Details

analyze67.0ms (2.8%)

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
25%	74.9%	0.1%	5
40.6%	59.3%	0.1%	6
53.1%	45.3%	1.7%	7
64%	31.2%	4.8%	8
70.2%	21.9%	7.9%	9
75.7%	15.2%	9.1%	10
78.8%	10.5%	10.6%	11
81.6%	7.5%	10.9%	12
83.1%	5.2%	11.7%	13
84.5%	3.7%	11.8%	14

sample12.0ms (0.5%)

Algorithm

1×

intervals

Results

5.0ms

256×

body

valid

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	44	7
1	44	7

prune5.0ms (0.2%)

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: 0.0b

Counts

2 → 1

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+ (+ (* x y) x) y)
0.0b	(+ (* x y) x)

rewrite10.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-log-exp`
4×	`*-un-lft-identity` `sum-log`
2×	`pow1` `add-exp-log` `+-commutative` `add-sqr-sqrt` `add-cube-cbrt` `flip3-+` `add-cbrt-cube` `flip-+`
1×	`associate-+l+` `distribute-lft-out`

Counts

2 → 25

Calls

2 calls:

6.0ms	(+ (+ (* x y) x) y)
4.0ms	(+ (* x y) x)

series9.0ms (0.4%)

Counts

2 → 6

Calls

2 calls:

5.0ms	(+ (* x y) x)
4.0ms	(+ (+ (* x y) x) y)

simplify33.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5115	268

prune39.0ms (1.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	30	1	31
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	30	2	32

Merged error: 0.0b

Counts

32 → 2

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ x (* x y))) (cbrt (+ x (* x y))))
0.6b	(cbrt (+ x (* x y)))
0.6b	(cbrt (+ x (* x y)))
0.6b	(cbrt (+ x (* x y)))

rewrite19.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`flip3-+` `pow1/3` `flip-+`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 87

Calls

4 calls:

9.0ms	(* (cbrt (+ x (* x y))) (cbrt (+ x (* x y))))
3.0ms	(cbrt (+ x (* x y)))
2.0ms	(cbrt (+ x (* x y)))
2.0ms	(cbrt (+ x (* x y)))

series64.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (cbrt (+ x (* x y))) (cbrt (+ x (* x y))))
16.0ms	(cbrt (+ x (* x y)))
14.0ms	(cbrt (+ x (* x y)))
14.0ms	(cbrt (+ x (* x y)))

simplify52.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4944	1326
1	4944	1326

prune132.0ms (5.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	98	1	99
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	99	2	101

Merged error: 0.0b

Counts

101 → 2

localize18.0ms (0.8%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ x (* x y)))
3.3b	(* (cbrt (+ x (* x y))) (+ (cbrt (* x y)) (* (/ (cbrt (* x y)) y) (+ 1/3 (/ -1/9 y)))))
8.5b	(cbrt (* x y))
8.5b	(cbrt (* x y))

rewrite17.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

8.0ms	(* (cbrt (+ x (* x y))) (+ (cbrt (* x y)) (* (/ (cbrt (* x y)) y) (+ 1/3 (/ -1/9 y)))))
2.0ms	(cbrt (* x y))
2.0ms	(cbrt (+ x (* x y)))
2.0ms	(cbrt (* x y))

series123.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

80.0ms	(* (cbrt (+ x (* x y))) (+ (cbrt (* x y)) (* (/ (cbrt (* x y)) y) (+ 1/3 (/ -1/9 y)))))
15.0ms	(cbrt (+ x (* x y)))
14.0ms	(cbrt (* x y))
14.0ms	(cbrt (* x y))

simplify40.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5487	2044

prune160.0ms (6.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	74	3	77

Merged error: 0b

Counts

77 → 3

localize36.0ms (1.5%)

Local error

Found 4 expressions with local error:

