Details

sample282.0ms

Algorithm

intervals

Results

13.0ms	256×	body	80	valid
10.0ms	235×	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 2 expressions with local error:

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

rewrite14.0ms

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` `associate-/r/` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-sub` `div-exp` `clear-num` `flip--` `flip-+` `div-inv`

Counts

2 → 53

Calls

2 calls:

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

series59.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(/ (- 1.0 x) (+ 1.0 x))
9.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

simplify95.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	233	384
1	688	359
2	3022	356
3	5002	356

prune108.0ms

Filtered

59 candidates to 42 candidates (71.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	56	3	59
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	56	4	60

Merged error: 0b

Counts

60 → 4

localize11.0ms

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))

rewrite41.0ms

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×	`associate-/r*` `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 → 193

Calls

4 calls:

8.0ms	(/ (- 1.0 x) (+ x 1.0))
1.0ms	(atan (sqrt (cbrt (pow (/ (- 1.0 x) (+ x 1.0)) 3))))
9.0ms	(pow (/ (- 1.0 x) (+ x 1.0)) 3)
13.0ms	(cbrt (pow (/ (- 1.0 x) (+ x 1.0)) 3))

series132.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ (- 1.0 x) (+ x 1.0))
2.0ms	(atan (sqrt (cbrt (pow (/ (- 1.0 x) (+ x 1.0)) 3))))
60.0ms	(pow (/ (- 1.0 x) (+ x 1.0)) 3)
33.0ms	(cbrt (pow (/ (- 1.0 x) (+ x 1.0)) 3))

simplify75.0ms

Algorithm

egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	580	1553
1	2518	1443
2	5002	1425

prune276.0ms

Filtered

205 candidates to 93 candidates (45.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	205	0	205
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	205	4	209

Merged error: 0b

Counts

209 → 4

localize11.0ms

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)

rewrite16.0ms

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×	`associate-/r*` `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 → 97

Calls

4 calls:

1.0ms	(atan (sqrt (/ (- 1.0 x) (+ x 1.0))))
7.0ms	(/ (- 1.0 x) (+ x 1.0))
2.0ms	(cbrt (pow (atan (sqrt (/ (- 1.0 x) (+ x 1.0)))) 3))
2.0ms	(pow (atan (sqrt (/ (- 1.0 x) (+ x 1.0)))) 3)

series73.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan (sqrt (/ (- 1.0 x) (+ x 1.0))))
35.0ms	(/ (- 1.0 x) (+ x 1.0))
2.0ms	(cbrt (pow (atan (sqrt (/ (- 1.0 x) (+ x 1.0)))) 3))
33.0ms	(pow (atan (sqrt (/ (- 1.0 x) (+ x 1.0)))) 3)

simplify42.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	306	810
1	1133	765
2	5001	755

prune184.0ms

Filtered

109 candidates to 63 candidates (57.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	109	4	113

Merged error: 0b

Counts

113 → 4

localize12.0ms

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))))))

rewrite15.0ms

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×	`associate-/r*` `log-pow`
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 → 79

Calls

4 calls:

2.0ms	(exp (atan (sqrt (/ (- 1.0 x) (+ 1.0 x)))))
1.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
8.0ms	(/ (- 1.0 x) (+ 1.0 x))
2.0ms	(log (exp (atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))))

series69.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(exp (atan (sqrt (/ (- 1.0 x) (+ 1.0 x)))))
2.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
31.0ms	(/ (- 1.0 x) (+ 1.0 x))
2.0ms	(log (exp (atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))))

simplify93.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	266	635
1	742	579
2	3105	576
3	5001	576

prune169.0ms

Filtered

91 candidates to 62 candidates (68.1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	91	4	95

Merged error: 0b

Counts

95 → 4

regimes93.0ms

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

sample887.0ms

Algorithm

intervals

Results

394.0ms	8000×	body	80	valid
286.0ms	8031×	body	80	nan