Details

sample375.0ms

Algorithm

intervals

Results

312.0ms

3247×

body

valid

simplify67.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	90	61
1	389	58
2	2115	36
3	5001	36

prune14.0ms

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: 1.4b

Counts

2 → 2

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (* (+ (+ (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (pow (/ 1.0 (fabs x)) 3)) (+ (/ 3.0 4.0) (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 15.0 8.0)))) (/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3)))) (/ 1.0 (fabs x))) 1.0) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))
0.7b	(pow (/ 1.0 (fabs x)) 3)
0.7b	(pow (/ 1.0 (fabs x)) 3)
1.0b	(sqrt PI)

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

216×	`frac-add`
180×	`associate-*l/`
153×	`frac-times`
94×	`times-frac`
83×	`associate-/l/`
63×	`associate-*r/`
62×	`add-sqr-sqrt`
61×	`add-cube-cbrt` `*-un-lft-identity`
42×	`cube-div`
26×	`unpow-prod-down` `cube-prod`
22×	`associate-/r*` `add-cbrt-cube`
21×	`sqrt-prod`
20×	`add-exp-log`
10×	`flip3-+` `flip-+`
8×	`cbrt-undiv` `div-exp`
7×	`pow1` `div-inv`
6×	`pow-unpow`
4×	`pow-exp` `add-log-exp` `rem-cube-cbrt`
2×	`cube-mult` `pow-to-exp` `pow-pow` `unpow3` `prod-exp` `cbrt-unprod` `sqr-pow`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/r/` `associate-/l*`

Counts

4 → 252

Calls

4 calls:

110.0ms	(/ (* (+ (+ (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (pow (/ 1.0 (fabs x)) 3)) (+ (/ 3.0 4.0) (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 15.0 8.0)))) (/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3)))) (/ 1.0 (fabs x))) 1.0) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))
5.0ms	(pow (/ 1.0 (fabs x)) 3)
6.0ms	(pow (/ 1.0 (fabs x)) 3)
1.0ms	(sqrt PI)

series496.0ms

Counts

4 → 10

Calls

4 calls:

431.0ms	(/ (* (+ (+ (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (pow (/ 1.0 (fabs x)) 3)) (+ (/ 3.0 4.0) (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 15.0 8.0)))) (/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3)))) (/ 1.0 (fabs x))) 1.0) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))
32.0ms	(pow (/ 1.0 (fabs x)) 3)
32.0ms	(pow (/ 1.0 (fabs x)) 3)
0.0ms	(sqrt PI)

simplify90.0ms

Algorithm

egg-herbie

Counts

262 → 262

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	1663	5570
1	5001	4966

prune1.4s

Filtered

262 candidates to 184 candidates (70.2%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	243	19	262
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	245	19	264

Merged error: 0.1b

Counts

264 → 19

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 0.75 (/ 1 (pow (fabs x) 5)))
0.3b	(/ 1 (pow (fabs x) 3))
0.3b	(/ 1 (pow (fabs x) 5))
0.4b	(* (* (exp (pow (fabs x) 2)) (+ (* 0.5 (/ 1 (pow (fabs x) 3))) (+ (* 0.75 (/ 1 (pow (fabs x) 5))) (+ (* 1.0 (/ 1 (fabs x))) (* 1.875 (/ 1 (pow (fabs x) 7))))))) (sqrt (/ 1 PI)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

146×	`associate-*r/`
136×	`frac-add`
93×	`times-frac`
85×	`un-div-inv`
83×	`add-sqr-sqrt`
71×	`*-un-lft-identity`
68×	`add-cube-cbrt`
46×	`add-exp-log`
41×	`associate-r`
35×	`unpow-prod-down`
31×	`sqrt-div`
30×	`frac-times` `associate-*l/`
19×	`associate-/r*`
18×	`div-exp` `add-cbrt-cube`
14×	`flip3-+` `flip-+`
13×	`prod-exp` `sqrt-prod` `sqr-pow`
12×	`cube-prod`
11×	`pow1`
9×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp`
7×	`unswap-sqr`
6×	`associate-/l*`
5×	`cbrt-unprod`
4×	`cube-mult` `unpow3` `associate-l` `pow-prod-down` `div-inv` `add-log-exp`
3×	`cbrt-undiv`
2×	`pow-flip` `frac-2neg` `clear-num` `*-commutative` `inv-pow`

Counts

4 → 276

Calls

4 calls:

