Details

analyze464.0ms

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

sample34.0ms

Algorithm

intervals

Results

18.0ms	256×	body	80	valid
3.0ms	38×	body	80	invalid
1.0ms	18×	body	80	nan

simplify107.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (105.0ms)

Iter	Nodes	Cost
0	5577	24

prune14.0ms

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: 7.2b

Counts

2 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778))
0.1b	(+ (* (- x 0.5) (log x)) (+ 0.91893853320467 (- (/ (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) x) x)))
0.2b	(* (- x 0.5) (log x))
6.6b	(/ (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) x)

rewrite51.0ms

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:

9.0ms	(* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778))
21.0ms	(+ (* (- x 0.5) (log x)) (+ 0.91893853320467 (- (/ (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) x) x)))
6.0ms	(* (- x 0.5) (log x))
11.0ms	(/ (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) x)

series77.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778))
31.0ms	(+ (* (- x 0.5) (log x)) (+ 0.91893853320467 (- (/ (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) x) x)))
21.0ms	(* (- x 0.5) (log x))
18.0ms	(/ (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) x)

simplify67.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5114	2223

prune241.0ms

Filtered

93 candidates to 117 candidates (-25.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	109	8	117
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	111	8	119

Merged error: 0.3b

Counts

119 → 8

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
6.6b	(/ (+ (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)) 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)
11.0ms	(/ (+ (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)) 0.083333333333333) x)

series83.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(cbrt x)
22.0ms	(cbrt x)
23.0ms	(cbrt x)
16.0ms	(/ (+ (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)) 0.083333333333333) x)

simplify44.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5046	765

prune141.0ms

Filtered

56 candidates to 74 candidates (-32.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	72	2	74
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	73	9	82

Merged error: 0.3b

Counts

82 → 9

localize22.0ms

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)
6.6b	(/ (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) x)

rewrite32.0ms

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:

13.0ms	(+ (* (- x 0.5) (* 2 (log (cbrt x)))) (* (- x 0.5) (log (cbrt x))))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
13.0ms	(/ (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) x)

series166.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(+ (* (- x 0.5) (* 2 (log (cbrt x)))) (* (- x 0.5) (log (cbrt x))))
21.0ms	(cbrt x)
21.0ms	(cbrt x)
15.0ms	(/ (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) x)

simplify45.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5197	1465

prune231.0ms

Filtered

99 candidates to 115 candidates (-16.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

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

Merged error: 0.3b

Counts

124 → 9

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (log x))
0.5b	(cbrt (log x))
0.5b	(* (cbrt (log x)) (cbrt (log x)))
6.6b	(/ (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) x)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

32×	`cbrt-prod`
30×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
22×	`add-cube-cbrt`
19×	`pow1`
9×	`times-frac` `swap-sqr`
8×	`add-exp-log` `pow1/3` `log-pow`
7×	`associate-r` `associate-l`
6×	`add-cbrt-cube`
4×	`add-log-exp` `unswap-sqr`
3×	`associate-/r` `associate-/l`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up` `associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-2neg` `flip3-+` `pow-plus` `div-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `flip-+` `div-inv`

Counts

4 → 98

Calls

4 calls:

1.0ms	(cbrt (log x))
1.0ms	(cbrt (log x))
6.0ms	(* (cbrt (log x)) (cbrt (log x)))
11.0ms	(/ (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) x)

series124.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(cbrt (log x))
37.0ms	(cbrt (log x))
38.0ms	(* (cbrt (log x)) (cbrt (log x)))
15.0ms	(/ (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) x)

simplify51.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4913	1060
1	4913	1060

prune134.0ms

Filtered

75 candidates to 110 candidates (-46.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	110	9	119

Merged error: 0.3b

Counts

119 → 9

regimes332.0ms

Accuracy

96.1% (0.2b remaining)

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

bsearch28.0ms

Steps

Iters	Range		Point
8	44241928228.57051	19895120842163.76	70802251299.52406

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	110	77
1	110	77

end0.0ms

sample934.0ms

Algorithm

intervals

Results

568.0ms	8000×	body	80	valid
88.0ms	1184×	body	80	invalid
49.0ms	740×	body	80	nan

Details

analyze464.0ms

sample34.0ms

simplify107.0ms

prune14.0ms

localize16.0ms

rewrite51.0ms

series77.0ms

simplify67.0ms

prune241.0ms

localize24.0ms

rewrite16.0ms

series83.0ms

simplify44.0ms

prune141.0ms

localize22.0ms

rewrite32.0ms

series166.0ms

simplify45.0ms

prune231.0ms

localize24.0ms

rewrite23.0ms

series124.0ms

simplify51.0ms

prune134.0ms

regimes332.0ms

bsearch28.0ms

simplify2.0ms

end0.0ms

sample934.0ms

Profiling