Details

analyze514.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
18.7%	81.1%	0.1%	7
21.8%	78%	0.1%	8
21.8%	78%	0.1%	9
49.1%	50.7%	0.1%	10
52.7%	47.2%	0.1%	11
52.7%	47.2%	0.1%	12
71.7%	28.2%	0.1%	13
74.1%	25.8%	0.1%	14

sample22.0ms

Algorithm

intervals

Results

13.0ms

256×

body

valid

simplify11.0ms

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: 17.4b

Counts

2 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (+ z 6.012459259764103))
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)))
16.8b	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 110

Calls

4 calls:

6.0ms	(* z (+ z 6.012459259764103))
6.0ms	(* z (+ (* z 0.0692910599291889) 0.4917317610505968))
16.0ms	(* y (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))
14.0ms	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))

series40.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify72.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4982	1944
1	4982	1944

prune214.0ms

Filtered

89 candidates to 122 candidates (-37.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	117	5	122
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	118	6	124

Merged error: 0.0b

Counts

124 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))) y)
0.3b	(* (* (sqrt (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))) y) (sqrt (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))))
16.8b	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
16.8b	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 134

Calls

4 calls:

16.0ms	(* (sqrt (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))) y)
29.0ms	(* (* (sqrt (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))) y) (sqrt (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))))
16.0ms	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
14.0ms	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))

series53.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (sqrt (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))) y)
14.0ms	(* (* (sqrt (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))) y) (sqrt (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))))
5.0ms	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
6.0ms	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))

simplify44.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5034	3589

prune418.0ms

Filtered

113 candidates to 146 candidates (-29.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	146	6	152

Merged error: 0.0b

Counts

152 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* z (+ (* z 0.0692910599291889) 0.4917317610505968))
0.1b	(* y (exp (log (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))))
0.5b	(exp (log (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))))
16.8b	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
32×	`log-prod` `exp-sum`
31×	`add-cube-cbrt` `*-un-lft-identity`
28×	`times-frac`
21×	`associate-r`
10×	`add-cbrt-cube`
9×	`pow1` `add-exp-log`
6×	`associate-l` `associate-/r/`
5×	`flip3-+` `flip-+`
4×	`exp-prod` `add-log-exp` `unswap-sqr`
3×	`associate-r/` `associate-/r` `div-inv` `associate-/l*`
2×	`log-div` `exp-diff` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `associate-/l/`
1×	`cbrt-undiv` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `div-exp` `clear-num` `log-pow` `rem-exp-log`

Counts

4 → 117

Calls

4 calls:

9.0ms	(* z (+ (* z 0.0692910599291889) 0.4917317610505968))
18.0ms	(* y (exp (log (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))))
13.0ms	(exp (log (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))))
15.0ms	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))

series42.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* z (+ (* z 0.0692910599291889) 0.4917317610505968))
24.0ms	(* y (exp (log (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))))
6.0ms	(exp (log (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))))
6.0ms	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))

simplify38.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5246	2587

prune251.0ms

Filtered

100 candidates to 129 candidates (-29.0%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	129	6	135

Merged error: 0.0b

Counts

135 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

9.0b	(* (/ y (sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))) (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))))
16.1b	(sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
16.1b	(sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
16.2b	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))

rewrite67.0ms

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:

35.0ms	(* (/ y (sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))) (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))))
6.0ms	(sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
6.0ms	(sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
14.0ms	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))

series39.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (/ y (sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))) (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))))
4.0ms	(sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
4.0ms	(sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
7.0ms	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))

simplify49.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5363	4141

prune355.0ms

Filtered

117 candidates to 162 candidates (-38.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	162	6	168

Merged error: 0.0b

Counts

168 → 6

regimes335.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 16.5b

bsearch39.0ms

Steps

Iters	Range		Point
9	83215.14908375134	70296017185.4883	255329.7025883972
9	-8.911420107790438e+21	-957827517889440.5	-8.971474415479851e+16

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	66	45
1	66	45

end0.0ms

sample597.0ms

Algorithm

intervals

Results

433.0ms

8000×

body

valid

Details

analyze514.0ms

sample22.0ms

simplify11.0ms

prune10.0ms

localize19.0ms

rewrite46.0ms

series40.0ms

simplify72.0ms

prune214.0ms

localize17.0ms

rewrite79.0ms

series53.0ms

simplify44.0ms

prune418.0ms

localize17.0ms

rewrite60.0ms

series42.0ms

simplify38.0ms

prune251.0ms

localize16.0ms

rewrite67.0ms

series39.0ms

simplify49.0ms

prune355.0ms

regimes335.0ms

bsearch39.0ms

simplify2.0ms

end0.0ms

sample597.0ms

Profiling