Details

sample22.0ms

Algorithm

intervals

Results

10.0ms

343×

body

valid

simplify27.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	15	5
1	25	5
2	41	5
3	63	5
4	80	5
5	96	5
6	113	5
7	121	5
8	124	5
9	124	5

prune2.0ms

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: 3.8b

Counts

2 → 1

localize8.0ms

Local error

Found 1 expressions with local error:

3.7b	(* x (- (/ y z) (/ t (- 1.0 z))))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

776×	`times-frac`
759×	`add-sqr-sqrt`
756×	`*-un-lft-identity`
571×	`add-cube-cbrt`
546×	`prod-diff`
275×	`distribute-rgt-in` `distribute-lft-in`
101×	`associate-*r/`
99×	`frac-sub`
91×	`distribute-lft-out--` `difference-of-squares`
78×	`associate-/r*`
68×	`div-inv`
60×	`associate-/l*`
52×	`associate-/r/`
27×	`flip3--` `flip--`
20×	`frac-2neg` `clear-num`
10×	`associate-r`
3×	`pow1` `add-exp-log` `associate-l` `add-cbrt-cube`
2×	`sub-neg`
1×	`expm1-log1p-u` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`

Counts

1 → 678

Calls

1 calls:

61.0ms

(* x (- (/ y z) (/ t (- 1.0 z))))

series315.0ms

Counts

1 → 3

Calls

1 calls:

315.0ms

(* x (- (/ y z) (/ t (- 1.0 z))))

simplify207.0ms

Algorithm

egg-herbie

Counts

681 → 681

Iterations

Useful iterations: 1 (55.0ms)

Iter	Nodes	Cost
0	2365	19668
1	5001	17032

prune783.0ms

Filtered

681 candidates to 224 candidates (32.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	668	13	681
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	669	13	682

Merged error: 0.1b

Counts

682 → 13

localize8.0ms

Local error

Found 1 expressions with local error:

3.7b	(* (- (/ y z) (/ t (- 1.0 z))) x)

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

101×	`associate-*l/`
99×	`frac-sub`
78×	`associate-/r*`
75×	`add-sqr-sqrt`
72×	`*-un-lft-identity`
60×	`associate-/l*`
43×	`add-cube-cbrt`
20×	`frac-2neg` `clear-num`
13×	`distribute-lft-out--` `difference-of-squares`
10×	`associate-l`
8×	`times-frac`
3×	`pow1` `add-exp-log` `associate-r` `add-cbrt-cube`
1×	`expm1-log1p-u` `flip3--` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`

Counts

1 → 128

Calls

1 calls:

34.0ms

(* (- (/ y z) (/ t (- 1.0 z))) x)

series37.0ms

Counts

1 → 3

Calls

1 calls:

37.0ms

(* (- (/ y z) (/ t (- 1.0 z))) x)

simplify123.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (109.0ms)

Iter	Nodes	Cost
0	1028	1207
1	4371	1177
2	5001	1157

prune213.0ms

Filtered

131 candidates to 80 candidates (61.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	123	8	131
Fresh	8	4	12
Picked	0	1	1
Done	0	0	0
Total	131	13	144

Merged error: 0b

Counts

144 → 13

localize18.0ms

Local error

Found 4 expressions with local error:

1.2b	(/ (* (- (* (/ y (* (cbrt z) (cbrt z))) (cbrt (- 1.0 z))) (* (cbrt z) (/ t (* (cbrt (- 1.0 z)) (cbrt (- 1.0 z)))))) x) (* (cbrt z) (cbrt (- 1.0 z))))
1.4b	(* (- (* (/ y (* (cbrt z) (cbrt z))) (cbrt (- 1.0 z))) (* (cbrt z) (/ t (* (cbrt (- 1.0 z)) (cbrt (- 1.0 z)))))) x)
3.2b	(* (/ y (* (cbrt z) (cbrt z))) (cbrt (- 1.0 z)))
3.4b	(* (cbrt z) (/ t (* (cbrt (- 1.0 z)) (cbrt (- 1.0 z)))))

rewrite8.5s

Algorithm

rewrite-expression-head

Rules

87652×	`add-sqr-sqrt`
38640×	`cbrt-prod`
33193×	`unswap-sqr`
29633×	`times-frac`
17371×	`associate-l`
14175×	`associate-/r*`
12308×	`difference-of-squares`
11563×	`associate-*l/`
11335×	`*-un-lft-identity`
8686×	`frac-sub`
8501×	`associate-*r/`
7852×	`swap-sqr`
7130×	`add-cube-cbrt`
7096×	`associate-r`
5930×	`cbrt-div`
5746×	`frac-times`
4345×	`associate-/l/`
3059×	`*-commutative`
2967×	`flip3--` `flip--`
2052×	`associate-/l*`
1795×	`distribute-lft-out--`
668×	`clear-num`
465×	`frac-2neg`
406×	`un-div-inv`
87×	`add-cbrt-cube`
54×	`cbrt-unprod`
36×	`add-exp-log`
30×	`cbrt-undiv`
13×	`prod-exp`
10×	`pow1` `associate-/r/`
8×	`div-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `div-inv`

Counts

4 → 20626

Calls

4 calls:

1.6s	(/ (* (- (* (/ y (* (cbrt z) (cbrt z))) (cbrt (- 1.0 z))) (* (cbrt z) (/ t (* (cbrt (- 1.0 z)) (cbrt (- 1.0 z)))))) x) (* (cbrt z) (cbrt (- 1.0 z))))
1.1s	(* (- (* (/ y (* (cbrt z) (cbrt z))) (cbrt (- 1.0 z))) (* (cbrt z) (/ t (* (cbrt (- 1.0 z)) (cbrt (- 1.0 z)))))) x)
38.0ms	(* (/ y (* (cbrt z) (cbrt z))) (cbrt (- 1.0 z)))
50.0ms	(* (cbrt z) (/ t (* (cbrt (- 1.0 z)) (cbrt (- 1.0 z)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

