Details

analyze287.0ms (4.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
31.2%	68.6%	0.1%	8
35.9%	60.8%	3.3%	9
44.1%	48%	7.9%	10
54.8%	36.9%	8.3%	11
57.6%	31.5%	10.9%	12
61.9%	24%	14.1%	13
67.2%	18.6%	14.2%	14

sample16.0ms (0.2%)

Algorithm

1×

intervals

Results

7.0ms	256×	body	80	valid
1.0ms	20×	body	80	invalid

simplify28.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	733	9
1	733	9

prune6.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 2.4b

Counts

2 → 1

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(- 1.0 (* (- 1.0 y) z))
2.2b	(* x (- 1.0 (* (- 1.0 y) z)))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
3×	`sub-neg` `associate-r` `associate-l`
2×	`flip3--` `associate-*r/` `flip--`
1×	`distribute-rgt-in` `distribute-lft-in` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

2 → 33

Calls

2 calls:

7.0ms	(* x (- 1.0 (* (- 1.0 y) z)))
3.0ms	(- 1.0 (* (- 1.0 y) z))

series15.0ms (0.2%)

Counts

2 → 6

Calls

2 calls:

11.0ms	(* x (- 1.0 (* (- 1.0 y) z)))
4.0ms	(- 1.0 (* (- 1.0 y) z))

simplify46.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4953	418
1	4953	418

prune85.0ms (1.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	32	7	39
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	32	8	40

Merged error: 2.2b

Counts

40 → 8

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.7b	(* x (* (cbrt (+ 1.0 (* z (- y 1.0)))) (cbrt (+ 1.0 (* z (- y 1.0))))))
2.4b	(cbrt (+ 1.0 (* z (- y 1.0))))
2.4b	(cbrt (+ 1.0 (* z (- y 1.0))))
2.4b	(cbrt (- 1.0 (* (- 1.0 y) z)))

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`cbrt-div`
10×	`associate-*r/`
9×	`pow1` `add-exp-log` `cbrt-prod` `add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity` `flip3-+` `flip-+`
7×	`add-cbrt-cube`
4×	`frac-times` `add-log-exp`
3×	`pow1/3` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`associate-*l/`
1×	`flip3--` `associate-r` `*-commutative` `flip--` `unswap-sqr`

Counts

4 → 66

Calls

4 calls:

11.0ms	(* x (* (cbrt (+ 1.0 (* z (- y 1.0)))) (cbrt (+ 1.0 (* z (- y 1.0))))))
3.0ms	(cbrt (+ 1.0 (* z (- y 1.0))))
2.0ms	(cbrt (- 1.0 (* (- 1.0 y) z)))
2.0ms	(cbrt (+ 1.0 (* z (- y 1.0))))

series105.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

51.0ms	(* x (* (cbrt (+ 1.0 (* z (- y 1.0)))) (cbrt (+ 1.0 (* z (- y 1.0))))))
18.0ms	(cbrt (+ 1.0 (* z (- y 1.0))))
18.0ms	(cbrt (- 1.0 (* (- 1.0 y) z)))
18.0ms	(cbrt (+ 1.0 (* z (- y 1.0))))

simplify57.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4951	1344
1	4951	1344

prune237.0ms (3.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	76	2	78
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	77	9	86

Merged error: 2.2b

Counts

86 → 9

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt (* x (+ 1.0 (* z (- y 1.0)))))
2.2b	(* x (+ 1.0 (* z (- y 1.0))))
2.2b	(* x (+ 1.0 (* z (- y 1.0))))
2.2b	(* x (+ 1.0 (* z (- y 1.0))))

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
9×	`associate-r` `associate-l`
8×	`associate-*r/`
4×	`flip3-+` `flip-+` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`cbrt-div`
1×	`cbrt-prod` `pow1/3`

Counts

4 → 77

Calls

4 calls:

5.0ms	(* x (+ 1.0 (* z (- y 1.0))))
5.0ms	(* x (+ 1.0 (* z (- y 1.0))))
5.0ms	(* x (+ 1.0 (* z (- y 1.0))))
4.0ms	(cbrt (* x (+ 1.0 (* z (- y 1.0)))))

series74.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

42.0ms	(cbrt (* x (+ 1.0 (* z (- y 1.0)))))
11.0ms	(* x (+ 1.0 (* z (- y 1.0))))
11.0ms	(* x (+ 1.0 (* z (- y 1.0))))
10.0ms	(* x (+ 1.0 (* z (- y 1.0))))

simplify77.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4960	1046
1	4960	1046

prune246.0ms (3.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	89	9	98

Merged error: 2.2b

Counts

98 → 9

localize25.0ms (0.4%)

