Details

analyze1.3s (15.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
3.1%	46.8%	50%	5
4.7%	45.3%	50%	6
5.5%	44.5%	50%	7
5.9%	44.1%	50%	8
6%	43.9%	50%	9
6.1%	43.8%	50%	10
6.2%	43.8%	50%	11
6.2%	43.7%	50%	12
6.2%	43.7%	50%	13
6.2%	43.7%	50%	14

sample164.0ms (1.9%)

Algorithm

1×

intervals

Results

104.0ms	110×	body	1280	valid
36.0ms	83×	body	640	valid
8.0ms	33×	body	320	valid
4.0ms	256×	pre	80	true
3.0ms	21×	body	160	valid
1.0ms	9×	body	80	valid

simplify58.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5257	9

prune8.0ms (0.1%)

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: 61.3b

Counts

2 → 1

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
7.2b	(log (- 1.0 x))
7.3b	(log (+ 1.0 x))

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
16×	`times-frac`
15×	`pow1` `add-cube-cbrt`
12×	`log-pow`
9×	`log-prod`
7×	`add-exp-log`
6×	`log-div`
5×	`add-cbrt-cube`
4×	`associate-/r` `associate-/l`
3×	`add-log-exp`
2×	`flip3--` `div-sub` `rem-log-exp` `flip--`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 69

Calls

3 calls:

6.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
3.0ms	(log (- 1.0 x))
3.0ms	(log (+ 1.0 x))

series20.0ms (0.2%)

Counts

3 → 9

Calls

3 calls:

14.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
3.0ms	(log (+ 1.0 x))
3.0ms	(log (- 1.0 x))

simplify41.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5003	1101

prune217.0ms (2.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	70	8	78
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	8	79

Merged error: 59.1b

Counts

79 → 8

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(* (* (/ x 1.0) (/ x 1.0)) -1/2)
0.0b	(/ (log (- 1.0 x)) (+ (* 1.0 x) (+ (log 1.0) (* (* (/ x 1.0) (/ x 1.0)) -1/2))))
7.2b	(log (- 1.0 x))

rewrite25.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-exp-log`
23×	`add-cbrt-cube`
17×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
14×	`add-cube-cbrt`
13×	`pow1`
12×	`times-frac`
9×	`prod-exp` `cbrt-unprod`
5×	`cbrt-undiv` `log-prod` `div-exp` `log-pow`
4×	`log-div` `associate-l/` `associate-/l`
3×	`associate-r` `pow-prod-down` `associate-/r*` `add-log-exp`
2×	`flip3--` `div-sub` `associate-/r/` `flip--`
1×	`frac-times` `frac-2neg` `flip3-+` `associate-r/` `rem-log-exp` `associate-l` `clear-num` `-commutative` `flip-+` `div-inv` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

3 → 79

Calls

3 calls:

10.0ms	(/ (log (- 1.0 x)) (+ (* 1.0 x) (+ (log 1.0) (* (* (/ x 1.0) (/ x 1.0)) -1/2))))
9.0ms	(* (* (/ x 1.0) (/ x 1.0)) -1/2)
3.0ms	(log (- 1.0 x))

series16.0ms (0.2%)

Counts

3 → 9

Calls

3 calls:

10.0ms	(/ (log (- 1.0 x)) (+ (* 1.0 x) (+ (log 1.0) (* (* (/ x 1.0) (/ x 1.0)) -1/2))))
3.0ms	(log (- 1.0 x))
3.0ms	(* (* (/ x 1.0) (/ x 1.0)) -1/2)

simplify31.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5086	1764

prune255.0ms (3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	93	3	96

Merged error: 0.0b

Counts

96 → 3

localize18.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b

(- (* x (/ (* x (/ -1/2 1.0)) 1.0)) (* 1.0 x))

0.0b

(* (* (/ x 1.0) (/ x 1.0)) -1/2)

0.0b

(/ (+ (log 1.0) (- (* x (/ (* x (/ -1/2 1.0)) 1.0)) (* 1.0 x))) (+ (* 1.0 x) (+ (log 1.0) (* (* (/ x 1.0) (/ x 1.0)) -1/2))))

rewrite36.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`*-un-lft-identity`
23×	`add-exp-log` `add-cbrt-cube`
15×	`add-sqr-sqrt` `times-frac`
14×	`add-cube-cbrt`
12×	`pow1`
9×	`prod-exp` `cbrt-unprod`
8×	`distribute-lft-out`
5×	`cbrt-undiv` `div-exp` `associate-/l*` `add-log-exp`
4×	`associate-*l/` `log-pow`
3×	`associate-r` `pow-prod-down` `associate-/r*`
2×	`flip3-+` `associate-/r/` `flip-+` `associate-/l/`
1×	`frac-times` `associate-+r-` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-sub` `associate-r/` `associate-l` `clear-num` `-commutative` `flip--` `div-inv` `unswap-sqr`

Counts

3 → 79

Calls

3 calls:

16.0ms

(/ (+ (log 1.0) (- (* x (/ (* x (/ -1/2 1.0)) 1.0)) (* 1.0 x))) (+ (* 1.0 x) (+ (log 1.0) (* (* (/ x 1.0) (/ x 1.0)) -1/2))))

9.0ms

(* (* (/ x 1.0) (/ x 1.0)) -1/2)

8.0ms

(- (* x (/ (* x (/ -1/2 1.0)) 1.0)) (* 1.0 x))

series17.0ms (0.2%)

Counts

3 → 9

Calls

3 calls:

8.0ms

(/ (+ (log 1.0) (- (* x (/ (* x (/ -1/2 1.0)) 1.0)) (* 1.0 x))) (+ (* 1.0 x) (+ (log 1.0) (* (* (/ x 1.0) (/ x 1.0)) -1/2))))

