Details

sample361.0ms

Algorithm

intervals

Results

296.0ms

3657×

body

valid

simplify68.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (66.0ms)

Iter	Nodes	Cost
0	90	61
1	406	58
2	2267	36
3	5001	35

prune20.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 1.1b

Counts

2 → 2

localize35.0ms

Local error

Found 4 expressions with local error:

0.8b	(pow (/ 1.0 (fabs x)) 3)
0.9b	(pow (/ 1.0 (fabs x)) 4)
1.0b	(sqrt PI)
1.3b	(pow (/ 1.0 (fabs x)) 6)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

39×	`unpow-prod-down`
37×	`add-sqr-sqrt`
36×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`add-exp-log` `cube-prod`
9×	`pow-unpow`
8×	`pow1`
7×	`add-cbrt-cube`
6×	`pow-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `div-exp` `sqrt-prod` `sqr-pow`
2×	`rem-cube-cbrt`
1×	`cbrt-undiv` `cube-div` `cube-mult` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `unpow3`

Counts

4 → 123

Calls

4 calls:

5.0ms	(pow (/ 1.0 (fabs x)) 3)
5.0ms	(pow (/ 1.0 (fabs x)) 4)
1.0ms	(sqrt PI)
5.0ms	(pow (/ 1.0 (fabs x)) 6)

series118.0ms

Counts

4 → 10

Calls

4 calls:

33.0ms	(pow (/ 1.0 (fabs x)) 3)
33.0ms	(pow (/ 1.0 (fabs x)) 4)
0.0ms	(sqrt PI)
51.0ms	(pow (/ 1.0 (fabs x)) 6)

simplify82.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	545	752
1	2496	663
2	5001	647

prune618.0ms

Filtered

133 candidates to 82 candidates (61.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	123	10	133
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	124	11	135

Merged error: 0.2b

Counts

135 → 11

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1.0 (fabs x)) (+ (/ (* (/ 1.0 (pow (fabs x) 6)) 15.0) 8.0) (fma (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4) 1)))
0.8b	(pow (/ 1.0 (fabs x)) 3)
0.9b	(pow (/ 1.0 (fabs x)) 4)
1.0b	(sqrt PI)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
37×	`times-frac`
36×	`add-cube-cbrt`
26×	`unpow-prod-down`
15×	`add-exp-log`
13×	`cube-prod` `associate-l`
12×	`add-cbrt-cube`
9×	`pow1`
6×	`pow-unpow`
4×	`expm1-log1p-u` `associate-r` `pow-exp` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`div-exp` `sqrt-prod`
2×	`cbrt-undiv` `frac-times` `pow-to-exp` `pow-pow` `flip3-+` `associate-*r/` `prod-exp` `cbrt-unprod` `flip-+` `rem-cube-cbrt` `unswap-sqr` `sqr-pow`
1×	`cube-div` `distribute-rgt-in` `cube-mult` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `unpow3` `pow-prod-down` `associate-l/` `-commutative` `distribute-lft-out`

Counts

4 → 134

Calls

4 calls:

15.0ms	(* (/ 1.0 (fabs x)) (+ (/ (* (/ 1.0 (pow (fabs x) 6)) 15.0) 8.0) (fma (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4) 1)))
5.0ms	(pow (/ 1.0 (fabs x)) 3)
5.0ms	(pow (/ 1.0 (fabs x)) 4)
2.0ms	(sqrt PI)

series245.0ms

Counts

4 → 10

Calls

4 calls:

177.0ms	(* (/ 1.0 (fabs x)) (+ (/ (* (/ 1.0 (pow (fabs x) 6)) 15.0) 8.0) (fma (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4) 1)))
33.0ms	(pow (/ 1.0 (fabs x)) 3)
35.0ms	(pow (/ 1.0 (fabs x)) 4)
0.0ms	(sqrt PI)

simplify109.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (94.0ms)

Iter	Nodes	Cost
0	720	1361
1	3609	1215
2	5002	1195

prune762.0ms

Filtered

144 candidates to 92 candidates (63.9%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	132	12	144
Fresh	4	6	10
Picked	0	1	1
Done	0	0	0
Total	136	19	155