11.0ms	(* 0.75 (/ 1 (pow (fabs x) 5)))
6.0ms	(/ 1 (pow (fabs x) 3))
10.0ms	(/ 1 (pow (fabs x) 5))
36.0ms	(* (* (exp (pow (fabs x) 2)) (+ (* 0.5 (/ 1 (pow (fabs x) 3))) (+ (* 0.75 (/ 1 (pow (fabs x) 5))) (+ (* 1.0 (/ 1 (fabs x))) (* 1.875 (/ 1 (pow (fabs x) 7))))))) (sqrt (/ 1 PI)))

series526.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* 0.75 (/ 1 (pow (fabs x) 5)))
34.0ms	(/ 1 (pow (fabs x) 3))
53.0ms	(/ 1 (pow (fabs x) 5))
384.0ms	(* (* (exp (pow (fabs x) 2)) (+ (* 0.5 (/ 1 (pow (fabs x) 3))) (+ (* 0.75 (/ 1 (pow (fabs x) 5))) (+ (* 1.0 (/ 1 (fabs x))) (* 1.875 (/ 1 (pow (fabs x) 7))))))) (sqrt (/ 1 PI)))

simplify80.0ms

Algorithm

egg-herbie

Counts

288 → 288

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1611	5389
1	5001	4865

prune892.0ms

Filtered

288 candidates to 121 candidates (42.0%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	282	6	288
Fresh	9	9	18
Picked	0	1	1
Done	0	0	0
Total	291	16	307

Merged error: 0.1b

Counts

307 → 16

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 0.75 (pow (fabs x) 5))
0.3b	(/ 0.5 (pow (fabs x) 3))
0.3b	(* (sqrt (sqrt (/ 1 PI))) (* (+ (+ (+ (/ 1.875 (pow (fabs x) 7)) (/ 1.0 (fabs x))) (/ 0.75 (pow (fabs x) 5))) (/ 0.5 (pow (fabs x) 3))) (exp (pow (fabs x) 2))))
0.5b	(* (* (sqrt (sqrt (/ 1 PI))) (* (+ (+ (+ (/ 1.875 (pow (fabs x) 7)) (/ 1.0 (fabs x))) (/ 0.75 (pow (fabs x) 5))) (/ 0.5 (pow (fabs x) 3))) (exp (pow (fabs x) 2)))) (sqrt (sqrt (/ 1 PI))))

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

80×	`sqrt-div`
75×	`times-frac`
63×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
60×	`associate-*l/`
58×	`sqrt-prod`
54×	`frac-add`
36×	`frac-times`
26×	`add-exp-log`
24×	`unpow-prod-down`
22×	`associate-*r/` `add-cbrt-cube`
20×	`associate-r` `associate-l`
19×	`associate-/r*`
18×	`pow1` `flip3-+` `flip-+`
12×	`cube-prod`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`sqr-pow`
6×	`div-exp` `associate-/l*`
4×	`cube-mult` `unpow3` `div-inv` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `*-commutative`

Counts

4 → 227

Calls

4 calls:

5.0ms	(/ 0.75 (pow (fabs x) 5))
5.0ms	(/ 0.5 (pow (fabs x) 3))
64.0ms	(* (sqrt (sqrt (/ 1 PI))) (* (+ (+ (+ (/ 1.875 (pow (fabs x) 7)) (/ 1.0 (fabs x))) (/ 0.75 (pow (fabs x) 5))) (/ 0.5 (pow (fabs x) 3))) (exp (pow (fabs x) 2))))
72.0ms	(* (* (sqrt (sqrt (/ 1 PI))) (* (+ (+ (+ (/ 1.875 (pow (fabs x) 7)) (/ 1.0 (fabs x))) (/ 0.75 (pow (fabs x) 5))) (/ 0.5 (pow (fabs x) 3))) (exp (pow (fabs x) 2)))) (sqrt (sqrt (/ 1 PI))))

series1.0s

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ 0.75 (pow (fabs x) 5))
41.0ms	(/ 0.5 (pow (fabs x) 3))
550.0ms	(* (sqrt (sqrt (/ 1 PI))) (* (+ (+ (+ (/ 1.875 (pow (fabs x) 7)) (/ 1.0 (fabs x))) (/ 0.75 (pow (fabs x) 5))) (/ 0.5 (pow (fabs x) 3))) (exp (pow (fabs x) 2))))
391.0ms	(* (* (sqrt (sqrt (/ 1 PI))) (* (+ (+ (+ (/ 1.875 (pow (fabs x) 7)) (/ 1.0 (fabs x))) (/ 0.75 (pow (fabs x) 5))) (/ 0.5 (pow (fabs x) 3))) (exp (pow (fabs x) 2)))) (sqrt (sqrt (/ 1 PI))))

simplify79.0ms

Algorithm

egg-herbie

Counts

239 → 239

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1153	5499
1	5001	4982

prune1.2s

Filtered

239 candidates to 157 candidates (65.7%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	234	5	239
Fresh	6	8	14
Picked	1	0	1
Done	0	1	1
Total	241	14	255

