Details

analyze237.0ms (5.1%)

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%	87.4%	12.6%	6
20.3%	59.3%	20.4%	7
21.1%	51.5%	27.4%	8
35.5%	30.4%	34%	9
35.7%	26.1%	38.1%	10
42.8%	15.4%	41.8%	11
42.9%	13.2%	44%	12
46.4%	7.8%	45.8%	13
46.4%	6.6%	47%	14

sample80.0ms (1.7%)

Algorithm

1×

intervals

Results

36.0ms	62×	body	1280	valid
16.0ms	46×	body	640	valid
12.0ms	120×	body	80	valid
5.0ms	22×	body	320	valid
1.0ms	6×	body	160	valid
0.0ms	4×	body	80	invalid
0.0ms	4×	body	80	overflowed

simplify43.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5720	27

prune11.0ms (0.2%)

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: 32.1b

Counts

2 → 2

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
0.0b	(* (- 1.0 eps) x)
0.0b	(* (+ 1.0 eps) x)
1.9b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

rewrite55.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`frac-sub`
76×	`exp-neg` `frac-times`
57×	`neg-sub0` `exp-diff`
42×	`associate-*l/`
38×	`associate-*r/`
31×	`flip3-+` `flip-+`
29×	`flip3--` `flip--`
19×	`un-div-inv`
18×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
13×	`associate-l`
10×	`pow1` `add-cube-cbrt` `add-cbrt-cube`
9×	`add-exp-log` `associate-r`
6×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`distribute-lft-out`
1×	`sub-neg` `diff-log` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 163

Calls

4 calls:

17.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))
12.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
8.0ms	(* (+ 1.0 eps) x)
6.0ms	(* (- 1.0 eps) x)

series68.0ms (1.5%)

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))
10.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
8.0ms	(* (+ 1.0 eps) x)
5.0ms	(* (- 1.0 eps) x)

simplify94.0ms (2%)

Algorithm

1×	egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5005	6596

prune772.0ms (16.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	172	3	175
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	174	3	177

Merged error: 0.2b

Counts

177 → 3

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.1b	(* (pow x 3) 0.6666666666666667)
5.8b	(+ (* (pow x 3) 0.6666666666666667) (- 2.0 (* 1.0 (* x x))))

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`associate-l`
7×	`add-exp-log` `add-log-exp`
6×	`add-cube-cbrt` `*-un-lft-identity`
4×	`unpow-prod-down` `cube-prod` `add-cbrt-cube` `unswap-sqr`
3×	`associate-r` `prod-exp`
2×	`pow1` `sum-log` `sqr-pow`
1×	`+-commutative` `cube-mult` `pow-to-exp` `associate-+r-` `sub-neg` `associate-+r+` `flip3-+` `diff-log` `unpow3` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`

Counts

2 → 45

Calls

2 calls:

7.0ms	(+ (* (pow x 3) 0.6666666666666667) (- 2.0 (* 1.0 (* x x))))
6.0ms	(* (pow x 3) 0.6666666666666667)

series8.0ms (0.2%)

Counts

2 → 6

Calls

2 calls:

4.0ms	(+ (* (pow x 3) 0.6666666666666667) (- 2.0 (* 1.0 (* x x))))
4.0ms	(* (pow x 3) 0.6666666666666667)

simplify55.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4959	458
1	4959	458

prune97.0ms (2.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	50	1	51
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	51	3	54

Merged error: 0.2b

Counts

54 → 3

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt x) (cbrt x))
0.7b	(cbrt x)
0.7b	(cbrt x)
5.8b	(+ (* (pow (* (cbrt x) (cbrt x)) 3) (* x 0.6666666666666667)) (- 2.0 (* 1.0 (* x x))))

rewrite19.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`cbrt-prod` `add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`add-log-exp`
8×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `unswap-sqr`
2×	`pow-prod-down` `sum-log` `pow-sqr` `pow-prod-up`
1×	`+-commutative` `pow2` `associate-+r-` `sub-neg` `associate-+r+` `flip3-+` `pow-plus` `diff-log` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+`

Counts

4 → 76

Calls

4 calls:

