Details

sample28.0ms

Algorithm

intervals

Results

8.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true
4.0ms	251×	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

prune1.0ms

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: 8.0b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

1.0b	(/ x0 (- 1.0 x1))
7.2b	(- (/ x0 (- 1.0 x1)) x0)

rewrite18.0ms

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:

5.0ms	(/ x0 (- 1.0 x1))
11.0ms	(- (/ x0 (- 1.0 x1)) x0)

series81.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(/ x0 (- 1.0 x1))
43.0ms	(- (/ x0 (- 1.0 x1)) x0)

simplify91.0ms

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

prune84.0ms

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: 7.0b

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))
6.7b	(- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0))

rewrite67.0ms

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:

33.0ms	(* (+ (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)) (- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)))
5.0ms	(/ x0 (- 1.0 x1))
5.0ms	(/ x0 (- 1.0 x1))
19.0ms	(- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0))

series321.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(* (+ (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)) (- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)))
39.0ms	(/ x0 (- 1.0 x1))
34.0ms	(/ x0 (- 1.0 x1))
68.0ms	(- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0))

simplify59.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (46.0ms)

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

prune296.0ms

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: 5.6b

Counts

148 → 2

localize26.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ x0 (- 1.0 x1))
1.0b	(* (+ (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3)) (- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3)))
1.0b	(+ (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3))
5.5b	(- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3))

rewrite248.0ms

Algorithm

rewrite-expression-head

Rules

214×	`add-sqr-sqrt`
112×	`sqrt-prod`
100×	`unpow-prod-down` `cube-prod` `difference-of-squares`
96×	`*-un-lft-identity`
61×	`associate-r`
39×	`times-frac`
28×	`sqr-pow`
22×	`distribute-lft-out--`
18×	`distribute-lft-out`
16×	`add-cube-cbrt`
13×	`associate-l`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1`
5×	`flip3--` `associate-/r*` `flip--`
4×	`frac-times` `flip3-+` `flip-+`
3×	`sub-neg` `associate-/l*`
2×	`difference-cubes` `distribute-rgt-in` `distribute-lft-in` `associate-r/` `associate-l/` `associate-/r/` `sum-cubes`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `diff-log` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `sum-log` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 226

Calls

4 calls:

6.0ms	(/ x0 (- 1.0 x1))
122.0ms	(* (+ (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3)) (- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3)))
51.0ms	(+ (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3))
51.0ms	(- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3))

series554.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ x0 (- 1.0 x1))
290.0ms	(* (+ (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3)) (- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3)))
110.0ms	(+ (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3))
115.0ms	(- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3))

simplify107.0ms

Algorithm

egg-herbie

Counts

238 → 238

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	682	3251
1	3200	3036
2	5001	2995

prune540.0ms

Filtered

238 candidates to 117 candidates (49.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	237	1	238
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	238	2	240

Merged error: 5.3b

Counts

240 → 2

localize42.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (pow (pow (sqrt (/ x0 (- 1.0 x1))) 3) 3) (pow (pow (sqrt x0) 3) 3))
1.3b	(pow (sqrt (/ x0 (- 1.0 x1))) 6)
1.3b	(pow (sqrt (/ x0 (- 1.0 x1))) 6)
5.7b	(- (pow (pow (sqrt (/ x0 (- 1.0 x1))) 3) 3) (pow (pow (sqrt x0) 3) 3))

rewrite422.0ms

Algorithm

rewrite-expression-head

Rules

560×	`unpow-prod-down`
512×	`cube-prod`
502×	`add-sqr-sqrt`
290×	`sqrt-prod`
258×	`difference-of-squares`
186×	`*-un-lft-identity`
98×	`sqr-pow`
86×	`times-frac`
43×	`distribute-lft-out--`
37×	`distribute-lft-out`
26×	`add-cube-cbrt`
8×	`pow1` `add-log-exp`
6×	`add-exp-log` `pow-unpow` `pow-pow`
4×	`associate-/r/` `add-cbrt-cube`
3×	`flip3--` `flip--`
2×	`pow-to-exp` `sqrt-pow1` `pow1/2` `pow-exp` `sqrt-pow2` `div-inv`
1×	`difference-cubes` `+-commutative` `sub-neg` `flip3-+` `diff-log` `sum-log` `sum-cubes` `flip-+`

Counts

4 → 433

Calls

4 calls:

182.0ms	(+ (pow (pow (sqrt (/ x0 (- 1.0 x1))) 3) 3) (pow (pow (sqrt x0) 3) 3))
8.0ms	(pow (sqrt (/ x0 (- 1.0 x1))) 6)
8.0ms	(pow (sqrt (/ x0 (- 1.0 x1))) 6)
188.0ms	(- (pow (pow (sqrt (/ x0 (- 1.0 x1))) 3) 3) (pow (pow (sqrt x0) 3) 3))

series441.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(+ (pow (pow (sqrt (/ x0 (- 1.0 x1))) 3) 3) (pow (pow (sqrt x0) 3) 3))
72.0ms	(pow (sqrt (/ x0 (- 1.0 x1))) 6)
73.0ms	(pow (sqrt (/ x0 (- 1.0 x1))) 6)
154.0ms	(- (pow (pow (sqrt (/ x0 (- 1.0 x1))) 3) 3) (pow (pow (sqrt x0) 3) 3))

simplify141.0ms

Algorithm

egg-herbie

Counts

445 → 445

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	774	7330
1	2659	7168
2	5002	6934

prune900.0ms

Filtered

445 candidates to 115 candidates (25.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	444	1	445
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	445	2	447

Merged error: 3.9b

Counts

447 → 2

regimes73.0ms

Accuracy

100% (0.0b remaining)

Error of 4.3b against oracle of 4.3b and baseline of 6.0b

bsearch1.0ms

Steps

Iters	Range		Point
0	0.9814	0.999791	0.9905955

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	112
1	65	112

end0.0ms

sample610.0ms

Algorithm

intervals

Results

128.0ms	8000×	body	80	valid
124.0ms	8000×	pre	80	true
124.0ms	8060×	pre	80	false