Details

analyze549.0ms

Algorithm: search

sample27.0ms

Algorithm

intervals

Results

15.0ms

256×

body

valid

simplify61.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	10
1	64	10
2	143	10
3	288	10
4	443	10
5	563	10
6	648	10
7	817	10
8	1060	10
9	1066	10
10	1066	10

prune3.0ms

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: 19.7b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
3.3b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
18.9b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

10.0ms	(+ x (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
6.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
9.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
14.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series114.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(+ x (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
6.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
11.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
26.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify73.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	534	840
1	2452	738
2	5003	738

prune151.0ms

Filtered

65 candidates to 91 candidates (-40.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	86	5	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	5	92

Merged error: 0b

Counts

92 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
0.1b	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
14.4b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

3.0ms	(+ x (* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
6.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
15.0ms	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
14.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series104.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(+ x (* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
6.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
26.0ms	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
6.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify71.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	554	1187
1	2427	1075
2	5002	1075

prune176.0ms

Filtered

80 candidates to 108 candidates (-35.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	108	5	113

Merged error: 0b

Counts

113 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

6.0b	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
13.9b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
13.9b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
13.9b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
66×	`times-frac`
47×	`add-cube-cbrt` `*-un-lft-identity`
42×	`sqrt-prod`
24×	`associate-r` `associate-l`
18×	`add-exp-log` `add-cbrt-cube`
10×	`sqrt-div`
9×	`unswap-sqr`
8×	`pow1`
6×	`flip3-+` `associate-/r*` `associate-/r/` `flip-+`
5×	`cbrt-undiv` `div-exp`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l/`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 150

Calls

4 calls:

32.0ms	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
8.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
6.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
14.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

series38.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
3.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
3.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
7.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

simplify86.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	720	2533
1	3090	2327
2	5002	2242

prune370.0ms

Filtered

116 candidates to 162 candidates (-39.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	162	5	167

Merged error: 0b

Counts

167 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
0.5b	(/ 1 (/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))))
3.3b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
18.8b	(/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

42×	`times-frac`
34×	`add-exp-log`
32×	`add-sqr-sqrt`
28×	`add-cube-cbrt` `*-un-lft-identity`
22×	`add-cbrt-cube`
14×	`div-exp`
12×	`associate-*r/`
11×	`associate-/r/`
10×	`associate-/r*`
9×	`pow1`
8×	`flip3-+` `flip-+`
7×	`cbrt-undiv`
6×	`associate-r` `associate-l` `prod-exp` `div-inv` `associate-/l*`
4×	`cbrt-unprod` `add-log-exp`
3×	`rec-exp` `1-exp`
2×	`frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `associate-/l/` `unswap-sqr`
1×	`distribute-rgt-in` `pow-flip` `distribute-lft-in` `inv-pow`

Counts

4 → 131

Calls

4 calls:

6.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
17.0ms	(/ 1 (/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))))
9.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
15.0ms	(/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)))

series43.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
13.0ms	(/ 1 (/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))))
11.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
13.0ms	(/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)))

simplify98.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	683	1682
1	3506	1493
2	5002	1448

prune187.0ms

Filtered

92 candidates to 143 candidates (-55.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	143	5	148

Merged error: 0b

Counts

148 → 5

regimes233.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 15.7b

bsearch200.0ms

Steps

Iters	Range		Point
5	669.6967484444802	2065.2582766853275	2029.4223314449496
8	-40371215918.7119	-6916210.485250052	-2033246127.3889399

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	15
1	46	15

end0.0ms

analyze745.0ms

Algorithm: search

sample640.0ms

Algorithm

intervals

Results

469.0ms

8000×

body

valid

Details

analyze549.0ms

sample27.0ms

simplify61.0ms

prune3.0ms

localize15.0ms

rewrite41.0ms

series114.0ms

simplify73.0ms

prune151.0ms

localize15.0ms

rewrite41.0ms

series104.0ms

simplify71.0ms

prune176.0ms

localize17.0ms

rewrite65.0ms

series38.0ms

simplify86.0ms

prune370.0ms

localize16.0ms

rewrite52.0ms

series43.0ms

simplify98.0ms

prune187.0ms

regimes233.0ms

bsearch200.0ms

simplify2.0ms

end0.0ms

analyze745.0ms

sample640.0ms

Profiling