Details

analyze2.7s

Algorithm

sampling

Space saved by range analysis: 0.243902%

Space saved by search: 1.437274%

Guaranteed chance to sample good point: 35.739437%

sample29.0ms

Algorithm

intervals

Results

8.0ms	210×	body	80	valid
2.0ms	14×	body	640	valid
1.0ms	36×	body	80	invalid
1.0ms	11×	body	320	valid
1.0ms	16×	body	160	valid
1.0ms	5×	body	1280	valid

simplify61.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	6
1	45	6
2	111	6
3	288	6
4	714	6
5	1498	6
6	3410	6
7	5001	6

prune4.0ms

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: 24.4b

Counts

2 → 1

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y z) (- t x))
4.2b	(+ x (/ (* (- y z) (- t x)) (- a z)))
17.5b	(/ (* (- y z) (- t x)) (- a z))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `*-un-lft-identity`
13×	`flip3--` `flip--`
10×	`add-exp-log` `add-cbrt-cube`
8×	`frac-times` `associate-/l/`
7×	`add-cube-cbrt`
5×	`pow1` `times-frac` `associate-r` `associate-l` `associate-/r*` `add-log-exp`
4×	`associate-r/` `associate-l/` `distribute-lft-out--` `difference-of-squares`
2×	`cbrt-undiv` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod`
1×	`+-commutative` `frac-2neg` `flip3-+` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+` `div-inv` `distribute-lft-out` `associate-/l` `unswap-sqr`

Counts

3 → 81

Calls

3 calls:

9.0ms	(* (- y z) (- t x))
7.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
12.0ms	(/ (* (- y z) (- t x)) (- a z))

series96.0ms

Counts

3 → 9

Calls

3 calls:

10.0ms	(* (- y z) (- t x))
52.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
34.0ms	(/ (* (- y z) (- t x)) (- a z))

simplify52.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	466	583
1	2158	534
2	5001	534

prune151.0ms

Filtered

67 candidates to 90 candidates (-34.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	79	11	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	11	91

Merged error: 2.9b

Counts

91 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
2.3b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
8.6b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

75×	`add-sqr-sqrt`
59×	`*-un-lft-identity`
52×	`times-frac`
46×	`associate-r`
37×	`cbrt-prod`
27×	`add-cube-cbrt`
25×	`add-exp-log`
18×	`cbrt-div` `add-cbrt-cube`
17×	`associate-l`
16×	`distribute-lft-out--` `difference-of-squares`
10×	`associate-/r/`
9×	`flip3--` `flip--`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `add-log-exp` `unswap-sqr`
5×	`frac-times`
3×	`associate-r/` `associate-l/`
2×	`pow1/3` `div-inv`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

4 → 134

Calls

4 calls:

7.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))
37.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
3.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series174.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(cbrt (- a z))
26.0ms	(cbrt (- a z))
57.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
63.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify85.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	752	1839
1	3320	1671
2	5001	1580

prune199.0ms

Filtered

103 candidates to 146 candidates (-41.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	140	6	146
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	144	13	157

Merged error: 2.9b

Counts

157 → 13

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
4.7b	(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 56

Calls

4 calls:

3.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))
5.0ms	(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

series136.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(cbrt (- a z))
27.0ms	(cbrt (- a z))
29.0ms	(cbrt (- a z))
52.0ms	(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

simplify133.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (125.0ms)

Iter	Nodes	Cost
0	270	701
1	842	645
2	4609	613
3	5002	595

prune144.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	67	14	81

Merged error: 1.2b

Counts

81 → 14

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- t x))
0.6b	(cbrt (- t x))
1.9b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))))
9.4b	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

73×	`add-exp-log`
40×	`cbrt-div`
39×	`add-cbrt-cube`
32×	`prod-exp` `cbrt-unprod`
22×	`cbrt-undiv` `div-exp`
21×	`add-sqr-sqrt`
17×	`associate-l`
16×	`associate-/r/`
15×	`*-un-lft-identity`
14×	`flip3--` `flip--`
13×	`associate-r`
10×	`cbrt-prod` `times-frac`
9×	`frac-times` `add-cube-cbrt`
6×	`pow1` `add-log-exp`
5×	`associate-r/` `associate-l/`
4×	`unswap-sqr`
3×	`distribute-lft-out--` `difference-of-squares`
2×	`pow1/3` `div-inv`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

4 → 117

Calls

4 calls:

3.0ms	(cbrt (- t x))
3.0ms	(cbrt (- t x))
37.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))))
3.0ms	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

series229.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(cbrt (- t x))
28.0ms	(cbrt (- t x))
119.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))))
55.0ms	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

simplify106.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	994	2891
1	4233	2240
2	5001	2164

prune131.0ms

Filtered

86 candidates to 129 candidates (-50.0%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	128	1	129
Fresh	0	12	12
Picked	1	0	1
Done	0	1	1
Total	129	14	143

Merged error: 1.2b

Counts

143 → 14

Details

analyze2.7s

sample29.0ms

simplify61.0ms

prune4.0ms

localize14.0ms

rewrite30.0ms

series96.0ms

simplify52.0ms

prune151.0ms

localize14.0ms

rewrite62.0ms

series174.0ms

simplify85.0ms

prune199.0ms

localize19.0ms

rewrite15.0ms

series136.0ms

simplify133.0ms

prune144.0ms

localize27.0ms

rewrite52.0ms

series229.0ms

simplify106.0ms

prune131.0ms

regimes647.0ms

bsearch1.0ms

Profiling