Details

analyze463.0ms

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
2.0ms	26×	body	80	invalid
1.0ms	24×	body	80	nan

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	138	24
1	138	24

prune9.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 6.2b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778))
0.1b	(* (- x 0.5) (log x))
0.1b	(+ (* (- x 0.5) (log x)) (+ 0.91893853320467 (- (/ (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) x) x)))
5.7b	(/ (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) x)

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

8.0ms	(* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778))
6.0ms	(* (- x 0.5) (log x))
23.0ms	(+ (* (- x 0.5) (log x)) (+ 0.91893853320467 (- (/ (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) x) x)))
12.0ms	(/ (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) x)

series79.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778))
24.0ms	(* (- x 0.5) (log x))
32.0ms	(+ (* (- x 0.5) (log x)) (+ 0.91893853320467 (- (/ (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) x) x)))
16.0ms	(/ (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) x)

simplify59.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5007	2239

prune268.0ms

Filtered

94 candidates to 117 candidates (-24.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	107	10	117
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	108	10	118

Merged error: 0.0b

Counts

118 → 10

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
5.7b	(/ (+ (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)) 0.083333333333333) x)

rewrite18.0ms

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)
13.0ms	(/ (+ (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)) 0.083333333333333) x)

series83.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(cbrt x)
21.0ms	(cbrt x)
22.0ms	(cbrt x)
16.0ms	(/ (+ (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)) 0.083333333333333) x)

simplify49.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4947	766
1	4947	766

prune149.0ms

Filtered

56 candidates to 74 candidates (-32.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	75	9	84

Merged error: 0.0b

Counts

84 → 9

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- x 0.5) (log (sqrt x)))
0.1b	(+ (* (- x 0.5) (log (sqrt x))) (+ (/ (+ (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)) 0.083333333333333) x) (+ (- 0.91893853320467 x) (* (- x 0.5) (log (sqrt x))))))
0.3b	(+ (- 0.91893853320467 x) (* (- x 0.5) (log (sqrt x))))
5.7b	(/ (+ (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)) 0.083333333333333) x)

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

40×	`frac-add`
36×	`log-prod`
30×	`add-sqr-sqrt` `associate-*l/`
28×	`*-un-lft-identity`
26×	`add-cube-cbrt`
23×	`add-log-exp`
21×	`flip3--` `flip--`
18×	`distribute-rgt-in` `distribute-lft-in` `sqrt-prod`
13×	`associate-+l+` `associate-+r+`
11×	`sum-log`
9×	`times-frac`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
7×	`flip3-+` `flip-+`
6×	`associate-r`
5×	`associate-l`
3×	`associate-/r` `log-pow` `associate-/l`
2×	`+-commutative` `associate-+l-` `associate-+r-` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 140

Calls

4 calls:

8.0ms	(* (- x 0.5) (log (sqrt x)))
27.0ms	(+ (* (- x 0.5) (log (sqrt x))) (+ (/ (+ (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)) 0.083333333333333) x) (+ (- 0.91893853320467 x) (* (- x 0.5) (log (sqrt x))))))
8.0ms	(+ (- 0.91893853320467 x) (* (- x 0.5) (log (sqrt x))))
11.0ms	(/ (+ (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)) 0.083333333333333) x)

series80.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* (- x 0.5) (log (sqrt x)))
41.0ms	(+ (* (- x 0.5) (log (sqrt x))) (+ (/ (+ (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)) 0.083333333333333) x) (+ (- 0.91893853320467 x) (* (- x 0.5) (log (sqrt x))))))
12.0ms	(+ (- 0.91893853320467 x) (* (- x 0.5) (log (sqrt x))))
20.0ms	(/ (+ (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)) 0.083333333333333) x)

simplify42.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	5009	4952

prune371.0ms

Filtered

117 candidates to 152 candidates (-29.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	151	1	152
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	152	9	161

Merged error: 0.0b

Counts

161 → 9

localize26.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt (- (* z (+ y 0.0007936500793651)) 0.0027777777777778))
1.0b	(cbrt (- (* z (+ y 0.0007936500793651)) 0.0027777777777778))
1.0b	(cbrt (- (* (+ y 0.0007936500793651) z) 0.0027777777777778))
5.7b	(/ (+ (* (* z (* (cbrt (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)) (cbrt (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)))) (cbrt (- (* (+ y 0.0007936500793651) z) 0.0027777777777778))) 0.083333333333333) x)

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

6.0ms	(cbrt (- (* z (+ y 0.0007936500793651)) 0.0027777777777778))
6.0ms	(cbrt (- (* z (+ y 0.0007936500793651)) 0.0027777777777778))
7.0ms	(cbrt (- (* (+ y 0.0007936500793651) z) 0.0027777777777778))
30.0ms	(/ (+ (* (* z (* (cbrt (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)) (cbrt (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)))) (cbrt (- (* (+ y 0.0007936500793651) z) 0.0027777777777778))) 0.083333333333333) x)

series76.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(cbrt (- (* z (+ y 0.0007936500793651)) 0.0027777777777778))
19.0ms	(cbrt (- (* z (+ y 0.0007936500793651)) 0.0027777777777778))
20.0ms	(cbrt (- (* (+ y 0.0007936500793651) z) 0.0027777777777778))
17.0ms	(/ (+ (* (* z (* (cbrt (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)) (cbrt (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)))) (cbrt (- (* (+ y 0.0007936500793651) z) 0.0027777777777778))) 0.083333333333333) x)

simplify67.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4955	1348
1	4955	1348

prune214.0ms

Filtered

71 candidates to 80 candidates (-12.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	80	9	89

Merged error: 0.0b

Counts

89 → 9

regimes348.0ms

Accuracy

96.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 5.8b

bsearch86.0ms

Steps

Iters	Range		Point
3	9768089789862.129	13049810350211.21	12844702815189.393

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	68
1	55	68

end0.0ms

analyze519.0ms

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

sample905.0ms

Algorithm

intervals

Results

559.0ms	8000×	body	80	valid
86.0ms	1220×	body	80	invalid
46.0ms	737×	body	80	nan

Details

analyze463.0ms

sample32.0ms

simplify5.0ms

prune9.0ms

localize17.0ms

rewrite53.0ms

series79.0ms

simplify59.0ms

prune268.0ms

localize24.0ms

rewrite18.0ms

series83.0ms

simplify49.0ms

prune149.0ms

localize21.0ms

rewrite60.0ms

series80.0ms

simplify42.0ms

prune371.0ms

localize26.0ms

rewrite51.0ms

series76.0ms

simplify67.0ms

prune214.0ms

regimes348.0ms

bsearch86.0ms

simplify1.0ms

end0.0ms

analyze519.0ms

sample905.0ms

Profiling