Details

sample31.0ms

Algorithm

intervals

Results

13.0ms

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

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: 23.2b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ z 6.012459259764103) z)
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
4.1b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
23.0b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

9.0ms	(* (+ z 6.012459259764103) z)
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))

series279.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (+ z 6.012459259764103) z)
62.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
54.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
118.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify69.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	525	728
1	2508	623
2	5001	623

prune369.0ms

Filtered

100 candidates to 68 candidates (68.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	96	4	100
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	97	4	101

Merged error: 0b

Counts

101 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ z 6.012459259764103) z)
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)))
18.3b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
24×	`add-cube-cbrt`
21×	`associate-r`
19×	`times-frac`
15×	`add-exp-log` `add-cbrt-cube`
10×	`pow1` `associate-l`
5×	`flip3-+` `flip-+`
4×	`associate-*l/` `prod-exp` `associate-/r/` `cbrt-unprod` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `associate-/r` `-commutative` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `div-inv` `associate-/l/`
1×	`frac-2neg` `associate-*r/` `clear-num` `distribute-lft-out`

Counts

4 → 106

Calls

4 calls:

5.0ms	(* (+ z 6.012459259764103) z)
6.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
18.0ms	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
13.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series290.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (+ z 6.012459259764103) z)
65.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
121.0ms	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
63.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify69.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	545	1085
1	2456	970
2	5002	970

prune428.0ms

Filtered

118 candidates to 84 candidates (71.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	118	4	122

Merged error: 0b

Counts

122 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

7.7b	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
17.0b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
17.6b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
17.6b	(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:

31.0ms	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
17.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
6.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
6.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series344.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
121.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
49.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
55.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify83.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (59.0ms)

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

prune659.0ms

Filtered

162 candidates to 115 candidates (71.0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	162	4	166

Merged error: 0b

Counts

166 → 4

localize19.0ms

Local error

Found 4 expressions with local error:

16.3b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (* (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)) (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
18.2b	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
18.2b	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
18.2b	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

23.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (* (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)) (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
5.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
5.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
9.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series660.0ms

Counts

4 → 12

Calls

4 calls:

334.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (* (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)) (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
114.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
105.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
106.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify56.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	524	1129
1	2047	976
2	5002	967

prune437.0ms

Filtered

82 candidates to 68 candidates (82.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	82	4	86

Merged error: 0b

Counts

86 → 4

regimes233.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 16.4b

bsearch153.0ms

Steps

Iters	Range		Point
10	1.8814443039852147e-08	114238954.84408061	709659.872836454
6	-8873168495547579.0	-1035328379673980.5	-1908715664828292.0

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	19
1	53	19

end0.0ms

sample698.0ms

Algorithm

intervals

Results

403.0ms

8000×

body

valid

Details

sample31.0ms

simplify61.0ms

prune4.0ms

localize14.0ms

rewrite40.0ms

series279.0ms

simplify69.0ms

prune369.0ms

localize14.0ms

rewrite46.0ms

series290.0ms

simplify69.0ms

prune428.0ms

localize17.0ms

rewrite65.0ms

series344.0ms

simplify83.0ms

prune659.0ms

localize19.0ms

rewrite45.0ms

series660.0ms

simplify56.0ms

prune437.0ms

regimes233.0ms

bsearch153.0ms

simplify1.0ms

end0.0ms

sample698.0ms

Profiling