Details

analyze451.0ms

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	23×	body	80	nan

simplify110.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (108.0ms)

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: 6.2b

Counts

2 → 2

localize19.0ms

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

rewrite52.0ms

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))
22.0ms	(+ (* (- 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))
12.0ms	(/ (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) x)

series77.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* 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)))
24.0ms	(* (- x 0.5) (log x))
16.0ms	(/ (+ (* 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

prune276.0ms

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: 0.0b

Counts

119 → 12

localize24.0ms

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)
5.7b	(/ (+ (* 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:

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

series167.0ms

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)
25.0ms	(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

prune236.0ms

Filtered

98 candidates to 115 candidates (-17.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	112	3	115
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	118	9	127

Merged error: 0.0b

Counts

127 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- x 0.5) (log (sqrt x)))
0.2b	(+ (* (- 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)

rewrite63.0ms

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)))
29.0ms	(+ (* (- 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)

series75.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* (- x 0.5) (log (sqrt x)))
42.0ms	(+ (* (- 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))))))
11.0ms	(+ (- 0.91893853320467 x) (* (- x 0.5) (log (sqrt x))))
15.0ms	(/ (+ (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)) 0.083333333333333) x)

simplify40.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	5294	4951

prune340.0ms

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

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

21×	`cbrt-prod`
17×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`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 → 68

Calls

4 calls:

1.0ms	(cbrt x)
2.0ms	(cbrt (cbrt x))
1.0ms	(cbrt (cbrt x))
11.0ms	(/ (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) x)

series96.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(cbrt x)
28.0ms	(cbrt (cbrt x))
32.0ms	(cbrt (cbrt x))
15.0ms	(/ (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) x)

simplify56.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4915	847
1	4915	847

prune126.0ms

Filtered

64 candidates to 80 candidates (-25.0%)

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

regimes329.0ms

Accuracy

95.7% (0.2b remaining)

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

bsearch17.0ms

Steps

Iters	Range		Point
5	3.1703696115566176e+17	6.629545316358911e+17	5.109353660521276e+17

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	111	71
1	111	71

end0.0ms

sample902.0ms

Algorithm

intervals

Results

544.0ms	8000×	body	80	valid
83.0ms	1206×	body	80	invalid
48.0ms	758×	body	80	nan

Details

analyze451.0ms

sample33.0ms

simplify110.0ms

prune11.0ms

localize19.0ms

rewrite52.0ms

series77.0ms

simplify67.0ms

prune276.0ms

localize24.0ms

rewrite32.0ms

series167.0ms

simplify45.0ms

prune236.0ms

localize18.0ms

rewrite63.0ms

series75.0ms

simplify40.0ms

prune340.0ms

localize29.0ms

rewrite17.0ms

series96.0ms

simplify56.0ms

prune126.0ms

regimes329.0ms

bsearch17.0ms

simplify2.0ms

end0.0ms

sample902.0ms

Profiling