Merged error: 0.0b

Counts

155 → 19

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (pow (fabs x) 4))
0.3b	(* 0.75 (/ 1 (pow (fabs x) 4)))
0.8b	(pow (/ 1.0 (fabs x)) 3)
1.0b	(sqrt PI)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-sqr-sqrt`
66×	`times-frac`
54×	`*-un-lft-identity`
51×	`add-cube-cbrt`
36×	`add-exp-log` `unpow-prod-down`
25×	`associate-r`
14×	`add-cbrt-cube`
13×	`cube-prod` `div-exp`
10×	`prod-exp` `sqr-pow`
8×	`pow1` `pow-exp`
7×	`pow-to-exp` `associate-/r*` `unswap-sqr`
6×	`rec-exp` `1-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`cbrt-undiv` `pow-unpow` `associate-l` `sqrt-prod` `associate-/l*`
2×	`cbrt-unprod` `rem-cube-cbrt`
1×	`cube-div` `cube-mult` `rem-sqrt-square` `pow-flip` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `unpow3` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 178

Calls

4 calls:

5.0ms	(/ 1 (pow (fabs x) 4))
11.0ms	(* 0.75 (/ 1 (pow (fabs x) 4)))
5.0ms	(pow (/ 1.0 (fabs x)) 3)
2.0ms	(sqrt PI)

series116.0ms

Counts

4 → 10

Calls

4 calls:

40.0ms	(/ 1 (pow (fabs x) 4))
38.0ms	(* 0.75 (/ 1 (pow (fabs x) 4)))
38.0ms	(pow (/ 1.0 (fabs x)) 3)
0.0ms	(sqrt PI)

simplify76.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	616	1089
1	2913	881
2	5001	857

prune758.0ms

Filtered

188 candidates to 97 candidates (51.6%)

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	187	1	188
Fresh	2	15	17
Picked	0	1	1
Done	0	1	1
Total	189	18	207

Merged error: 0.0b

Counts

207 → 18

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (/ 1.0 (fabs x))) (* (sqrt (/ 1.0 (fabs x))) (+ (/ (* (/ 1.0 (pow (fabs x) 6)) 15.0) 8.0) (fma (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4) 1))))
0.8b	(pow (/ 1.0 (fabs x)) 3)
0.9b	(pow (/ 1.0 (fabs x)) 4)
1.0b	(sqrt PI)

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
36×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
26×	`unpow-prod-down`
16×	`associate-l` `sqrt-prod`
15×	`add-exp-log`
13×	`cube-prod`
12×	`pow1` `sqrt-div` `add-cbrt-cube`
9×	`frac-times` `associate-*r/`
6×	`pow-unpow`
4×	`distribute-rgt-in` `expm1-log1p-u` `distribute-lft-in` `flip3-+` `pow-exp` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow-prod-down` `associate-*l/` `prod-exp` `cbrt-unprod`
2×	`pow-to-exp` `pow-pow` `div-exp` `rem-cube-cbrt` `sqr-pow`
1×	`cbrt-undiv` `cube-div` `cube-mult` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `unpow3` `associate-r` `*-commutative`

Counts

4 → 141

Calls

4 calls:

24.0ms	(* (sqrt (/ 1.0 (fabs x))) (* (sqrt (/ 1.0 (fabs x))) (+ (/ (* (/ 1.0 (pow (fabs x) 6)) 15.0) 8.0) (fma (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4) 1))))
5.0ms	(pow (/ 1.0 (fabs x)) 3)
5.0ms	(pow (/ 1.0 (fabs x)) 4)
2.0ms	(sqrt PI)

series307.0ms

Counts

4 → 10

Calls

4 calls:

239.0ms	(* (sqrt (/ 1.0 (fabs x))) (* (sqrt (/ 1.0 (fabs x))) (+ (/ (* (/ 1.0 (pow (fabs x) 6)) 15.0) 8.0) (fma (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4) 1))))
32.0ms	(pow (/ 1.0 (fabs x)) 3)
35.0ms	(pow (/ 1.0 (fabs x)) 4)
0.0ms	(sqrt PI)

simplify102.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	729	1664
1	3653	1470
2	5001	1456

prune824.0ms

Filtered

151 candidates to 95 candidates (62.9%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	148	3	151
Fresh	6	9	15
Picked	1	0	1
Done	1	1	2
Total	156	13	169

Merged error: 0.0b

Counts

169 → 13

regimes332.0ms

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	33
1	43	33

end0.0ms

sample6.3s

Algorithm

intervals

Results

5.4s

67719×

body

valid

Details

sample361.0ms

simplify68.0ms

prune20.0ms

localize35.0ms

rewrite20.0ms

series118.0ms

simplify82.0ms

prune618.0ms

localize36.0ms

rewrite35.0ms

series245.0ms

simplify109.0ms

prune762.0ms

localize35.0ms

rewrite30.0ms

series116.0ms

simplify76.0ms

prune758.0ms

localize38.0ms

rewrite41.0ms

series307.0ms

simplify102.0ms

prune824.0ms

regimes332.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample6.3s

Profiling