy

77.1% (1.5b remaining)

Error of 7.3b against oracle of 5.8b and baseline of 12.4b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	46
1	54	46

end0.0ms

sample957.0ms

Algorithm

intervals

Results

290.0ms	6356×	body	80	valid
174.0ms	8000×	pre	80	true
126.0ms	542×	body	1280	valid
110.0ms	588×	body	640	valid
45.0ms	335×	body	320	valid
16.0ms	179×	body	160	valid

Details

sample41.0ms

simplify54.0ms

prune2.0ms

localize12.0ms

rewrite69.0ms

series581.0ms

simplify100.0ms

prune336.0ms

localize15.0ms

rewrite220.0ms

series867.0ms

simplify131.0ms

prune1.0s

localize18.0ms

rewrite224.0ms

series1.1s

simplify131.0ms

prune1.2s

localize22.0ms

rewrite135.0ms

series885.0ms

simplify134.0ms

prune834.0ms

regimes349.0ms

bsearch2.0ms

simplify2.0ms

end0.0ms

sample957.0ms

Profiling