280.0ms	(/ (* (- (* (/ y (* (cbrt z) (cbrt z))) (cbrt (- 1.0 z))) (* (cbrt z) (/ t (* (cbrt (- 1.0 z)) (cbrt (- 1.0 z)))))) x) (* (cbrt z) (cbrt (- 1.0 z))))
316.0ms	(* (- (* (/ y (* (cbrt z) (cbrt z))) (cbrt (- 1.0 z))) (* (cbrt z) (/ t (* (cbrt (- 1.0 z)) (cbrt (- 1.0 z)))))) x)
200.0ms	(* (/ y (* (cbrt z) (cbrt z))) (cbrt (- 1.0 z)))
282.0ms	(* (cbrt z) (/ t (* (cbrt (- 1.0 z)) (cbrt (- 1.0 z)))))

simplify6.8s

Algorithm

egg-herbie

Counts

20638 → 20638

Iterations

Useful iterations: 0 (380.0ms)

Iter	Nodes	Cost
0	22246	809095

prune1.2m

Filtered

20638 candidates to 11372 candidates (55.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	20633	5	20638
Fresh	5	6	11
Picked	1	0	1
Done	0	1	1
Total	20639	12	20651

Merged error: 0b

Counts

20651 → 12

localize33.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt z)
1.2b	(/ (* (- (* (/ y (* (cbrt z) (cbrt z))) (cbrt (- 1.0 z))) (* (* (cbrt z) (/ 1 (* (cbrt (- 1.0 z)) (cbrt (* (cbrt (- 1.0 z)) (cbrt (- 1.0 z))))))) (/ t (cbrt (cbrt (- 1.0 z)))))) x) (* (cbrt z) (cbrt (- 1.0 z))))
1.4b	(* (- (* (/ y (* (cbrt z) (cbrt z))) (cbrt (- 1.0 z))) (* (* (cbrt z) (/ 1 (* (cbrt (- 1.0 z)) (cbrt (* (cbrt (- 1.0 z)) (cbrt (- 1.0 z))))))) (/ t (cbrt (cbrt (- 1.0 z)))))) x)
3.2b	(* (/ y (* (cbrt z) (cbrt z))) (cbrt (- 1.0 z)))

rewrite3.9m

Algorithm

rewrite-expression-head

Rules

2248701×	`add-sqr-sqrt`
1589035×	`cbrt-prod`
1023637×	`unswap-sqr`
674600×	`associate-/r*`
639555×	`times-frac`
467374×	`frac-times`
438734×	`*-un-lft-identity`
407209×	`associate-*l/`
338584×	`associate-l`
294718×	`frac-sub`
289246×	`associate-*r/`
278683×	`associate-r`
240798×	`add-cube-cbrt`
225116×	`difference-of-squares`
198494×	`cbrt-div`
171968×	`swap-sqr`
147361×	`associate-/l/`
99249×	`flip3--` `flip--`
97450×	`associate-/l*`
64930×	`*-commutative`
49313×	`distribute-lft-out--`
32594×	`clear-num`
28756×	`frac-2neg`
11312×	`un-div-inv`
59×	`add-cbrt-cube`
34×	`cbrt-unprod`
27×	`add-exp-log`
20×	`cbrt-undiv`
9×	`prod-exp`
8×	`pow1`
6×	`div-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `associate-/r/` `div-inv`
1×	`pow1/3`

Counts

4 → 478709

Calls

4 calls:

1.0ms	(cbrt z)
32.1s	(/ (* (- (* (/ y (* (cbrt z) (cbrt z))) (cbrt (- 1.0 z))) (* (* (cbrt z) (/ 1 (* (cbrt (- 1.0 z)) (cbrt (* (cbrt (- 1.0 z)) (cbrt (- 1.0 z))))))) (/ t (cbrt (cbrt (- 1.0 z)))))) x) (* (cbrt z) (cbrt (- 1.0 z))))
21.5s	(* (- (* (/ y (* (cbrt z) (cbrt z))) (cbrt (- 1.0 z))) (* (* (cbrt z) (/ 1 (* (cbrt (- 1.0 z)) (cbrt (* (cbrt (- 1.0 z)) (cbrt (- 1.0 z))))))) (/ t (cbrt (cbrt (- 1.0 z)))))) x)
35.0ms	(* (/ y (* (cbrt z) (cbrt z))) (cbrt (- 1.0 z)))

series1.1s

Counts

4 → 12

Calls

4 calls:

182.0ms	(cbrt z)
300.0ms	(/ (* (- (* (/ y (* (cbrt z) (cbrt z))) (cbrt (- 1.0 z))) (* (* (cbrt z) (/ 1 (* (cbrt (- 1.0 z)) (cbrt (* (cbrt (- 1.0 z)) (cbrt (- 1.0 z))))))) (/ t (cbrt (cbrt (- 1.0 z)))))) x) (* (cbrt z) (cbrt (- 1.0 z))))
336.0ms	(* (- (* (/ y (* (cbrt z) (cbrt z))) (cbrt (- 1.0 z))) (* (* (cbrt z) (/ 1 (* (cbrt (- 1.0 z)) (cbrt (* (cbrt (- 1.0 z)) (cbrt (- 1.0 z))))))) (/ t (cbrt (cbrt (- 1.0 z)))))) x)
211.0ms	(* (/ y (* (cbrt z) (cbrt z))) (cbrt (- 1.0 z)))

simplify4.6m

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (17.2s)

Iter	Nodes	Cost
0	484344	24261059