Details

sample277.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
8.0ms	274×	body	80	nan

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

localize11.0ms

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×	`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 → 91

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))))

series152.0ms

Counts

3 → 9

Calls

3 calls:

93.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
50.0ms	(/ (- 1.0 x) (+ 1.0 x))
9.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

simplify41.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	354	753
1	1071	709
2	5001	690

prune219.0ms

Filtered

100 candidates to 70 candidates (70.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	99	2	101

Merged error: 0b

Counts

101 → 2

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 x))
0.0b	(sqrt (+ 1.0 x))
0.0b	(atan (sqrt (* (/ 1 (sqrt (+ 1.0 x))) (/ (- 1.0 x) (sqrt (+ 1.0 x))))))
0.0b	(* (/ 1 (sqrt (+ 1.0 x))) (/ (- 1.0 x) (sqrt (+ 1.0 x))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

100×	`add-sqr-sqrt`
78×	`*-un-lft-identity` `times-frac`
51×	`sqrt-prod`
41×	`associate-r`
38×	`add-cube-cbrt`
27×	`associate-l`
26×	`add-exp-log`
16×	`add-cbrt-cube`
15×	`unswap-sqr`
10×	`distribute-lft-out`
8×	`pow1` `sqrt-div` `div-exp` `prod-exp`
7×	`distribute-lft-out--` `difference-of-squares`
4×	`cbrt-undiv` `flip3-+` `associate-/r/` `cbrt-unprod` `flip-+` `add-log-exp`
2×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `div-inv`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 146

Calls

4 calls:

3.0ms	(sqrt (+ 1.0 x))
3.0ms	(sqrt (+ 1.0 x))
1.0ms	(atan (sqrt (* (/ 1 (sqrt (+ 1.0 x))) (/ (- 1.0 x) (sqrt (+ 1.0 x))))))
34.0ms	(* (/ 1 (sqrt (+ 1.0 x))) (/ (- 1.0 x) (sqrt (+ 1.0 x))))

series103.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(sqrt (+ 1.0 x))
30.0ms	(sqrt (+ 1.0 x))
2.0ms	(atan (sqrt (* (/ 1 (sqrt (+ 1.0 x))) (/ (- 1.0 x) (sqrt (+ 1.0 x))))))
37.0ms	(* (/ 1 (sqrt (+ 1.0 x))) (/ (- 1.0 x) (sqrt (+ 1.0 x))))

simplify73.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	582	1523
1	2676	1301
2	5003	1210

prune320.0ms

Filtered

158 candidates to 92 candidates (58.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	158	2	160

Merged error: 0b

Counts

160 → 2

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b

(- (* (/ (pow x 2) (sqrt 1.0)) (- 1.0 (/ 0.5 1.0))) (- (* 1.0 (/ x (sqrt 1.0))) (sqrt 1.0)))

0.0b

(* (/ (pow x 2) (sqrt 1.0)) (- 1.0 (/ 0.5 1.0)))

0.0b

(atan (- (* (/ (pow x 2) (sqrt 1.0)) (- 1.0 (/ 0.5 1.0))) (- (* 1.0 (/ x (sqrt 1.0))) (sqrt 1.0))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-sqr-sqrt`
57×	`times-frac`
52×	`associate-l`
35×	`*-un-lft-identity`
33×	`add-cube-cbrt`
28×	`sqrt-prod`
20×	`unpow-prod-down`
13×	`add-exp-log`
12×	`flip3--` `flip--`
10×	`frac-sub`
9×	`unswap-sqr`
8×	`add-cbrt-cube` `unpow2` `add-log-exp` `sqr-pow`
6×	`frac-times` `sub-neg` `associate-r/` `associate-r*`
5×	`pow1`
4×	`distribute-rgt-in` `distribute-lft-in` `prod-exp` `associate--l+`
3×	`diff-log` `div-exp` `associate-*l/`
2×	`cbrt-unprod` `associate--r+` `difference-of-squares`
1×	`cbrt-undiv` `pow-to-exp` `pow-prod-down` `pow-exp` `*-commutative` `div-inv` `distribute-lft-out--` `associate--r-`

Counts

3 → 128

Calls

3 calls:

21.0ms

(- (* (/ (pow x 2) (sqrt 1.0)) (- 1.0 (/ 0.5 1.0))) (- (* 1.0 (/ x (sqrt 1.0))) (sqrt 1.0)))

21.0ms

(* (/ (pow x 2) (sqrt 1.0)) (- 1.0 (/ 0.5 1.0)))

1.0ms

(atan (- (* (/ (pow x 2) (sqrt 1.0)) (- 1.0 (/ 0.5 1.0))) (- (* 1.0 (/ x (sqrt 1.0))) (sqrt 1.0))))

series181.0ms

Counts

3 → 9

Calls

3 calls:

91.0ms

(- (* (/ (pow x 2) (sqrt 1.0)) (- 1.0 (/ 0.5 1.0))) (- (* 1.0 (/ x (sqrt 1.0))) (sqrt 1.0)))

72.0ms

(* (/ (pow x 2) (sqrt 1.0)) (- 1.0 (/ 0.5 1.0)))

17.0ms

(atan (- (* (/ (pow x 2) (sqrt 1.0)) (- 1.0 (/ 0.5 1.0))) (- (* 1.0 (/ x (sqrt 1.0))) (sqrt 1.0))))

simplify106.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	744	1788
1	3660	1664
2	5002	1663

prune390.0ms

Filtered

137 candidates to 97 candidates (70.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	137	2	139

Merged error: 0b

Counts

139 → 2

regimes18.0ms

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	18	11
1	18	11

end0.0ms

sample677.0ms

Algorithm

intervals

Results

299.0ms	8000×	body	80	valid
194.0ms	8018×	body	80	nan