Details

analyze467.0ms

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
2.0ms	36×	body	80	invalid
2.0ms	30×	body	80	nan

simplify107.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (105.0ms)

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: 5.5b

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))
5.0b	(/ (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) x)

rewrite54.0ms

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)))
7.0ms	(* (- x 0.5) (log x))
14.0ms	(/ (+ (* 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))
35.0ms	(+ (* (- 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))
16.0ms	(/ (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) x)

simplify66.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5114	2223

prune261.0ms

Filtered

93 candidates to 117 candidates (-25.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	105	12	117
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	107	12	119

Merged error: 0.3b

Counts

119 → 12

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.5b	(cbrt x)
0.5b	(* (cbrt x) (cbrt x))
5.0b	(/ (+ (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)) 0.083333333333333) x)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
22×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`times-frac`
8×	`add-exp-log` `pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `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 → 91

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
5.0ms	(* (cbrt x) (cbrt x))
11.0ms	(/ (+ (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)) 0.083333333333333) x)

series87.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(cbrt x)
25.0ms	(cbrt x)
24.0ms	(* (cbrt x) (cbrt x))
15.0ms	(/ (+ (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)) 0.083333333333333) x)

simplify33.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5055	926

prune197.0ms

Filtered

72 candidates to 103 candidates (-43.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	101	2	103
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	103	12	115

Merged error: 0.3b

Counts

115 → 12

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))))
0.5b	(cbrt x)
0.5b	(cbrt x)
5.0b	(/ (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) x)

rewrite35.0ms

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:

16.0ms	(+ (* (- x 0.5) (* 2 (log (cbrt x)))) (* (- x 0.5) (log (cbrt x))))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
12.0ms	(/ (+ (* 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)
22.0ms	(cbrt x)
16.0ms	(/ (+ (* 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

prune240.0ms

Filtered

98 candidates to 115 candidates (-17.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	113	2	115
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	116	11	127

Merged error: 0.3b

Counts

127 → 11

localize35.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (cbrt x))
0.5b	(* (cbrt x) (cbrt x))
0.6b	(cbrt (* (cbrt x) (cbrt x)))
5.0b	(/ (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) x)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
26×	`cbrt-prod`
22×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`times-frac`
8×	`add-exp-log` `pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `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 → 92

Calls

4 calls:

2.0ms	(cbrt (cbrt x))
6.0ms	(* (cbrt x) (cbrt x))
4.0ms	(cbrt (* (cbrt x) (cbrt x)))
12.0ms	(/ (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) x)

series108.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(cbrt (cbrt x))
24.0ms	(* (cbrt x) (cbrt x))
39.0ms	(cbrt (* (cbrt x) (cbrt x)))
15.0ms	(/ (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) x)

simplify65.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4925	964
1	4925	964

prune191.0ms

Filtered

77 candidates to 104 candidates (-35.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	104	11	115

Merged error: 0.3b

Counts

115 → 11

regimes380.0ms

Accuracy

95.8% (0.2b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 5.9b

bsearch33.0ms

Steps

Iters	Range		Point
9	0.20831797989322398	30371378.727052115	4529838.128365544

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	110	83
1	110	83

end0.0ms

sample1.1s

Algorithm

intervals

Results

651.0ms	8000×	body	80	valid
96.0ms	1159×	body	80	invalid
53.0ms	746×	body	80	nan

Details

analyze467.0ms

sample34.0ms

simplify107.0ms

prune11.0ms

localize16.0ms

rewrite54.0ms

series79.0ms

simplify66.0ms

prune261.0ms

localize26.0ms

rewrite22.0ms

series87.0ms

simplify33.0ms

prune197.0ms

localize22.0ms

rewrite35.0ms

series166.0ms

simplify45.0ms

prune240.0ms

localize35.0ms

rewrite25.0ms

series108.0ms

simplify65.0ms

prune191.0ms

regimes380.0ms

bsearch33.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling