Details

sample24.0ms

Algorithm

intervals

Results

4.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true
4.0ms	248×	pre	80	false

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	3
1	12	3
2	12	3

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: 8.2b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

1.0b	(/ x0 (- 1.0 x1))
7.3b	(- (/ x0 (- 1.0 x1)) x0)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
16×	`times-frac`
12×	`add-cube-cbrt`
6×	`difference-of-squares`
5×	`associate-/r*` `distribute-lft-out--`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/l*`
2×	`pow1` `flip3--` `associate-/r/` `flip--`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

2 → 52

Calls

2 calls:

9.0ms	(/ x0 (- 1.0 x1))
12.0ms	(- (/ x0 (- 1.0 x1)) x0)

series80.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(/ x0 (- 1.0 x1))
45.0ms	(- (/ x0 (- 1.0 x1)) x0)

simplify96.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	244	328
1	801	315
2	3123	310
3	5001	310

prune86.0ms

Filtered

58 candidates to 44 candidates (75.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	56	2	58
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	57	2	59

Merged error: 7.1b

Counts

59 → 2

localize9.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (+ (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)) (- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)))
1.0b	(/ x0 (- 1.0 x1))
1.0b	(/ x0 (- 1.0 x1))
6.8b	(- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 134

Calls

4 calls:

39.0ms	(* (+ (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)) (- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)))
6.0ms	(/ x0 (- 1.0 x1))
6.0ms	(/ x0 (- 1.0 x1))
17.0ms	(- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0))

series319.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(* (+ (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)) (- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)))
35.0ms	(/ x0 (- 1.0 x1))
35.0ms	(/ x0 (- 1.0 x1))
70.0ms	(- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0))

simplify64.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	459	1265
1	2078	1135
2	5001	1115

prune299.0ms

Filtered

146 candidates to 104 candidates (71.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	144	2	146
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	146	2	148

Merged error: 5.7b

Counts

148 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ x0 (- 1.0 x1))
1.0b	(/ x0 (- 1.0 x1))
1.0b	(* (+ (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)) (/ (- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3)) (+ (+ (/ x0 (- 1.0 x1)) x0) (* (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)))))
5.7b	(- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3))

rewrite247.0ms

Algorithm

rewrite-expression-head

Rules

487×	`add-sqr-sqrt`
262×	`times-frac`
200×	`difference-of-squares`
194×	`sqrt-prod`
191×	`associate-r`
182×	`*-un-lft-identity`
168×	`unpow-prod-down` `cube-prod`
90×	`add-cube-cbrt`
56×	`sqr-pow`
44×	`distribute-lft-out--`
13×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r*`
8×	`associate-/r/`
6×	`pow1` `associate-/l*` `add-log-exp`
5×	`associate-l`
4×	`difference-cubes` `flip3-+` `associate-*l/` `flip-+`
3×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `div-inv`
2×	`frac-times` `frac-2neg` `sqrt-div` `frac-add` `prod-exp` `clear-num` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`
1×	`sub-neg` `diff-log` `associate-r/` `pow-prod-down` `-commutative`

Counts

4 → 360

Calls

4 calls:

6.0ms	(/ x0 (- 1.0 x1))
6.0ms	(/ x0 (- 1.0 x1))
140.0ms	(* (+ (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)) (/ (- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3)) (+ (+ (/ x0 (- 1.0 x1)) x0) (* (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)))))
59.0ms	(- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3))

series791.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ x0 (- 1.0 x1))
35.0ms	(/ x0 (- 1.0 x1))
604.0ms	(* (+ (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)) (/ (- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3)) (+ (+ (/ x0 (- 1.0 x1)) x0) (* (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)))))
116.0ms	(- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3))

simplify92.0ms

Algorithm

egg-herbie

Counts

372 → 372

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1062	7081
1	5002	6848

prune697.0ms

Filtered

372 candidates to 163 candidates (43.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	371	1	372
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	372	2	374

Merged error: 4.9b

Counts

374 → 2

localize20.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ x0 (- 1.0 x1))
1.0b	(* (+ (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)) (/ (- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3)) (+ (+ (/ x0 (- 1.0 x1)) x0) (* (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)))))
5.7b	(- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3))
5.7b	(log (exp (* (+ (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)) (/ (- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3)) (+ (+ (/ x0 (- 1.0 x1)) x0) (* (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)))))))

rewrite251.0ms

Algorithm

rewrite-expression-head

Rules

470×	`add-sqr-sqrt`
247×	`times-frac`
196×	`difference-of-squares`
194×	`sqrt-prod`
191×	`associate-r`
168×	`unpow-prod-down` `cube-prod`
165×	`*-un-lft-identity`
81×	`add-cube-cbrt`
56×	`sqr-pow`
40×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
9×	`add-log-exp`
7×	`pow1`
6×	`associate-/r/`
5×	`associate-l` `associate-/r*`
4×	`difference-cubes` `flip3-+` `associate-*l/` `log-pow` `flip-+`
3×	`log-prod` `associate-/l*`
2×	`cbrt-undiv` `frac-times` `flip3--` `exp-to-pow` `sqrt-div` `div-exp` `frac-add` `prod-exp` `flip--` `cbrt-unprod` `div-inv` `distribute-lft-out` `unswap-sqr`
1×	`sub-neg` `exp-prod` `frac-2neg` `diff-log` `associate-r/` `rem-log-exp` `pow-prod-down` `clear-num` `sum-log` `-commutative`

Counts

4 → 338

Calls

4 calls:

6.0ms	(/ x0 (- 1.0 x1))
135.0ms	(* (+ (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)) (/ (- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3)) (+ (+ (/ x0 (- 1.0 x1)) x0) (* (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)))))
56.0ms	(- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3))
19.0ms	(log (exp (* (+ (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)) (/ (- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3)) (+ (+ (/ x0 (- 1.0 x1)) x0) (* (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)))))))

series1.4s

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ x0 (- 1.0 x1))
600.0ms	(* (+ (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)) (/ (- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3)) (+ (+ (/ x0 (- 1.0 x1)) x0) (* (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)))))
116.0ms	(- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3))
609.0ms	(log (exp (* (+ (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)) (/ (- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3)) (+ (+ (/ x0 (- 1.0 x1)) x0) (* (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)))))))

simplify92.0ms

Algorithm

egg-herbie

Counts

350 → 350

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1088	7367
1	5002	7059

prune733.0ms

Filtered

350 candidates to 148 candidates (42.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	350	0	350
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	350	2	352

Merged error: 4.9b

Counts

352 → 2

regimes54.0ms

Accuracy

100% (0.0b remaining)

Error of 5.1b against oracle of 5.1b and baseline of 7.0b

bsearch38.0ms

Steps

Iters	Range		Point
7	0.000209	0.0186	0.018204597656249998

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	53
1	36	53

end0.0ms

sample616.0ms

Algorithm

intervals

Results

128.0ms	8000×	body	80	valid
121.0ms	8000×	pre	80	true
120.0ms	8053×	pre	80	false