Details

sample16.0ms

Algorithm

intervals

Results

8.0ms

256×

body

valid

simplify81.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	22	8
1	39	6
2	66	6
3	98	6
4	108	6
5	130	6
6	158	6
7	211	6
8	277	6
9	512	6
10	881	6
11	1338	6
12	2728	6
13	5001	6

prune5.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 0.0b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 2.30753 (* x 0.27061))
0.1b	(* (+ 0.99229 (* x 0.04481)) x)
14.0b	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

120×	`*-un-lft-identity`
56×	`distribute-lft-out`
39×	`associate-l`
35×	`times-frac`
22×	`add-sqr-sqrt`
20×	`add-cube-cbrt`
7×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
5×	`pow1` `associate-/l*` `add-log-exp`
4×	`flip3-+` `flip-+`
3×	`expm1-log1p-u` `fma-def` `associate-r` `log1p-expm1-u`
2×	`associate-*l/` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `sum-log` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

3 → 107

Calls

3 calls:

10.0ms	(+ 2.30753 (* x 0.27061))
8.0ms	(* (+ 0.99229 (* x 0.04481)) x)
18.0ms	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x)))

series350.0ms

Counts

3 → 9

Calls

3 calls:

221.0ms	(+ 2.30753 (* x 0.27061))
69.0ms	(* (+ 0.99229 (* x 0.04481)) x)
60.0ms	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x)))

simplify51.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	362	883
1	1411	774
2	5001	749

prune167.0ms

Filtered

116 candidates to 68 candidates (41.4%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	115	1	116
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	116	1	117

Merged error: 0b

Counts

117 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1 (sqrt (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x)))) (/ (fma 0.27061 x 2.30753) (sqrt (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x)))))
0.1b	(/ 1 (sqrt (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x))))
13.9b	(sqrt (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x)))
13.9b	(sqrt (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x)))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

628×	`*-un-lft-identity`
350×	`associate-/r*`
333×	`sqrt-prod`
276×	`distribute-lft-out`
256×	`frac-times`
220×	`associate-l`
219×	`add-sqr-sqrt`
161×	`add-cube-cbrt`
112×	`times-frac`
106×	`associate-/l*`
36×	`associate-r` `clear-num`
35×	`frac-2neg`
30×	`add-exp-log`
18×	`add-cbrt-cube`
17×	`unswap-sqr`
16×	`associate-r/` `associate-l/`
10×	`pow1` `sqrt-div` `div-exp`
8×	`prod-exp`
6×	`associate-/r/`
5×	`cbrt-undiv` `flip3-+` `flip-+`
4×	`expm1-log1p-u` `cbrt-unprod` `hypot-def` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `pow-flip` `sqrt-pow1` `pow1/2` `1-exp` `div-inv`
2×	`rem-sqrt-square` `un-div-inv`
1×	`pow-prod-down` `*-commutative` `inv-pow`

Counts

4 → 511

Calls

4 calls:

56.0ms	(* (/ 1 (sqrt (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x)))) (/ (fma 0.27061 x 2.30753) (sqrt (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x)))))
16.0ms	(/ 1 (sqrt (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x))))
12.0ms	(sqrt (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x)))
12.0ms	(sqrt (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x)))

series329.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (/ 1 (sqrt (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x)))) (/ (fma 0.27061 x 2.30753) (sqrt (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x)))))
103.0ms	(/ 1 (sqrt (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x))))
80.0ms	(sqrt (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x)))
85.0ms	(sqrt (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x)))

simplify108.0ms

Algorithm

egg-herbie

Counts

523 → 523

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1232	7460
1	5002	6165

prune538.0ms

Filtered

523 candidates to 169 candidates (67.7%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	523	0	523
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	523	1	524

Merged error: 0b

Counts

524 → 1

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	15
1	24	15

end0.0ms

sample339.0ms

Algorithm

intervals

Results

249.0ms

8000×

body

valid