Details

analyze450.0ms

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%	74.9%	25.1%	5
0%	74.9%	25.1%	6
0%	74.9%	25.1%	7
6.2%	56.2%	37.6%	8
7.8%	53%	39.2%	9
10.9%	45.6%	43.4%	10
18.3%	31.4%	50.3%	11
19.1%	29.5%	51.3%	12
21.4%	24.8%	53.8%	13
25.8%	16.7%	57.5%	14

sample32.0ms

Algorithm

intervals

Results

17.0ms	256×	body	80	valid
3.0ms	46×	body	80	invalid
1.0ms	22×	body	80	nan

simplify103.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (101.0ms)

Iter	Nodes	Cost
0	5577	24

prune11.0ms

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: 6.5b

Counts

2 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.2b	(* (- x 0.5) (log x))
0.2b	(- (* (- x 0.5) (log x)) x)
6.0b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
12×	`log-prod`
10×	`add-exp-log` `add-cbrt-cube`
9×	`pow1` `times-frac`
8×	`associate-l`
7×	`associate-r`
6×	`distribute-rgt-in` `distribute-lft-in` `associate--l+` `add-log-exp`
4×	`associate-*l/`
3×	`flip3--` `associate-/r` `flip--` `associate-/l`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `log-pow` `flip-+` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 95

Calls

4 calls:

8.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
7.0ms	(* (- x 0.5) (log x))
7.0ms	(- (* (- x 0.5) (log x)) x)
11.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series89.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
21.0ms	(* (- x 0.5) (log x))
38.0ms	(- (* (- x 0.5) (log x)) x)
21.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify58.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5026	1375

prune227.0ms

Filtered

83 candidates to 107 candidates (-28.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	95	12	107
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	97	12	109

Merged error: 0.0b

Counts

109 → 12

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
6.0b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
12.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series87.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt x)
21.0ms	(cbrt x)
21.0ms	(cbrt x)
23.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify56.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4934	765
1	4934	765

prune154.0ms

Filtered

58 candidates to 74 candidates (-27.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	75	11	86

Merged error: 0.0b

Counts

86 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- x 0.5) (log x))
0.2b	(- (* (- x 0.5) (log x)) x)
0.3b	(/ 1 (/ x (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333)))
6.0b	(/ x (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
66×	`add-sqr-sqrt`
64×	`*-un-lft-identity`
62×	`add-cube-cbrt`
19×	`add-exp-log`
18×	`associate-/r*`
13×	`add-cbrt-cube`
12×	`log-prod`
11×	`associate-/r/`
8×	`pow1` `div-exp`
6×	`distribute-rgt-in` `distribute-lft-in` `associate--l+` `div-inv` `associate-/l*` `add-log-exp`
5×	`flip3-+` `associate-l` `flip-+`
4×	`cbrt-undiv` `associate-r`
2×	`rec-exp` `flip3--` `frac-2neg` `1-exp` `associate-*l/` `clear-num` `flip--`
1×	`sub-neg` `pow-flip` `diff-log` `pow-prod-down` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `distribute-lft-out--` `inv-pow` `difference-of-squares` `unswap-sqr`

Counts

4 → 159

Calls

4 calls:

7.0ms	(* (- x 0.5) (log x))
7.0ms	(- (* (- x 0.5) (log x)) x)
14.0ms	(/ 1 (/ x (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333)))
11.0ms	(/ x (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333))

series116.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (- x 0.5) (log x))
35.0ms	(- (* (- x 0.5) (log x)) x)
22.0ms	(/ 1 (/ x (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333)))
35.0ms	(/ x (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333))

simplify76.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4968	3241
1	4968	3241

prune302.0ms

Filtered

120 candidates to 171 candidates (-42.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	171	11	182

Merged error: 0.0b

Counts

182 → 11

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* (log x) (- x 0.5)) x)
0.2b	(- (* (log x) (- x 0.5)) x)
0.4b	(* (sqrt (- (* (log x) (- x 0.5)) x)) (sqrt (- (* (log x) (- x 0.5)) x)))
6.0b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
20×	`add-cube-cbrt` `*-un-lft-identity`
19×	`pow1`
18×	`sqrt-prod`
12×	`sqrt-div`
9×	`times-frac`
8×	`add-exp-log` `flip3--` `sqrt-pow1` `pow1/2` `swap-sqr` `add-cbrt-cube` `flip--` `add-log-exp`
6×	`sub-neg` `associate-r` `associate-l`
5×	`pow-prod-up`
4×	`frac-times` `associate--l+` `unswap-sqr`
3×	`pow-prod-down` `associate-/r` `pow-sqr` `associate-/l`
2×	`distribute-rgt-in` `distribute-lft-in` `diff-log` `associate-r/` `associate-l/` `associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-2neg` `flip3-+` `pow-plus` `sqrt-unprod` `div-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `flip-+` `div-inv`

Counts

4 → 112

Calls

4 calls:

6.0ms	(- (* (log x) (- x 0.5)) x)
6.0ms	(- (* (log x) (- x 0.5)) x)
18.0ms	(* (sqrt (- (* (log x) (- x 0.5)) x)) (sqrt (- (* (log x) (- x 0.5)) x)))
11.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series130.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* (log x) (- x 0.5)) x)
35.0ms	(- (* (log x) (- x 0.5)) x)
38.0ms	(* (sqrt (- (* (log x) (- x 0.5)) x)) (sqrt (- (* (log x) (- x 0.5)) x)))
22.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify58.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5011	1788

prune224.0ms

Filtered

80 candidates to 124 candidates (-55.0%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	124	11	135

Merged error: 0.0b

Counts

135 → 11

regimes705.0ms

Accuracy

94.4% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 6.1b

bsearch22.0ms

Steps

Iters	Range		Point
7	103318.05877047259	18128939.965710558	9338607.118840637

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	95	65
1	95	65

end0.0ms

sample891.0ms

Algorithm

intervals

Results

544.0ms	8000×	body	80	valid
88.0ms	1226×	body	80	invalid
46.0ms	748×	body	80	nan

Details

analyze450.0ms

sample32.0ms

simplify103.0ms

prune11.0ms

localize19.0ms

rewrite36.0ms

series89.0ms

simplify58.0ms

prune227.0ms

localize24.0ms

rewrite16.0ms

series87.0ms

simplify56.0ms

prune154.0ms

localize18.0ms

rewrite46.0ms

series116.0ms

simplify76.0ms

prune302.0ms

localize22.0ms

rewrite46.0ms

series130.0ms

simplify58.0ms

prune224.0ms

regimes705.0ms

bsearch22.0ms

simplify2.0ms

end0.0ms

sample891.0ms

Profiling