Details

analyze468.0ms

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

sample33.0ms

Algorithm

intervals

Results

17.0ms	256×	body	80	valid
3.0ms	42×	body	80	invalid
1.0ms	21×	body	80	nan

simplify106.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (104.0ms)

Iter	Nodes	Cost
0	5577	24

prune8.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 5.0b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (- x 0.5) (log x)) x)
0.2b	(* (- x 0.5) (log x))
0.2b	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
4.5b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

8.0ms	(- (* (- x 0.5) (log x)) x)
7.0ms	(* (- x 0.5) (log x))
10.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
11.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series113.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (* (- x 0.5) (log x)) x)
21.0ms	(* (- x 0.5) (log x))
37.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
21.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify48.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5109	1424

prune216.0ms

Filtered

88 candidates to 108 candidates (-22.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	98	10	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	99	10	109

Merged error: 0.0b

Counts

109 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- x 0.5) (log (sqrt x)))
0.2b	(* (- x 0.5) (log (sqrt x)))
0.3b	(+ (* (- x 0.5) (log (sqrt x))) (+ 0.91893853320467 (- (* (- x 0.5) (log (sqrt x))) x)))
4.5b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 134

Calls

4 calls:

7.0ms	(* (- x 0.5) (log (sqrt x)))
8.0ms	(* (- x 0.5) (log (sqrt x)))
15.0ms	(+ (* (- x 0.5) (log (sqrt x))) (+ 0.91893853320467 (- (* (- x 0.5) (log (sqrt x))) x)))
11.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series51.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* (- x 0.5) (log (sqrt x)))
7.0ms	(* (- x 0.5) (log (sqrt x)))
16.0ms	(+ (* (- x 0.5) (log (sqrt x))) (+ 0.91893853320467 (- (* (- x 0.5) (log (sqrt x))) x)))
21.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify38.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5548	2433

prune249.0ms

Filtered

105 candidates to 146 candidates (-39.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	145	1	146
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	147	9	156

Merged error: 0.0b

Counts

156 → 9

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (* (- x 0.5) (* 2 (log (cbrt x)))) (* (- x 0.5) (log (cbrt x))))
0.6b	(cbrt x)
0.6b	(cbrt x)
4.5b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

36×	`log-prod`
30×	`distribute-rgt-in` `distribute-lft-in`
26×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
24×	`cbrt-prod` `associate-+l+`
12×	`associate-+r+`
9×	`times-frac`
8×	`associate-*l/`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `flip3--` `frac-add` `flip--`
3×	`associate-/r` `associate-/l`
2×	`flip3-+` `pow1/3` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv` `distribute-lft-out`

Counts

4 → 103

Calls

4 calls:

14.0ms	(+ (* (- x 0.5) (* 2 (log (cbrt x)))) (* (- x 0.5) (log (cbrt x))))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
11.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series168.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(+ (* (- x 0.5) (* 2 (log (cbrt x)))) (* (- x 0.5) (log (cbrt x))))
21.0ms	(cbrt x)
21.0ms	(cbrt x)
21.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify45.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5165	1465

prune231.0ms

Filtered

98 candidates to 115 candidates (-17.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	114	1	115
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	115	9	124

Merged error: 0.0b

Counts

124 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (log x) (- x 0.5))
0.2b	(+ (* (sqrt (- (* (log x) (- x 0.5)) x)) (sqrt (- (* (log x) (- x 0.5)) x))) 0.91893853320467)
0.5b	(* (sqrt (- (* (log x) (- x 0.5)) x)) (sqrt (- (* (log x) (- x 0.5)) x)))
4.5b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
22×	`pow1` `add-cube-cbrt`
18×	`sqrt-prod`
12×	`sqrt-div`
11×	`associate-r`
10×	`add-exp-log` `associate-l` `add-cbrt-cube`
9×	`times-frac`
8×	`sqrt-pow1` `pow1/2` `swap-sqr`
7×	`flip3--` `flip--`
6×	`add-log-exp`
5×	`pow-prod-up` `unswap-sqr`
4×	`frac-times` `associate-*r/` `pow-prod-down`
3×	`associate-/r` `pow-sqr` `associate-/l`
2×	`sub-neg` `flip3-+` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `pow2` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-plus` `sqrt-unprod` `div-exp` `clear-num` `sum-log` `rem-square-sqrt` `log-pow` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 122

Calls

4 calls:

6.0ms	(* (log x) (- x 0.5))
16.0ms	(+ (* (sqrt (- (* (log x) (- x 0.5)) x)) (sqrt (- (* (log x) (- x 0.5)) x))) 0.91893853320467)
16.0ms	(* (sqrt (- (* (log x) (- x 0.5)) x)) (sqrt (- (* (log x) (- x 0.5)) x)))
13.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series112.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (log x) (- x 0.5))
34.0ms	(+ (* (sqrt (- (* (log x) (- x 0.5)) x)) (sqrt (- (* (log x) (- x 0.5)) x))) 0.91893853320467)
36.0ms	(* (sqrt (- (* (log x) (- x 0.5)) x)) (sqrt (- (* (log x) (- x 0.5)) x)))
21.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify67.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5041	1849

prune198.0ms

Filtered

84 candidates to 134 candidates (-59.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	134	9	143

Merged error: 0.0b

Counts

143 → 9

regimes582.0ms

Accuracy

95.8% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 6.0b

bsearch31.0ms

Steps

Iters	Range		Point
9	0.03951628308809181	360984.35702539235	331400.32504989253

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	104	72
1	104	72

end0.0ms

sample913.0ms

Algorithm

intervals

Results

545.0ms	8000×	body	80	valid
88.0ms	1311×	body	80	invalid
51.0ms	785×	body	80	nan

Details

analyze468.0ms

sample33.0ms

simplify106.0ms

prune8.0ms

localize21.0ms

rewrite38.0ms

series113.0ms

simplify48.0ms

prune216.0ms

localize21.0ms

rewrite45.0ms

series51.0ms

simplify38.0ms

prune249.0ms

localize21.0ms

rewrite33.0ms

series168.0ms

simplify45.0ms

prune231.0ms

localize19.0ms

rewrite55.0ms

series112.0ms

simplify67.0ms

prune198.0ms

regimes582.0ms

bsearch31.0ms

simplify2.0ms

end0.0ms

sample913.0ms

Profiling