Details

sample293.0ms

Algorithm

intervals

Results

12.0ms	256×	body	80	valid
6.0ms	249×	body	80	nan

simplify13.0ms

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 3 expressions with local error:

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

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

64×	`*-un-lft-identity`
45×	`add-sqr-sqrt`
41×	`times-frac`
26×	`sqrt-prod`
24×	`add-cube-cbrt`
11×	`distribute-lft-out`
9×	`distribute-lft-out--` `difference-of-squares`
5×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
4×	`pow1` `associate-/r*` `associate-/r/`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `flip3-+` `flip-+` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num` `flip--`

Counts

3 → 97

Calls

3 calls:

8.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
10.0ms	(/ (- 1.0 x) (+ 1.0 x))
1.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

series153.0ms

Counts

3 → 9

Calls

3 calls:

92.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
51.0ms	(/ (- 1.0 x) (+ 1.0 x))
9.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

simplify43.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	370	779
1	1128	734
2	5001	719

prune235.0ms

Filtered

106 candidates to 76 candidates (71.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	104	2	106
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	105	2	107

Merged error: 0b

Counts

107 → 2

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (expm1 (/ (- 1.0 x) (+ 1.0 x))))
0.0b	(atan (sqrt (log1p (expm1 (/ (- 1.0 x) (+ 1.0 x))))))
0.0b	(/ (- 1.0 x) (+ 1.0 x))
1.0b	(expm1 (/ (- 1.0 x) (+ 1.0 x)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

1.0ms	(log1p (expm1 (/ (- 1.0 x) (+ 1.0 x))))
1.0ms	(atan (sqrt (log1p (expm1 (/ (- 1.0 x) (+ 1.0 x))))))
8.0ms	(/ (- 1.0 x) (+ 1.0 x))
1.0ms	(expm1 (/ (- 1.0 x) (+ 1.0 x)))

series281.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(log1p (expm1 (/ (- 1.0 x) (+ 1.0 x))))
2.0ms	(atan (sqrt (log1p (expm1 (/ (- 1.0 x) (+ 1.0 x))))))
37.0ms	(/ (- 1.0 x) (+ 1.0 x))
106.0ms	(expm1 (/ (- 1.0 x) (+ 1.0 x)))

simplify115.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 3 (107.0ms)

Iter	Nodes	Cost
0	316	598
1	910	550
2	3904	543
3	5001	537

prune236.0ms

Filtered

91 candidates to 69 candidates (75.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	91	2	93

Merged error: 0b

Counts

93 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))
0.0b	(/ (/ (- 1.0 x) (* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))) (cbrt (+ 1.0 x)))
0.0b	(/ (- 1.0 x) (* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x))))
1.0b	(expm1 (/ (/ (- 1.0 x) (* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))) (cbrt (+ 1.0 x))))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

164×	`times-frac`
136×	`*-un-lft-identity`
122×	`cbrt-div`
96×	`cbrt-prod`
94×	`add-sqr-sqrt`
74×	`associate-/r/`
66×	`add-cube-cbrt`
61×	`flip3-+` `flip-+`
40×	`frac-times`
24×	`distribute-lft-out`
22×	`associate-/l*`
20×	`add-exp-log` `associate-r/` `associate-l/`
11×	`pow1` `add-cbrt-cube`
10×	`div-inv` `distribute-lft-out--` `difference-of-squares`
9×	`swap-sqr`
8×	`associate-/r*`
7×	`cbrt-undiv` `div-exp` `associate-r` `associate-l`
6×	`pow1/3`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `add-log-exp` `unswap-sqr`
3×	`div-sub` `prod-exp` `cbrt-unprod` `associate-/l/`
2×	`frac-2neg` `pow-prod-down` `clear-num` `pow-sqr` `pow-prod-up`
1×	`pow2` `expm1-log1p` `flip3--` `pow-plus` `*-commutative` `flip--` `expm1-udef`

Counts

4 → 269

Calls

4 calls:

11.0ms	(* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))
21.0ms	(/ (/ (- 1.0 x) (* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))) (cbrt (+ 1.0 x)))
14.0ms	(/ (- 1.0 x) (* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x))))
1.0ms	(expm1 (/ (/ (- 1.0 x) (* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))) (cbrt (+ 1.0 x))))

series390.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))
37.0ms	(/ (/ (- 1.0 x) (* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))) (cbrt (+ 1.0 x)))
138.0ms	(/ (- 1.0 x) (* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x))))
110.0ms	(expm1 (/ (/ (- 1.0 x) (* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))) (cbrt (+ 1.0 x))))

simplify129.0ms

Algorithm

egg-herbie

Counts

281 → 281

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	988	4050
1	4188	3846
2	5001	3695

prune825.0ms

Filtered

281 candidates to 177 candidates (63.0%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	281	0	281
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	281	2	283

Merged error: 0b

Counts

283 → 2

regimes29.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	8
1	13	8

end0.0ms

sample723.0ms

Algorithm

intervals

Results

318.0ms	8000×	body	80	valid
206.0ms	8139×	body	80	nan