8.5b	(cbrt (* x y))
8.5b	(cbrt (* x y))
12.2b	(/ (* x y) (pow (/ y (+ 1/3 (/ -1/9 y))) 3))
31.4b	(/ (* (cbrt (+ x (* x y))) (+ (* x y) (/ (* x y) (pow (/ y (+ 1/3 (/ -1/9 y))) 3)))) (+ (* (cbrt (* x y)) (cbrt (* x y))) (- (* (* (/ (cbrt (* x y)) y) (+ 1/3 (/ -1/9 y))) (* (/ (cbrt (* x y)) y) (+ 1/3 (/ -1/9 y)))) (* (cbrt (* x y)) (* (/ (cbrt (* x y)) y) (+ 1/3 (/ -1/9 y)))))))

rewrite77.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Rules

93×	`times-frac`
64×	`*-un-lft-identity`
45×	`associate-/r*`
40×	`add-sqr-sqrt` `add-cube-cbrt`
36×	`unpow-prod-down` `cube-prod`
29×	`add-exp-log`
13×	`add-cbrt-cube`
12×	`div-exp` `distribute-lft-out`
11×	`flip3-+` `associate-/r/` `flip-+`
8×	`associate-/l/`
6×	`cbrt-div` `div-inv`
5×	`prod-exp`
4×	`pow1` `cbrt-undiv` `frac-times` `pow-exp` `add-log-exp`
2×	`cbrt-prod` `cube-mult` `pow-to-exp` `frac-2neg` `pow1/3` `unpow3` `associate-r/` `associate-l/` `clear-num` `cbrt-unprod` `associate-/l*` `sqr-pow`
1×	`cube-div`

Counts

4 → 155

Calls

4 calls:

47.0ms	(/ (* (cbrt (+ x (* x y))) (+ (* x y) (/ (* x y) (pow (/ y (+ 1/3 (/ -1/9 y))) 3)))) (+ (* (cbrt (* x y)) (cbrt (* x y))) (- (* (* (/ (cbrt (* x y)) y) (+ 1/3 (/ -1/9 y))) (* (/ (cbrt (* x y)) y) (+ 1/3 (/ -1/9 y)))) (* (cbrt (* x y)) (* (/ (cbrt (* x y)) y) (+ 1/3 (/ -1/9 y)))))))
19.0ms	(/ (* x y) (pow (/ y (+ 1/3 (/ -1/9 y))) 3))
2.0ms	(cbrt (* x y))
2.0ms	(cbrt (* x y))

series262.0ms (11.1%)

Counts

4 → 12

Calls

4 calls:

218.0ms	(/ (* (cbrt (+ x (* x y))) (+ (* x y) (/ (* x y) (pow (/ y (+ 1/3 (/ -1/9 y))) 3)))) (+ (* (cbrt (* x y)) (cbrt (* x y))) (- (* (* (/ (cbrt (* x y)) y) (+ 1/3 (/ -1/9 y))) (* (/ (cbrt (* x y)) y) (+ 1/3 (/ -1/9 y)))) (* (cbrt (* x y)) (* (/ (cbrt (* x y)) y) (+ 1/3 (/ -1/9 y)))))))
15.0ms	(cbrt (* x y))
15.0ms	(/ (* x y) (pow (/ y (+ 1/3 (/ -1/9 y))) 3))
14.0ms	(cbrt (* x y))

simplify63.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5034	5006

prune686.0ms (29.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	167	0	167
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	167	3	170

Merged error: 0b

Counts

170 → 3

regimes116.0ms (4.9%)

Accuracy

Total 0.0b remaining (25.6%)

Threshold costs 0.0b (25.6%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	7
1	8	7

end0.0ms (0%)

sample294.0ms (12.5%)

Algorithm

1×

intervals

Results

169.0ms	7999×	body	80	valid
1.0ms	70×	body	80	invalid
0.0ms	1×	body	320	valid

Details

analyze67.0ms (2.8%)

sample12.0ms (0.5%)

simplify4.0ms (0.2%)

prune5.0ms (0.2%)

localize5.0ms (0.2%)

rewrite10.0ms (0.4%)

series9.0ms (0.4%)

simplify33.0ms (1.4%)

prune39.0ms (1.7%)

localize10.0ms (0.4%)

rewrite19.0ms (0.8%)

series64.0ms (2.7%)

simplify52.0ms (2.2%)

prune132.0ms (5.6%)

localize18.0ms (0.8%)

rewrite17.0ms (0.7%)

series123.0ms (5.2%)

simplify40.0ms (1.7%)

prune160.0ms (6.8%)

localize36.0ms (1.5%)

rewrite77.0ms (3.3%)

series262.0ms (11.1%)

simplify63.0ms (2.7%)

prune686.0ms (29.2%)

regimes116.0ms (4.9%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample294.0ms (12.5%)

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