Details

analyze2.4s

Algorithm

sampling

Space saved by range analysis: 0.243902%

Space saved by search: 0.779702%

Guaranteed chance to sample good point: 39.865611%

sample28.0ms

Algorithm

intervals

Results

8.0ms	215×	body	80	valid
2.0ms	13×	body	640	valid
1.0ms	14×	body	320	valid
1.0ms	8×	body	1280	valid
1.0ms	24×	body	80	invalid
0.0ms	6×	body	160	valid

simplify119.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	6
1	52	6
2	109	6
3	195	6
4	445	6
5	828	6
6	1434	6
7	2520	6
8	4830	6
9	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: 18.3b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- z t) y)
1.8b	(- (+ x y) (/ (* (- z t) y) (- a t)))
11.4b	(/ (* (- z t) y) (- a t))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 70

Calls

3 calls:

6.0ms	(* (- z t) y)
10.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
13.0ms	(/ (* (- z t) y) (- a t))

series57.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(* (- z t) y)
34.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
16.0ms	(/ (* (- z t) y) (- a t))

simplify47.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	383	461
1	1704	422
2	5001	422

prune136.0ms

Filtered

56 candidates to 79 candidates (-41.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	68	11	79
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	11	80

Merged error: 4.8b

Counts

80 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a t))
0.6b	(cbrt (- a t))
3.4b	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
7.4b	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
36×	`times-frac`
35×	`*-un-lft-identity`
30×	`associate-r`
27×	`cbrt-prod`
25×	`add-exp-log`
23×	`add-cube-cbrt`
18×	`cbrt-div` `add-cbrt-cube`
17×	`associate-l`
10×	`flip3--` `associate-/r/` `flip--`
9×	`add-log-exp`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `frac-times` `div-exp`
6×	`pow1` `frac-sub` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
5×	`associate-r/` `associate-l/`
3×	`flip3-+` `flip-+`
2×	`pow1/3` `diff-log` `div-inv`
1×	`sub-neg` `pow-prod-down` `associate--l+` `sum-log` `*-commutative`

Counts

4 → 127

Calls

4 calls:

3.0ms	(cbrt (- a t))
3.0ms	(cbrt (- a t))
32.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
6.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

series115.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(cbrt (- a t))
26.0ms	(cbrt (- a t))
26.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
36.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

simplify91.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	793	1744
1	3353	1585
2	5001	1502

prune186.0ms

Filtered

105 candidates to 139 candidates (-32.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	136	3	139
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	138	12	150

Merged error: 4.8b

Counts

150 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a t))
0.6b	(cbrt (- a t))
3.4b	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
14.0b	(- y (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
36×	`times-frac`
35×	`*-un-lft-identity`
30×	`associate-r`
27×	`cbrt-prod`
25×	`add-exp-log`
23×	`add-cube-cbrt`
18×	`cbrt-div` `add-cbrt-cube`
17×	`associate-l`
10×	`flip3--` `associate-/r/` `flip--`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `distribute-lft-out--` `add-log-exp` `difference-of-squares` `unswap-sqr`
5×	`frac-times`
3×	`associate-r/` `associate-l/`
2×	`pow1/3` `div-inv`
1×	`sub-neg` `diff-log` `pow-prod-down` `*-commutative`

Counts

4 → 119

Calls

4 calls:

3.0ms	(cbrt (- a t))
5.0ms	(cbrt (- a t))
29.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
3.0ms	(- y (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

series100.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(cbrt (- a t))
26.0ms	(cbrt (- a t))
22.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
23.0ms	(- y (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

simplify76.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	665	1532
1	2823	1381
2	5001	1298

prune165.0ms

Filtered

99 candidates to 131 candidates (-32.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	131	12	143

Merged error: 4.8b

Counts

143 → 12

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a t))
0.6b	(cbrt (- a t))
1.6b	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (* (cbrt y) (cbrt y)) (* (cbrt (cbrt (- a t))) (cbrt (cbrt (- a t))))))
7.9b	(- (+ x y) (* (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (* (cbrt y) (cbrt y)) (* (cbrt (cbrt (- a t))) (cbrt (cbrt (- a t)))))) (/ (cbrt y) (cbrt (cbrt (- a t))))))

rewrite55.0ms

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`
19×	`frac-times`
17×	`associate-l`
16×	`associate-/r/`
15×	`flip3--` `-un-lft-identity` `associate-l/` `flip--`
14×	`frac-sub`
13×	`associate-r`
11×	`associate-*r/`
10×	`cbrt-prod` `times-frac`
9×	`add-cube-cbrt` `add-log-exp`
7×	`flip3-+` `flip-+`
6×	`pow1`
4×	`unswap-sqr`
3×	`distribute-lft-out--` `difference-of-squares`
2×	`pow1/3` `diff-log` `div-inv`
1×	`sub-neg` `pow-prod-down` `associate--l+` `sum-log` `*-commutative`

Counts

4 → 134

Calls

4 calls:

3.0ms	(cbrt (- a t))
3.0ms	(cbrt (- a t))
36.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (* (cbrt y) (cbrt y)) (* (cbrt (cbrt (- a t))) (cbrt (cbrt (- a t))))))
7.0ms	(- (+ x y) (* (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (* (cbrt y) (cbrt y)) (* (cbrt (cbrt (- a t))) (cbrt (cbrt (- a t)))))) (/ (cbrt y) (cbrt (cbrt (- a t))))))

series202.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(cbrt (- a t))
27.0ms	(cbrt (- a t))
102.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (* (cbrt y) (cbrt y)) (* (cbrt (cbrt (- a t))) (cbrt (cbrt (- a t))))))
47.0ms	(- (+ x y) (* (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (* (cbrt y) (cbrt y)) (* (cbrt (cbrt (- a t))) (cbrt (cbrt (- a t)))))) (/ (cbrt y) (cbrt (cbrt (- a t))))))

simplify56.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1218	3423
1	5002	2786

prune178.0ms

Filtered

110 candidates to 146 candidates (-32.7%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	145	1	146
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	145	13	158

Merged error: 4.8b

Counts

158 → 13

Details

analyze2.4s

sample28.0ms

simplify119.0ms

prune4.0ms

localize9.0ms

rewrite31.0ms

series57.0ms

simplify47.0ms

prune136.0ms

localize14.0ms

rewrite50.0ms

series115.0ms

simplify91.0ms

prune186.0ms

localize13.0ms

rewrite44.0ms

series100.0ms

simplify76.0ms

prune165.0ms

localize21.0ms

rewrite55.0ms

series202.0ms

simplify56.0ms

prune178.0ms

regimes528.0ms

bsearch1.0ms

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