Details

sample274.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
8.0ms	273×	body	80	nan

simplify11.0ms

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

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 110

Calls

3 calls:

9.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
1.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
11.0ms	(/ (- 1.0 x) (+ 1.0 x))

series152.0ms

Counts

3 → 9

Calls

3 calls:

92.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
3.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
57.0ms	(/ (- 1.0 x) (+ 1.0 x))

simplify42.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	392	859
1	1163	822
2	5002	804

prune266.0ms

Filtered

119 candidates to 85 candidates (71.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	117	2	119
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	118	2	120

Merged error: 0b

Counts

120 → 2

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

300×	`add-sqr-sqrt`
165×	`sqrt-prod`
125×	`difference-of-squares`
109×	`*-un-lft-identity`
108×	`times-frac`
60×	`swap-sqr`
50×	`*-commutative` `unswap-sqr`
49×	`add-cube-cbrt`
36×	`associate-/l*`
25×	`distribute-lft-out--`
20×	`associate-l`
5×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `sqrt-div`
3×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

3 → 219

Calls

3 calls:

35.0ms	(sqrt (- (* 1.0 1.0) (* x x)))
17.0ms	(atan (/ (sqrt (- (* 1.0 1.0) (* x x))) (fabs (+ 1.0 x))))
25.0ms	(/ (sqrt (- (* 1.0 1.0) (* x x))) (fabs (+ 1.0 x)))

series143.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(sqrt (- (* 1.0 1.0) (* x x)))
4.0ms	(atan (/ (sqrt (- (* 1.0 1.0) (* x x))) (fabs (+ 1.0 x))))
81.0ms	(/ (sqrt (- (* 1.0 1.0) (* x x))) (fabs (+ 1.0 x)))

simplify61.0ms

Algorithm

egg-herbie

Counts

228 → 228

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	507	2386
1	1620	2336
2	5002	2334

prune315.0ms

Filtered

228 candidates to 87 candidates (38.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	227	1	228
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	229	1	230

Merged error: 0b

Counts

230 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

636×	`add-sqr-sqrt`
330×	`sqrt-prod`
324×	`times-frac`
256×	`*-un-lft-identity`
250×	`difference-of-squares`
224×	`exp-prod`
136×	`add-cube-cbrt`
120×	`swap-sqr`
113×	`log-pow`
100×	`*-commutative` `unswap-sqr`
50×	`distribute-lft-out--`
40×	`associate-l`
36×	`associate-/l*`
7×	`add-exp-log`
6×	`add-cbrt-cube`
5×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`log-prod` `associate-/r*` `div-inv`
2×	`sqrt-div` `rem-log-exp` `associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--` `rem-exp-log`

Counts

4 → 421

Calls

4 calls:

1.0ms	(atan (log (exp (/ (sqrt (- (* 1.0 1.0) (* x x))) (fabs (+ 1.0 x))))))
37.0ms	(log (exp (/ (sqrt (- (* 1.0 1.0) (* x x))) (fabs (+ 1.0 x)))))
41.0ms	(exp (/ (sqrt (- (* 1.0 1.0) (* x x))) (fabs (+ 1.0 x))))
25.0ms	(/ (sqrt (- (* 1.0 1.0) (* x x))) (fabs (+ 1.0 x)))

series206.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(atan (log (exp (/ (sqrt (- (* 1.0 1.0) (* x x))) (fabs (+ 1.0 x))))))
76.0ms	(log (exp (/ (sqrt (- (* 1.0 1.0) (* x x))) (fabs (+ 1.0 x)))))
48.0ms	(exp (/ (sqrt (- (* 1.0 1.0) (* x x))) (fabs (+ 1.0 x))))
79.0ms	(/ (sqrt (- (* 1.0 1.0) (* x x))) (fabs (+ 1.0 x)))

simplify82.0ms

Algorithm

egg-herbie

Counts

433 → 433

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	629	4155
1	1888	4056
2	5001	4018

prune738.0ms

Filtered

433 candidates to 175 candidates (40.4%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	433	0	433
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	433	1	434

Merged error: 0b

Counts

434 → 1

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	11
1	16	11

end0.0ms

sample709.0ms

Algorithm

intervals

Results

322.0ms	8000×	body	80	valid
198.0ms	7716×	body	80	nan