7.0ms

(- (* x (/ (* x (/ -1/2 1.0)) 1.0)) (* 1.0 x))

3.0ms

(* (* (/ x 1.0) (/ x 1.0)) -1/2)

simplify33.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5601	2146

prune305.0ms (3.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	86	2	88
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	87	4	91

Merged error: 0b

Counts

91 → 4

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (log 1.0) (* x (- (* (/ -1/2 1.0) (/ x 1.0)) 1.0))) (+ (log 1.0) (* x (+ (* (/ -1/2 1.0) (/ x 1.0)) 1.0))))
0.0b	(* x (- (* (/ -1/2 1.0) (/ x 1.0)) 1.0))
0.0b	(cbrt (pow (/ (+ (log 1.0) (* x (- (* (/ -1/2 1.0) (/ x 1.0)) 1.0))) (+ (log 1.0) (* x (+ (* (/ -1/2 1.0) (/ x 1.0)) 1.0)))) 3))
0.0b	(pow (/ (+ (log 1.0) (* x (- (* (/ -1/2 1.0) (/ x 1.0)) 1.0))) (+ (log 1.0) (* x (+ (* (/ -1/2 1.0) (/ x 1.0)) 1.0)))) 3)

rewrite42.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
45×	`times-frac`
44×	`add-cube-cbrt` `*-un-lft-identity`
36×	`cbrt-prod`
30×	`unpow-prod-down` `cube-prod`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
7×	`pow1`
6×	`flip3-+` `flip-+`
5×	`div-inv`
4×	`add-log-exp`
3×	`pow-unpow` `associate-r` `associate-l` `associate-/r` `associate-/l`
2×	`cbrt-undiv` `cube-div` `cube-mult` `sub-neg` `unpow3` `associate-*r/` `div-exp` `pow-exp` `associate-/l/` `rem-cube-cbrt` `sqr-pow`
1×	`distribute-rgt-in` `pow-to-exp` `cbrt-div` `flip3--` `pow-pow` `frac-2neg` `distribute-lft-in` `pow1/3` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `flip--` `rem-cbrt-cube` `cbrt-unprod` `unswap-sqr`

Counts

4 → 149

Calls

4 calls:

10.0ms	(* x (- (* (/ -1/2 1.0) (/ x 1.0)) 1.0))
10.0ms	(cbrt (pow (/ (+ (log 1.0) (* x (- (* (/ -1/2 1.0) (/ x 1.0)) 1.0))) (+ (log 1.0) (* x (+ (* (/ -1/2 1.0) (/ x 1.0)) 1.0)))) 3))
8.0ms	(pow (/ (+ (log 1.0) (* x (- (* (/ -1/2 1.0) (/ x 1.0)) 1.0))) (+ (log 1.0) (* x (+ (* (/ -1/2 1.0) (/ x 1.0)) 1.0)))) 3)
7.0ms	(/ (+ (log 1.0) (* x (- (* (/ -1/2 1.0) (/ x 1.0)) 1.0))) (+ (log 1.0) (* x (+ (* (/ -1/2 1.0) (/ x 1.0)) 1.0))))

series33.0ms (0.4%)

Counts

4 → 12

Calls

4 calls:

9.0ms	(pow (/ (+ (log 1.0) (* x (- (* (/ -1/2 1.0) (/ x 1.0)) 1.0))) (+ (log 1.0) (* x (+ (* (/ -1/2 1.0) (/ x 1.0)) 1.0)))) 3)
9.0ms	(/ (+ (log 1.0) (* x (- (* (/ -1/2 1.0) (/ x 1.0)) 1.0))) (+ (log 1.0) (* x (+ (* (/ -1/2 1.0) (/ x 1.0)) 1.0))))
8.0ms	(cbrt (pow (/ (+ (log 1.0) (* x (- (* (/ -1/2 1.0) (/ x 1.0)) 1.0))) (+ (log 1.0) (* x (+ (* (/ -1/2 1.0) (/ x 1.0)) 1.0)))) 3))
7.0ms	(* x (- (* (/ -1/2 1.0) (/ x 1.0)) 1.0))

simplify65.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5058	6164

prune771.0ms (9.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	161	0	161
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	161	4	165

Merged error: 0b

Counts

165 → 4

regimes39.0ms (0.5%)

Accuracy

Total 0.4b remaining (86.8%)

Threshold costs 0.4b (86.8%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	32
1	33	32

end0.0ms (0%)

sample4.9s (57.6%)

Algorithm

1×

intervals

Results

3.1s	3419×	body	1280	valid
1.1s	2493×	body	640	valid
278.0ms	1210×	body	320	valid
131.0ms	8000×	pre	80	true
86.0ms	646×	body	160	valid
13.0ms	232×	body	80	valid

Details

analyze1.3s (15.8%)

sample164.0ms (1.9%)

simplify58.0ms (0.7%)

prune8.0ms (0.1%)

localize7.0ms (0.1%)

rewrite14.0ms (0.2%)

series20.0ms (0.2%)

simplify41.0ms (0.5%)

prune217.0ms (2.6%)

localize12.0ms (0.1%)

rewrite25.0ms (0.3%)

series16.0ms (0.2%)

simplify31.0ms (0.4%)

prune255.0ms (3%)

localize18.0ms (0.2%)

rewrite36.0ms (0.4%)

series17.0ms (0.2%)

simplify33.0ms (0.4%)

prune305.0ms (3.6%)

localize16.0ms (0.2%)

rewrite42.0ms (0.5%)

series33.0ms (0.4%)

simplify65.0ms (0.8%)

prune771.0ms (9.1%)

regimes39.0ms (0.5%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample4.9s (57.6%)

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