Local error

Found 4 expressions with local error:

2.6b	(* (- 1.0 y) (* z (* z (- y 1.0))))
4.7b	(/ (* (cbrt (+ (* 1.0 1.0) (* (- 1.0 y) (* z (* z (- y 1.0)))))) (* (cbrt (+ (* 1.0 1.0) (* (- 1.0 y) (* z (* z (- y 1.0)))))) x)) (* (cbrt (- 1.0 (* z (- y 1.0)))) (cbrt (- 1.0 (* z (- y 1.0))))))
13.0b	(cbrt (+ (* 1.0 1.0) (* (- 1.0 y) (* z (* z (- y 1.0))))))
13.0b	(cbrt (+ (* 1.0 1.0) (* (- 1.0 y) (* z (* z (- y 1.0))))))

rewrite48.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-exp-log`
28×	`cbrt-div`
22×	`add-cbrt-cube`
18×	`associate-*r/`
15×	`prod-exp` `cbrt-unprod`
13×	`pow1`
12×	`distribute-rgt-in` `frac-times` `flip3--` `distribute-lft-in` `associate-*l/` `flip--`
9×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`sub-neg` `flip3-+` `associate-/r/` `flip-+` `associate-/l/`
7×	`add-cube-cbrt`
6×	`cbrt-undiv` `cbrt-prod` `div-exp` `pow-prod-down`
5×	`associate-l`
4×	`add-log-exp`
2×	`pow1/3`
1×	`frac-2neg` `times-frac` `associate-r` `clear-num` `associate-/r` `-commutative` `div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 106

Calls

4 calls:

22.0ms	(/ (* (cbrt (+ (* 1.0 1.0) (* (- 1.0 y) (* z (* z (- y 1.0)))))) (* (cbrt (+ (* 1.0 1.0) (* (- 1.0 y) (* z (* z (- y 1.0)))))) x)) (* (cbrt (- 1.0 (* z (- y 1.0)))) (cbrt (- 1.0 (* z (- y 1.0))))))
13.0ms	(* (- 1.0 y) (* z (* z (- y 1.0))))
4.0ms	(cbrt (+ (* 1.0 1.0) (* (- 1.0 y) (* z (* z (- y 1.0))))))
4.0ms	(cbrt (+ (* 1.0 1.0) (* (- 1.0 y) (* z (* z (- y 1.0))))))

series3.6s (54.5%)

Counts

4 → 12

Calls

4 calls:

3.5s	(/ (* (cbrt (+ (* 1.0 1.0) (* (- 1.0 y) (* z (* z (- y 1.0)))))) (* (cbrt (+ (* 1.0 1.0) (* (- 1.0 y) (* z (* z (- y 1.0)))))) x)) (* (cbrt (- 1.0 (* z (- y 1.0)))) (cbrt (- 1.0 (* z (- y 1.0))))))
40.0ms	(cbrt (+ (* 1.0 1.0) (* (- 1.0 y) (* z (* z (- y 1.0))))))
38.0ms	(cbrt (+ (* 1.0 1.0) (* (- 1.0 y) (* z (* z (- y 1.0))))))
8.0ms	(* (- 1.0 y) (* z (* z (- y 1.0))))

simplify48.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	6310	3787

prune586.0ms (8.9%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	118	9	127

Merged error: 2.2b

Counts

127 → 9

regimes487.0ms (7.4%)

Accuracy

Total 0.1b remaining (4.3%)

Threshold costs 0.1b (4.3%)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	203	9
1	203	9

end0.0ms (0%)

sample425.0ms (6.5%)

Algorithm

1×

intervals

Results

229.0ms	8000×	body	80	valid
18.0ms	686×	body	80	invalid

Details

analyze287.0ms (4.4%)

sample16.0ms (0.2%)

simplify28.0ms (0.4%)

prune6.0ms (0.1%)

localize6.0ms (0.1%)

rewrite11.0ms (0.2%)

series15.0ms (0.2%)

simplify46.0ms (0.7%)

prune85.0ms (1.3%)

localize16.0ms (0.3%)

rewrite20.0ms (0.3%)

series105.0ms (1.6%)

simplify57.0ms (0.9%)

prune237.0ms (3.6%)

localize11.0ms (0.2%)

rewrite22.0ms (0.3%)

series74.0ms (1.1%)

simplify77.0ms (1.2%)

prune246.0ms (3.7%)

localize25.0ms (0.4%)

rewrite48.0ms (0.7%)

series3.6s (54.5%)

simplify48.0ms (0.7%)

prune586.0ms (8.9%)

regimes487.0ms (7.4%)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample425.0ms (6.5%)

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