Details

analyze500.0ms

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

sample21.0ms

Algorithm

intervals

Results

12.0ms

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

prune13.0ms

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: 17.6b

Counts

2 → 2

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 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)))
17.0b	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))

rewrite50.0ms

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` `distribute-rgt-in` `associate-+l+` `distribute-lft-in` `div-exp` `pow-prod-down` `*-commutative` `div-inv` `associate-/l/`
1×	`+-commutative` `frac-2neg` `clear-num` `sum-log`

Counts

4 → 100

Calls

4 calls:

6.0ms	(+ (* z (+ z 6.012459259764103)) 3.350343815022304)
6.0ms	(* z (+ (* z 0.0692910599291889) 0.4917317610505968))
17.0ms	(* y (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))
18.0ms	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))

series40.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(+ (* z (+ z 6.012459259764103)) 3.350343815022304)
5.0ms	(* z (+ (* z 0.0692910599291889) 0.4917317610505968))
26.0ms	(* y (/ (+ (* 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))

simplify32.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5407	1960

prune207.0ms

Filtered

85 candidates to 112 candidates (-31.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	106	6	112
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	108	6	114

Merged error: 0b

Counts

114 → 6

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))
17.0b	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))

rewrite79.0ms

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:

24.0ms	(* y (cbrt (pow (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304)) 3)))
15.0ms	(pow (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304)) 3)
17.0ms	(cbrt (pow (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304)) 3))
15.0ms	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))

series45.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* 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)
5.0ms	(cbrt (pow (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304)) 3))
5.0ms	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))

simplify58.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5291	4795

prune296.0ms

Filtered

112 candidates to 200 candidates (-78.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	200	0	200
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	200	6	206

Merged error: 0b

Counts

206 → 6

localize18.0ms

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))))
17.0b	(/ (+ (* 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:

7.0ms	(* z (+ (* z 0.0692910599291889) 0.4917317610505968))
20.0ms	(* y (exp (log (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))))
14.0ms	(exp (log (/ (+ (* 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))

series45.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* 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)))))
5.0ms	(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

97 candidates to 129 candidates (-33.0%)

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: 0b

Counts

135 → 6

localize20.0ms

Local error

Found 4 expressions with local error:

7.8b	(* (/ y (sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))) (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))))
16.2b	(sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
16.2b	(sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
16.3b	(/ (+ (* 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:

34.0ms	(* (/ 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))
15.0ms	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))

series42.0ms

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))
3.0ms	(sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
11.0ms	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))

simplify46.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5363	4141

prune350.0ms

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: 0b

Counts

168 → 6

regimes232.0ms

Accuracy

99.6% (0.1b remaining)

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

bsearch44.0ms

Steps

Iters	Range		Point
10	40996.60794223927	1938066891906217.0	499520.8894908489
10	-116638916481307.84	-3914.041477490829	-552517.0760122167

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	88	52
1	88	52

end0.0ms

sample561.0ms

Algorithm

intervals

Results

397.0ms

8000×

body

valid

Details

analyze500.0ms

sample21.0ms

simplify11.0ms

prune13.0ms

localize14.0ms

rewrite50.0ms

series40.0ms

simplify32.0ms

prune207.0ms

localize17.0ms

rewrite79.0ms

series45.0ms

simplify58.0ms

prune296.0ms

localize18.0ms

rewrite60.0ms

series45.0ms

simplify38.0ms

prune251.0ms

localize20.0ms

rewrite67.0ms

series42.0ms

simplify46.0ms

prune350.0ms

regimes232.0ms

bsearch44.0ms

simplify2.0ms

end0.0ms

sample561.0ms

Profiling