Details

analyze238.0ms (5.5%)

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

sample76.0ms (1.7%)

Algorithm

1×

intervals

Results

30.0ms	50×	body	1280	valid
17.0ms	47×	body	640	valid
10.0ms	125×	body	80	valid
7.0ms	29×	body	320	valid
1.0ms	5×	body	160	valid
1.0ms	9×	body	80	overflowed
1.0ms	7×	body	80	invalid
1.0ms	1×	body	1280	invalid

simplify53.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5720	27

prune12.0ms (0.3%)

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: 31.1b

Counts

2 → 2

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

rewrite47.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`frac-sub`
72×	`exp-neg` `frac-times`
54×	`neg-sub0` `exp-diff`
40×	`associate-*l/`
36×	`associate-*r/`
29×	`flip3--` `flip3-+` `flip--` `flip-+`
18×	`un-div-inv`
14×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`associate-l`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube` `add-log-exp`
6×	`associate-r`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`
1×	`+-commutative` `sub-neg` `diff-log` `sum-log` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 147

Calls

4 calls:

19.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))
6.0ms	(* (- 1.0 eps) x)
6.0ms	(* (+ 1.0 eps) x)
6.0ms	(+ 1.0 (/ 1.0 eps))

series60.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))
4.0ms	(* (- 1.0 eps) x)
4.0ms	(* (+ 1.0 eps) x)
3.0ms	(+ 1.0 (/ 1.0 eps))

simplify80.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5126	6250

prune696.0ms (15.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	155	4	159
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	157	4	161

Merged error: 0.6b

Counts

161 → 4

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.1b	(* (pow x 3) 0.6666666666666667)
6.8b	(- (+ (* (pow x 3) 0.6666666666666667) 2.0) (* 1.0 (* x x)))

rewrite15.0ms (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` `diff-log` `sqr-pow`
1×	`cube-mult` `pow-to-exp` `sub-neg` `flip3--` `unpow3` `pow-exp` `associate--l+` `sum-log` `*-commutative` `flip--` `cbrt-unprod`

Counts

2 → 44

Calls

2 calls:

8.0ms	(- (+ (* (pow x 3) 0.6666666666666667) 2.0) (* 1.0 (* x x)))
5.0ms	(* (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)

simplify27.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5346	457

prune104.0ms (2.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	48	2	50
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	48	6	54

Merged error: 0.6b

Counts

54 → 6

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(pow (+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0))) 3)
0.0b	(* (* x x) (- (* x 0.6666666666666667) 1.0))
3.8b	(cbrt (pow (+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0))) 3))

rewrite20.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cbrt-prod`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`unpow-prod-down` `cube-prod`
4×	`cube-div`
3×	`pow-unpow` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
2×	`cube-mult` `sub-neg` `cbrt-div` `flip3-+` `unpow3` `associate-*r/` `flip-+` `sqr-pow`
1×	`distribute-rgt-in` `pow-to-exp` `flip3--` `pow-pow` `distribute-lft-in` `pow1/3` `associate-l` `pow-exp` `*-commutative` `flip--` `rem-cbrt-cube` `rem-cube-cbrt` `unswap-sqr`

Counts

3 → 71

Calls

3 calls:

10.0ms	(* (* x x) (- (* x 0.6666666666666667) 1.0))
4.0ms	(pow (+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0))) 3)
4.0ms	(cbrt (pow (+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0))) 3))

series16.0ms (0.4%)

Counts

3 → 9

Calls

3 calls:

7.0ms	(* (* x x) (- (* x 0.6666666666666667) 1.0))
5.0ms	(pow (+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0))) 3)
4.0ms	(cbrt (pow (+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0))) 3))

simplify54.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4966	1202
1	4966	1202

prune165.0ms (3.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	78	2	80
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	80	6	86

Merged error: 0.6b

Counts

86 → 6

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.1b	(* (* x x) (- (* x 8.0) 12.0))
0.2b	(/ (cbrt (+ 8.0 (* (* x x) (- (* x 8.0) 12.0)))) 2.0)
10.2b	(cbrt (+ 8.0 (* (* x x) (- (* x 8.0) 12.0))))

rewrite18.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
20×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
15×	`cbrt-prod`
10×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
6×	`associate-/l*`
4×	`cbrt-div`
3×	`associate-r` `pow-prod-down` `prod-exp` `associate-/r*` `cbrt-unprod` `add-log-exp`
2×	`sub-neg` `flip3-+` `associate-*r/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `distribute-rgt-in` `flip3--` `frac-2neg` `distribute-lft-in` `pow1/3` `div-exp` `associate-l` `clear-num` `*-commutative` `flip--` `div-inv` `unswap-sqr`

Counts

3 → 77

Calls

3 calls:

9.0ms	(* (* x x) (- (* x 8.0) 12.0))
5.0ms	(/ (cbrt (+ 8.0 (* (* x x) (- (* x 8.0) 12.0)))) 2.0)
3.0ms	(cbrt (+ 8.0 (* (* x x) (- (* x 8.0) 12.0))))

series29.0ms (0.7%)

Counts

3 → 9

Calls

3 calls:

11.0ms	(/ (cbrt (+ 8.0 (* (* x x) (- (* x 8.0) 12.0)))) 2.0)
9.0ms	(cbrt (+ 8.0 (* (* x x) (- (* x 8.0) 12.0))))
8.0ms	(* (* x x) (- (* x 8.0) 12.0))

simplify57.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4945	1660
1	4945	1660

prune168.0ms (3.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	86	6	92

Merged error: 0.6b

Counts

92 → 6

regimes138.0ms (3.2%)

Accuracy

Total 0.6b remaining (61.2%)

Threshold costs 0.6b (61.2%)

bsearch77.0ms (1.8%)

Steps

Iters	Range		Point
9	0.24996242650620346	137710839.58421397	301.0358346712036

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	475	49
1	475	49

end0.0ms (0%)

sample2.2s (49.3%)

Algorithm

1×

intervals

Results

963.0ms	1752×	body	1280	valid
444.0ms	1244×	body	640	valid
325.0ms	4059×	body	80	valid
152.0ms	629×	body	320	valid
49.0ms	316×	body	160	valid
17.0ms	209×	body	80	invalid
16.0ms	202×	body	80	overflowed
12.0ms	22×	body	1280	invalid
6.0ms	14×	body	640	invalid
3.0ms	9×	body	320	invalid
0.0ms	2×	body	160	invalid

Details

analyze238.0ms (5.5%)

sample76.0ms (1.7%)

simplify53.0ms (1.2%)

prune12.0ms (0.3%)

localize18.0ms (0.4%)

rewrite47.0ms (1.1%)

series60.0ms (1.4%)

simplify80.0ms (1.8%)

prune696.0ms (15.9%)

localize9.0ms (0.2%)

rewrite15.0ms (0.3%)

series8.0ms (0.2%)

simplify27.0ms (0.6%)

prune104.0ms (2.4%)

localize10.0ms (0.2%)

rewrite20.0ms (0.5%)

series16.0ms (0.4%)

simplify54.0ms (1.2%)

prune165.0ms (3.8%)

localize9.0ms (0.2%)

rewrite18.0ms (0.4%)

series29.0ms (0.7%)

simplify57.0ms (1.3%)

prune168.0ms (3.9%)

regimes138.0ms (3.2%)

bsearch77.0ms (1.8%)

simplify9.0ms (0.2%)

end0.0ms (0%)

sample2.2s (49.3%)

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