Details

sample287.0ms

Algorithm

intervals

Results

13.0ms	256×	body	80	valid
10.0ms	235×	body	80	nan

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	6
1	19	6
2	21	6
3	21	6

prune4.0ms

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: 0.0b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- 1.0 x) (+ 1.0 x))
0.0b	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
20×	`times-frac`
13×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
2×	`pow1` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-sub` `div-exp` `clear-num` `flip--` `flip-+` `div-inv`

Counts

2 → 57

Calls

2 calls:

10.0ms	(/ (- 1.0 x) (+ 1.0 x))
1.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

series63.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(/ (- 1.0 x) (+ 1.0 x))
9.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

simplify102.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (94.0ms)

Iter	Nodes	Cost
0	242	403
1	723	377
2	3210	375
3	5001	372

prune124.0ms

Filtered

63 candidates to 46 candidates (73.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	60	3	63
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	60	4	64

Merged error: 0b

Counts

64 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- 1.0 x) (+ x 1.0))
0.0b	(atan (sqrt (cbrt (pow (/ (- 1.0 x) (+ x 1.0)) 3))))
0.0b	(pow (/ (- 1.0 x) (+ x 1.0)) 3)
0.0b	(cbrt (pow (/ (- 1.0 x) (+ x 1.0)) 3))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

151×	`*-un-lft-identity`
100×	`times-frac`
99×	`add-sqr-sqrt`
58×	`cbrt-prod`
57×	`add-cube-cbrt`
52×	`unpow-prod-down` `cube-prod`
26×	`distribute-lft-out`
21×	`distribute-lft-out--` `difference-of-squares`
10×	`associate-/r/`
9×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3-+` `flip-+` `div-inv` `associate-/l*`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`cbrt-undiv` `cube-div` `cube-mult` `unpow3` `div-exp` `pow-exp` `associate-/l/` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `cbrt-div` `flip3--` `pow-pow` `frac-2neg` `pow1/3` `div-sub` `clear-num` `flip--` `rem-cbrt-cube`

Counts

4 → 201

Calls

4 calls:

9.0ms	(/ (- 1.0 x) (+ x 1.0))
1.0ms	(atan (sqrt (cbrt (pow (/ (- 1.0 x) (+ x 1.0)) 3))))
10.0ms	(pow (/ (- 1.0 x) (+ x 1.0)) 3)
12.0ms	(cbrt (pow (/ (- 1.0 x) (+ x 1.0)) 3))

series142.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ (- 1.0 x) (+ x 1.0))
2.0ms	(atan (sqrt (cbrt (pow (/ (- 1.0 x) (+ x 1.0)) 3))))
61.0ms	(pow (/ (- 1.0 x) (+ x 1.0)) 3)
41.0ms	(cbrt (pow (/ (- 1.0 x) (+ x 1.0)) 3))

simplify80.0ms

Algorithm

egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	597	1594
1	2575	1477
2	5002	1459

prune306.0ms

Filtered

213 candidates to 101 candidates (47.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	213	0	213
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	213	4	217

Merged error: 0b

Counts

217 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan (sqrt (/ (- 1.0 x) (+ x 1.0))))
0.0b	(/ (- 1.0 x) (+ x 1.0))
0.0b	(cbrt (pow (atan (sqrt (/ (- 1.0 x) (+ x 1.0)))) 3))
1.0b	(pow (atan (sqrt (/ (- 1.0 x) (+ x 1.0)))) 3)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity`
31×	`add-sqr-sqrt`
21×	`add-cube-cbrt`
20×	`times-frac`
12×	`cbrt-prod`
7×	`add-exp-log` `add-cbrt-cube`
6×	`unpow-prod-down` `cube-prod` `distribute-lft-out`
5×	`pow1` `associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`cube-mult` `unpow3` `associate-/r/` `associate-/l/` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `flip3--` `pow-pow` `frac-2neg` `flip3-+` `pow1/3` `div-sub` `div-exp` `pow-exp` `clear-num` `flip--` `rem-cbrt-cube` `flip-+` `div-inv` `rem-cube-cbrt`

Counts

4 → 105

Calls

4 calls:

1.0ms	(atan (sqrt (/ (- 1.0 x) (+ x 1.0))))
9.0ms	(/ (- 1.0 x) (+ x 1.0))
2.0ms	(cbrt (pow (atan (sqrt (/ (- 1.0 x) (+ x 1.0)))) 3))
3.0ms	(pow (atan (sqrt (/ (- 1.0 x) (+ x 1.0)))) 3)

series75.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan (sqrt (/ (- 1.0 x) (+ x 1.0))))
34.0ms	(/ (- 1.0 x) (+ x 1.0))
2.0ms	(cbrt (pow (atan (sqrt (/ (- 1.0 x) (+ x 1.0)))) 3))
37.0ms	(pow (atan (sqrt (/ (- 1.0 x) (+ x 1.0)))) 3)

simplify49.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	319	855
1	1176	809
2	5001	800

prune214.0ms

Filtered

117 candidates to 71 candidates (60.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	117	4	121

Merged error: 0b

Counts

121 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (atan (sqrt (/ (- 1.0 x) (+ 1.0 x)))))
0.0b	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
0.0b	(/ (- 1.0 x) (+ 1.0 x))
1.0b	(log (exp (atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

40×	`*-un-lft-identity`
28×	`add-sqr-sqrt`
20×	`times-frac`
18×	`add-cube-cbrt`
6×	`add-exp-log` `exp-prod` `add-cbrt-cube` `distribute-lft-out`
5×	`pow1` `associate-/l*` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
4×	`expm1-log1p-u` `associate-/r*` `log-pow` `log1p-expm1-u`
3×	`log-prod`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-sub` `div-exp` `rem-log-exp` `clear-num` `flip--` `flip-+` `div-inv` `rem-exp-log`

Counts

4 → 87

Calls

4 calls:

2.0ms	(exp (atan (sqrt (/ (- 1.0 x) (+ 1.0 x)))))
1.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
9.0ms	(/ (- 1.0 x) (+ 1.0 x))
2.0ms	(log (exp (atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))))

series75.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(exp (atan (sqrt (/ (- 1.0 x) (+ 1.0 x)))))
2.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
35.0ms	(/ (- 1.0 x) (+ 1.0 x))
2.0ms	(log (exp (atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))))

simplify99.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 3 (90.0ms)

Iter	Nodes	Cost
0	279	680
1	781	623
2	3298	621
3	5001	618

prune200.0ms

Filtered

99 candidates to 70 candidates (70.7%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	99	4	103

Merged error: 0b

Counts

103 → 4

regimes94.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	6
1	11	6

end0.0ms

sample874.0ms

Algorithm

intervals

Results

385.0ms	8000×	body	80	valid
276.0ms	8031×	body	80	nan