Details

sample29.0ms

Algorithm

intervals

Results

13.0ms

256×

body

valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	452	21
1	452	21

prune10.0ms

Filtered

1 candidates to 1 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: 17.1b

Counts

2 → 2

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (* y (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))))
0.1b	(* z (+ (* z 0.0692910599291889) 0.4917317610505968))
0.1b	(* y (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))
16.6b	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 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×	`associate-r/` `prod-exp` `associate-/r` `cbrt-unprod` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv` `associate-/l/`
1×	`+-commutative` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `sum-log`

Counts

4 → 98

Calls

4 calls:

3.0ms	(+ x (* y (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))))
6.0ms	(* z (+ (* z 0.0692910599291889) 0.4917317610505968))
15.0ms	(* y (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))
13.0ms	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))

series106.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(+ x (* y (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))))
6.0ms	(* z (+ (* z 0.0692910599291889) 0.4917317610505968))
24.0ms	(* y (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))
8.0ms	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))

simplify35.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5595	2166

prune201.0ms

Filtered

86 candidates to 110 candidates (-27.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	106	4	110
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	108	4	112

Merged error: 0.0b

Counts

112 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* y (cbrt (pow (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304)) 3)))
0.5b	(pow (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304)) 3)
0.5b	(cbrt (pow (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304)) 3))
16.6b	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

78×	`cbrt-prod`
74×	`add-sqr-sqrt`
65×	`times-frac`
59×	`add-cube-cbrt` `*-un-lft-identity`
47×	`unpow-prod-down` `cube-prod`
39×	`associate-r`
14×	`associate-/r/`
11×	`add-exp-log`
10×	`add-cbrt-cube`
8×	`flip3-+` `flip-+`
7×	`pow1` `div-inv` `unswap-sqr`
4×	`add-log-exp` `sqr-pow`
3×	`cube-div` `cube-mult` `pow-unpow` `unpow3` `associate-l` `associate-/r` `associate-/l`
2×	`cbrt-undiv` `cbrt-div` `div-exp` `pow-exp` `associate-/l/` `rem-cube-cbrt`
1×	`pow-to-exp` `pow-pow` `frac-2neg` `pow1/3` `associate-r/` `pow-prod-down` `prod-exp` `clear-num` `-commutative` `rem-cbrt-cube` `cbrt-unprod`

Counts

4 → 188

Calls

4 calls:

23.0ms	(* y (cbrt (pow (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304)) 3)))
16.0ms	(pow (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304)) 3)
14.0ms	(cbrt (pow (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304)) 3))
14.0ms	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))

series45.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* y (cbrt (pow (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304)) 3)))
6.0ms	(pow (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304)) 3)
6.0ms	(cbrt (pow (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304)) 3))
6.0ms	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))

simplify57.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5177	4795

prune290.0ms

Filtered

114 candidates to 200 candidates (-75.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	200	0	200
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	200	4	204

Merged error: 0.0b

Counts

204 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

7.4b	(* (* (sqrt (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525)) y) (/ (sqrt (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525)) (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))
15.9b	(sqrt (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525))
15.9b	(sqrt (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525))
16.4b	(/ (sqrt (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525)) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 121

Calls

4 calls:

25.0ms	(* (* (sqrt (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525)) y) (/ (sqrt (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525)) (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))
9.0ms	(sqrt (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525))
6.0ms	(sqrt (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525))
14.0ms	(/ (sqrt (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525)) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))

series32.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(* (* (sqrt (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525)) y) (/ (sqrt (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525)) (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))
5.0ms	(sqrt (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525))
5.0ms	(sqrt (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525))
9.0ms	(/ (sqrt (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525)) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))

simplify42.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5081	3210

prune284.0ms

Filtered

96 candidates to 133 candidates (-38.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	133	0	133
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	133	4	137

Merged error: 0.0b

Counts

137 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* z (+ (* z 0.0692910599291889) 0.4917317610505968))
0.5b	(/ 1 (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
4.0b	(* (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) y)
18.9b	(* (* (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) y) (/ 1 (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))

rewrite45.0ms

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

Counts

4 → 119

Calls

4 calls:

6.0ms	(* z (+ (* z 0.0692910599291889) 0.4917317610505968))
7.0ms	(/ 1 (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
9.0ms	(* (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) y)
18.0ms	(* (* (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) y) (/ 1 (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))

series32.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(* z (+ (* z 0.0692910599291889) 0.4917317610505968))
3.0ms	(/ 1 (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
10.0ms	(* (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) y)
13.0ms	(* (* (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) y) (/ 1 (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))

simplify60.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5087	1942

prune156.0ms

Filtered

81 candidates to 131 candidates (-61.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	131	4	135

Merged error: 0.0b

Counts

135 → 4

regimes219.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 16.8b

bsearch32.0ms

Steps

Iters	Range		Point
6	0.003810670139712195	0.05773528338420037	0.05678399775022533
8	-5.072318464120713e+31	-3.2886569076271447e+28	-3.329625278298736e+28

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	44
1	49	44

end0.0ms

sample690.0ms

Algorithm

intervals

Results

400.0ms

8000×

body

valid

Details

sample29.0ms

simplify10.0ms

prune10.0ms

localize14.0ms

rewrite41.0ms

series106.0ms

simplify35.0ms

prune201.0ms

localize17.0ms

rewrite74.0ms

series45.0ms

simplify57.0ms

prune290.0ms

localize17.0ms

rewrite57.0ms

series32.0ms

simplify42.0ms

prune284.0ms

localize15.0ms

rewrite45.0ms

series32.0ms

simplify60.0ms

prune156.0ms

regimes219.0ms

bsearch32.0ms

simplify1.0ms

end0.0ms

sample690.0ms

Profiling