9.0ms	(+ (* (pow (* (cbrt x) (cbrt x)) 3) (* x 0.6666666666666667)) (- 2.0 (* 1.0 (* x x))))
6.0ms	(* (cbrt x) (cbrt x))
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series77.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (cbrt x) (cbrt x))
24.0ms	(cbrt x)
21.0ms	(cbrt x)
7.0ms	(+ (* (pow (* (cbrt x) (cbrt x)) 3) (* x 0.6666666666666667)) (- 2.0 (* 1.0 (* x x))))

simplify65.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4997	553
1	4997	553

prune148.0ms (3.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	88	3	91

Merged error: 0.2b

Counts

91 → 3

localize20.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(* (+ 1.0 eps) x)
1.6b	(exp (- (log (+ 1.0 (/ 1.0 eps))) (* (- 1.0 eps) x)))
2.2b	(log (+ 1.0 (/ 1.0 eps)))
16.2b	(- (exp (- (log (+ 1.0 (/ 1.0 eps))) (* (- 1.0 eps) x))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

rewrite41.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity`
13×	`exp-diff`
11×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `frac-sub`
8×	`log-prod` `add-log-exp`
7×	`pow1` `add-exp-log`
6×	`add-cbrt-cube`
5×	`exp-sum`
4×	`exp-neg` `frac-times` `flip3--` `associate-l` `associate-*l/` `associate--l+` `flip--`
3×	`neg-sub0` `exp-prod` `associate-r` `distribute-lft-out`
2×	`sub-neg` `log-div` `flip3-+` `diff-log` `associate-*r/` `flip-+` `rem-exp-log`
1×	`rem-log-exp` `pow-prod-down` `prod-exp` `log-pow` `un-div-inv` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 74

Calls

4 calls:

15.0ms	(- (exp (- (log (+ 1.0 (/ 1.0 eps))) (* (- 1.0 eps) x))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))
9.0ms	(exp (- (log (+ 1.0 (/ 1.0 eps))) (* (- 1.0 eps) x)))
8.0ms	(log (+ 1.0 (/ 1.0 eps)))
6.0ms	(* (+ 1.0 eps) x)

series43.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

26.0ms	(- (exp (- (log (+ 1.0 (/ 1.0 eps))) (* (- 1.0 eps) x))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))
10.0ms	(exp (- (log (+ 1.0 (/ 1.0 eps))) (* (- 1.0 eps) x)))
4.0ms	(* (+ 1.0 eps) x)
3.0ms	(log (+ 1.0 (/ 1.0 eps)))

simplify49.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4972	1529
1	4972	1529

prune233.0ms (5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	86	3	89

Merged error: 0.2b

Counts

89 → 3

regimes89.0ms (1.9%)

Accuracy

Total 0.5b remaining (58.4%)

Threshold costs 0.5b (58.4%)

bsearch89.0ms (1.9%)

Steps

Iters	Range		Point
10	8.333210867680476e-08	231781.61384385402	523.0649211994058

simplify12.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (11.0ms)

Iter	Nodes	Cost
0	592	63
1	592	63

end0.0ms (0%)

sample2.2s (47.1%)

Algorithm

1×

intervals

Results

989.0ms	1749×	body	1280	valid
443.0ms	1277×	body	640	valid
331.0ms	4050×	body	80	valid
156.0ms	639×	body	320	valid
44.0ms	285×	body	160	valid
17.0ms	202×	body	80	invalid
16.0ms	201×	body	80	overflowed
14.0ms	25×	body	1280	invalid
4.0ms	10×	body	640	invalid
1.0ms	5×	body	320	invalid
1.0ms	3×	body	160	invalid

Details

analyze237.0ms (5.1%)

sample80.0ms (1.7%)

simplify43.0ms (0.9%)

prune11.0ms (0.2%)

localize18.0ms (0.4%)

rewrite55.0ms (1.2%)

series68.0ms (1.5%)

simplify94.0ms (2%)

prune772.0ms (16.6%)

localize10.0ms (0.2%)

rewrite14.0ms (0.3%)

series8.0ms (0.2%)

simplify55.0ms (1.2%)

prune97.0ms (2.1%)

localize14.0ms (0.3%)

rewrite19.0ms (0.4%)

series77.0ms (1.7%)

simplify65.0ms (1.4%)

prune148.0ms (3.2%)

localize20.0ms (0.4%)

rewrite41.0ms (0.9%)

series43.0ms (0.9%)

simplify49.0ms (1.1%)

prune233.0ms (5%)

regimes89.0ms (1.9%)

bsearch89.0ms (1.9%)

simplify12.0ms (0.3%)

end0.0ms (0%)

sample2.2s (47.1%)

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