Merged error: 0.1b

Counts

255 → 14

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 0.5 (pow (fabs x) 3))
0.3b	(* (sqrt (sqrt (/ 1 PI))) (* (+ (+ (+ (/ 1.875 (pow (fabs x) 7)) (/ 1.0 (fabs x))) (/ 0.75 (pow (fabs x) 5))) (/ 0.5 (pow (fabs x) 3))) (exp (pow (fabs x) 2))))
0.5b	(/ (* (sqrt (sqrt (/ 1 PI))) (* (+ (+ (+ (/ 1.875 (pow (fabs x) 7)) (/ 1.0 (fabs x))) (/ 0.75 (pow (fabs x) 5))) (/ 0.5 (pow (fabs x) 3))) (exp (pow (fabs x) 2)))) (sqrt (sqrt PI)))
1.0b	(sqrt PI)

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

54×	`times-frac`
50×	`sqrt-prod`
46×	`add-sqr-sqrt`
45×	`add-cube-cbrt` `*-un-lft-identity`
36×	`frac-add`
32×	`sqrt-div`
30×	`associate-*l/`
21×	`add-exp-log` `associate-/r*`
20×	`add-cbrt-cube`
19×	`associate-l`
15×	`associate-/l/`
14×	`frac-times` `associate-*r/`
12×	`unpow-prod-down` `flip3-+` `cube-prod` `flip-+`
10×	`pow1`
6×	`div-exp` `prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `cube-mult` `unpow3` `associate-/l*` `add-log-exp` `sqr-pow`
3×	`pow-prod-down` `div-inv`
2×	`frac-2neg` `clear-num`
1×	`pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r` `pow-exp` `*-commutative`

Counts

4 → 177

Calls

4 calls:

5.0ms	(/ 0.5 (pow (fabs x) 3))
63.0ms	(* (sqrt (sqrt (/ 1 PI))) (* (+ (+ (+ (/ 1.875 (pow (fabs x) 7)) (/ 1.0 (fabs x))) (/ 0.75 (pow (fabs x) 5))) (/ 0.5 (pow (fabs x) 3))) (exp (pow (fabs x) 2))))
63.0ms	(/ (* (sqrt (sqrt (/ 1 PI))) (* (+ (+ (+ (/ 1.875 (pow (fabs x) 7)) (/ 1.0 (fabs x))) (/ 0.75 (pow (fabs x) 5))) (/ 0.5 (pow (fabs x) 3))) (exp (pow (fabs x) 2)))) (sqrt (sqrt PI)))
5.0ms	(sqrt PI)

series993.0ms

Counts

4 → 10

Calls

4 calls:

42.0ms	(/ 0.5 (pow (fabs x) 3))
555.0ms	(* (sqrt (sqrt (/ 1 PI))) (* (+ (+ (+ (/ 1.875 (pow (fabs x) 7)) (/ 1.0 (fabs x))) (/ 0.75 (pow (fabs x) 5))) (/ 0.5 (pow (fabs x) 3))) (exp (pow (fabs x) 2))))
396.0ms	(/ (* (sqrt (sqrt (/ 1 PI))) (* (+ (+ (+ (/ 1.875 (pow (fabs x) 7)) (/ 1.0 (fabs x))) (/ 0.75 (pow (fabs x) 5))) (/ 0.5 (pow (fabs x) 3))) (exp (pow (fabs x) 2)))) (sqrt (sqrt PI)))
0.0ms	(sqrt PI)

simplify137.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 2 (106.0ms)

Iter	Nodes	Cost
0	930	3721
1	4752	3362
2	5002	3355

prune870.0ms

Filtered

187 candidates to 122 candidates (65.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	182	5	187
Fresh	5	7	12
Picked	1	0	1
Done	0	1	1
Total	188	13	201

Merged error: 0.1b

Counts

201 → 13

regimes229.0ms

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	26
1	40	26

end0.0ms

sample888.0ms

Algorithm

intervals

Results

769.0ms

8115×

body

valid