Details

sample37.0ms

Algorithm

intervals

Results

19.0ms

256×

body

valid

simplify41.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	55	18
1	138	18
2	450	18
3	1597	18
4	5001	18

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 26.7b

Counts

2 → 1

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
0.1b	(* (+ (* x 4.16438922228) 78.6994924154) x)
0.1b	(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
25.9b	(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

9.0ms	(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
7.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
10.0ms	(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
29.0ms	(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

series375.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
60.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
45.0ms	(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
231.0ms	(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

simplify84.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	664	1209
1	3268	1044
2	5001	1044

prune387.0ms

Filtered

103 candidates to 74 candidates (71.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	98	5	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	99	5	104

Merged error: 0.1b

Counts

104 → 5

localize25.0ms

Local error

Found 4 expressions with local error:

8.0b	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
15.0b	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
15.2b	(* (/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))))
21.4b	(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

126×	`add-sqr-sqrt`
108×	`times-frac`
95×	`*-un-lft-identity`
69×	`add-cube-cbrt`
63×	`sqrt-prod`
36×	`associate-l`
24×	`associate-r`
20×	`add-exp-log` `add-cbrt-cube`
13×	`distribute-lft-out--` `difference-of-squares`
12×	`associate-/r*`
10×	`sqrt-div`
9×	`unswap-sqr`
8×	`associate-/r/` `associate-/l*`
7×	`pow1`
6×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+`
4×	`prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `flip--`

Counts

4 → 205

Calls

4 calls:

12.0ms	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
17.0ms	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
56.0ms	(* (/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))))
31.0ms	(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))

series742.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
127.0ms	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
239.0ms	(* (/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))))
310.0ms	(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))

simplify128.0ms

Algorithm

egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	894	5675
1	3611	5204
2	5001	5070

prune809.0ms

Filtered

217 candidates to 141 candidates (65.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	214	3	217
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	214	8	222

Merged error: 0.1b

Counts

222 → 8

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (+ (* (+ x 43.3400022514) x) 263.505074721)) (* (sqrt (+ (* (+ x 43.3400022514) x) 263.505074721)) x))
14.9b	(sqrt (+ (* (+ x 43.3400022514) x) 263.505074721))
14.9b	(sqrt (+ (* (+ x 43.3400022514) x) 263.505074721))
25.9b	(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (sqrt (+ (* (+ x 43.3400022514) x) 263.505074721)) (* (sqrt (+ (* (+ x 43.3400022514) x) 263.505074721)) x)) 313.399215894) x) 47.066876606))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

17.0ms	(* (sqrt (+ (* (+ x 43.3400022514) x) 263.505074721)) (* (sqrt (+ (* (+ x 43.3400022514) x) 263.505074721)) x))
6.0ms	(sqrt (+ (* (+ x 43.3400022514) x) 263.505074721))
7.0ms	(sqrt (+ (* (+ x 43.3400022514) x) 263.505074721))
44.0ms	(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (sqrt (+ (* (+ x 43.3400022514) x) 263.505074721)) (* (sqrt (+ (* (+ x 43.3400022514) x) 263.505074721)) x)) 313.399215894) x) 47.066876606))

series378.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (sqrt (+ (* (+ x 43.3400022514) x) 263.505074721)) (* (sqrt (+ (* (+ x 43.3400022514) x) 263.505074721)) x))
54.0ms	(sqrt (+ (* (+ x 43.3400022514) x) 263.505074721))
48.0ms	(sqrt (+ (* (+ x 43.3400022514) x) 263.505074721))
241.0ms	(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (sqrt (+ (* (+ x 43.3400022514) x) 263.505074721)) (* (sqrt (+ (* (+ x 43.3400022514) x) 263.505074721)) x)) 313.399215894) x) 47.066876606))

simplify78.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	606	1679
1	2577	1424
2	5001	1408

prune435.0ms

Filtered

102 candidates to 77 candidates (75.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	102	8	110

Merged error: 0.1b

Counts

110 → 8

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (* x 4.16438922228) 78.6994924154) x)
0.1b	(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
0.2b	(/ 1 (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
26.2b	(* (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (/ 1 (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-exp-log`
27×	`add-sqr-sqrt`
23×	`add-cube-cbrt` `*-un-lft-identity`
22×	`add-cbrt-cube`
21×	`associate-r`
18×	`times-frac`
16×	`frac-times` `associate-*l/`
14×	`pow1` `prod-exp`
10×	`flip3-+` `flip-+`
8×	`cbrt-unprod`
7×	`associate-l`
6×	`flip3--` `div-exp` `flip--`
5×	`associate-*r/` `pow-prod-down`
4×	`associate-/r/` `add-log-exp`
3×	`cbrt-undiv` `rec-exp` `1-exp` `associate-/r` `-commutative` `associate-/l*`
2×	`div-inv` `unswap-sqr`
1×	`pow-flip` `frac-2neg` `clear-num` `un-div-inv` `inv-pow`

Counts

4 → 129

Calls

4 calls:

7.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
10.0ms	(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
13.0ms	(/ 1 (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
33.0ms	(* (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (/ 1 (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))

series402.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
41.0ms	(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
56.0ms	(/ 1 (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
237.0ms	(* (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (/ 1 (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))

simplify47.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	912	2198
1	5001	1924

prune459.0ms

Filtered

141 candidates to 91 candidates (64.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	140	1	141
Fresh	3	2	5
Picked	0	1	1
Done	0	2	2
Total	143	6	149

Merged error: 0.1b

Counts

149 → 6

Details

sample37.0ms

simplify41.0ms

prune4.0ms

localize27.0ms

rewrite58.0ms

series375.0ms

simplify84.0ms

prune387.0ms

localize25.0ms

rewrite127.0ms

series742.0ms

simplify128.0ms

prune809.0ms

localize25.0ms

rewrite77.0ms

series378.0ms

simplify78.0ms

prune435.0ms

localize30.0ms

rewrite68.0ms

series402.0ms

simplify47.0ms

prune459.0ms

regimes234.0ms

bsearch9.0ms

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