Details

analyze4.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

sample15.0ms

Algorithm

intervals

Results

10.0ms

256×

body

valid

simplify61.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4977	17
1	4977	17

prune4.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 0.99229 (* x 0.04481))
0.0b	(+ 2.30753 (* x 0.27061))
0.1b	(* (+ 0.99229 (* x 0.04481)) x)
12.0b	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1`
5×	`flip3-+` `flip-+`
3×	`associate-r` `associate-l` `associate-/r` `associate-/l`
2×	`+-commutative` `associate-*l/` `sum-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 73

Calls

4 calls:

3.0ms	(+ 0.99229 (* x 0.04481))
3.0ms	(+ 2.30753 (* x 0.27061))
5.0ms	(* (+ 0.99229 (* x 0.04481)) x)
6.0ms	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x)))

series17.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(+ 0.99229 (* x 0.04481))
3.0ms	(+ 2.30753 (* x 0.27061))
6.0ms	(* (+ 0.99229 (* x 0.04481)) x)
5.0ms	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x)))

simplify34.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5005	1145

prune120.0ms

Filtered

66 candidates to 85 candidates (-28.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	83	2	85
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	2	86

Merged error: 0b

Counts

86 → 2

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (+ 0.99229 (* x 0.04481)))
0.1b	(pow (* x (+ 0.99229 (* x 0.04481))) 3)
12.0b	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (cbrt (pow (* x (+ 0.99229 (* x 0.04481))) 3))))
33.3b	(cbrt (pow (* x (+ 0.99229 (* x 0.04481))) 3))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
17×	`add-cube-cbrt`
12×	`times-frac`
11×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
8×	`cbrt-prod`
6×	`associate-*r/`
5×	`flip3-+` `flip-+`
4×	`cube-div` `associate-/r*` `distribute-lft-out` `add-log-exp`
3×	`pow-unpow` `associate-r` `associate-l` `associate-/l*`
2×	`cube-mult` `unpow-prod-down` `cbrt-div` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `associate-/l/` `rem-cube-cbrt` `sqr-pow`
1×	`cbrt-undiv` `distribute-rgt-in` `pow-to-exp` `frac-2neg` `distribute-lft-in` `pow1/3` `div-exp` `clear-num` `*-commutative` `rem-cbrt-cube` `div-inv` `unswap-sqr`

Counts

4 → 100

Calls

4 calls:

5.0ms	(* x (+ 0.99229 (* x 0.04481)))
5.0ms	(pow (* x (+ 0.99229 (* x 0.04481))) 3)
8.0ms	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (cbrt (pow (* x (+ 0.99229 (* x 0.04481))) 3))))
2.0ms	(cbrt (pow (* x (+ 0.99229 (* x 0.04481))) 3))

series26.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* x (+ 0.99229 (* x 0.04481)))
4.0ms	(pow (* x (+ 0.99229 (* x 0.04481))) 3)
8.0ms	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (cbrt (pow (* x (+ 0.99229 (* x 0.04481))) 3))))
8.0ms	(cbrt (pow (* x (+ 0.99229 (* x 0.04481))) 3))

simplify32.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	6217	1572

prune167.0ms

Filtered

80 candidates to 112 candidates (-40.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	113	1	114

Merged error: 0b

Counts

114 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (pow x 3) (pow (+ 0.99229 (* x 0.04481)) 3))
0.1b	(pow (+ 0.99229 (* x 0.04481)) 3)
12.0b	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (cbrt (* (pow x 3) (pow (+ 0.99229 (* x 0.04481)) 3)))))
33.3b	(cbrt (* (pow x 3) (pow (+ 0.99229 (* x 0.04481)) 3)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
22×	`add-cube-cbrt`
19×	`add-exp-log`
17×	`unpow-prod-down` `cube-prod`
16×	`unswap-sqr`
12×	`times-frac` `associate-r` `associate-l`
11×	`sqr-pow`
9×	`prod-exp` `add-cbrt-cube`
7×	`pow-to-exp` `pow-exp`
6×	`cube-div`
5×	`pow1` `flip3-+` `flip-+`
4×	`associate-r/` `associate-/r` `distribute-lft-out` `add-log-exp`
3×	`cube-mult` `pow-unpow` `unpow3` `associate-/l*`
2×	`cbrt-div` `pow-prod-down` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `cbrt-prod` `pow-pow` `frac-2neg` `pow1/3` `div-exp` `clear-num` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `div-inv` `rem-cube-cbrt`

Counts

4 → 133

Calls

4 calls:

10.0ms	(* (pow x 3) (pow (+ 0.99229 (* x 0.04481)) 3))
4.0ms	(pow (+ 0.99229 (* x 0.04481)) 3)
7.0ms	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (cbrt (* (pow x 3) (pow (+ 0.99229 (* x 0.04481)) 3)))))
8.0ms	(cbrt (* (pow x 3) (pow (+ 0.99229 (* x 0.04481)) 3)))

series24.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (pow x 3) (pow (+ 0.99229 (* x 0.04481)) 3))
3.0ms	(pow (+ 0.99229 (* x 0.04481)) 3)
9.0ms	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (cbrt (* (pow x 3) (pow (+ 0.99229 (* x 0.04481)) 3)))))
9.0ms	(cbrt (* (pow x 3) (pow (+ 0.99229 (* x 0.04481)) 3)))

simplify41.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5140	2428

prune252.0ms

Filtered

91 candidates to 145 candidates (-59.3%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	145	1	146

Merged error: 0b

Counts

146 → 1

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	73	22
1	73	22

end0.0ms

sample416.0ms

Algorithm

intervals

Results

330.0ms

8000×

body

valid

Details

analyze4.0ms

sample15.0ms

simplify61.0ms

prune4.0ms

localize10.0ms

rewrite18.0ms

series17.0ms

simplify34.0ms

prune120.0ms

localize14.0ms

rewrite26.0ms

series26.0ms

simplify32.0ms

prune167.0ms

localize15.0ms

rewrite33.0ms

series24.0ms

simplify41.0ms

prune252.0ms

simplify2.0ms

end0.0ms

sample416.0ms

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