Details

sample22.0ms

Algorithm

intervals

Results

10.0ms

256×

body

valid

simplify58.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

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: 20.7b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* z 0.0692910599291889) 0.4917317610505968)
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
4.7b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
19.7b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt` `*-un-lft-identity`
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` `associate-/l*`

Counts

4 → 78

Calls

4 calls:

4.0ms	(+ (* z 0.0692910599291889) 0.4917317610505968)
7.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
10.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
15.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series274.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ (* z 0.0692910599291889) 0.4917317610505968)
64.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
51.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
122.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify64.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	479	705
1	2236	601
2	5002	601

prune221.0ms

Filtered

90 candidates to 63 candidates (70.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	85	5	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	5	91

Merged error: 0.0b

Counts

91 → 5

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* z 0.0692910599291889) 0.4917317610505968)
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)))
16.3b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite45.0ms

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:

4.0ms	(+ (* z 0.0692910599291889) 0.4917317610505968)
7.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
17.0ms	(* 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))

series294.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (* z 0.0692910599291889) 0.4917317610505968)
69.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
123.0ms	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
68.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify73.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	499	1062
1	2187	948
2	5002	948

prune260.0ms

Filtered

108 candidates to 78 candidates (72.2%)

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: 0.0b

Counts

113 → 5

localize21.0ms

Local error

Found 4 expressions with local error:

8.1b	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
15.7b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
15.7b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
15.7b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

rewrite68.0ms

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:

34.0ms	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* 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))
16.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

series350.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
53.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
48.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
126.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

simplify105.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (70.0ms)

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

prune450.0ms

Filtered

162 candidates to 115 candidates (71.0%)

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: 0.0b

Counts

167 → 5

localize217.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
0.3b	(/ 1 (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
4.7b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
19.9b	(* (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (/ 1 (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

rewrite49.0ms

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×	`cbrt-unprod`
7×	`associate-r/` `associate-l*`
6×	`flip3-+` `div-exp` `flip-+`
5×	`pow-prod-down`
4×	`associate-*l/` `associate-/r/` `add-log-exp`
3×	`cbrt-undiv` `rec-exp` `1-exp` `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:

7.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
8.0ms	(/ 1 (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
10.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
20.0ms	(* (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (/ 1 (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

series278.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
37.0ms	(/ 1 (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
55.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
121.0ms	(* (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (/ 1 (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

simplify90.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	664	1171
1	3527	993
2	5001	966

prune239.0ms

Filtered

131 candidates to 77 candidates (58.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	131	5	136

Merged error: 0.0b

Counts

136 → 5

regimes138.0ms

Accuracy

98.4% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 16.4b

bsearch143.0ms

Steps

Iters	Range		Point
9	4.1340642299952195e-15	2.731921632534707e-06	2.6774044712547526e-06
8	-4255728308.2891407	-7888799.454350161	-9923844.034724582

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	19
1	53	19

end0.0ms

sample487.0ms

Algorithm

intervals

Results

323.0ms

8000×

body

valid

Details

sample22.0ms

simplify58.0ms

prune3.0ms

localize14.0ms

rewrite37.0ms

series274.0ms

simplify64.0ms

prune221.0ms

localize19.0ms

rewrite45.0ms

series294.0ms

simplify73.0ms

prune260.0ms

localize21.0ms

rewrite68.0ms

series350.0ms

simplify105.0ms

prune450.0ms

localize217.0ms

rewrite49.0ms

series278.0ms

simplify90.0ms

prune239.0ms

regimes138.0ms

bsearch143.0ms

simplify2.0ms

end0.0ms

sample487.0ms

Profiling