Details

analyze443.0ms

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

sample31.0ms

Algorithm

intervals

Results

17.0ms	256×	body	80	valid
3.0ms	42×	body	80	invalid
1.0ms	19×	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: 6.7b

Counts

2 → 1

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))
0.1b	(+ (* (- x 0.5) (log x)) (+ 0.91893853320467 (- (/ (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) x) x)))
6.2b	(/ (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) x)

rewrite50.0ms

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))
7.0ms	(* (- x 0.5) (log x))
20.0ms	(+ (* (- x 0.5) (log x)) (+ 0.91893853320467 (- (/ (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) x) x)))
11.0ms	(/ (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) x)

series81.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778))
22.0ms	(* (- x 0.5) (log x))
34.0ms	(+ (* (- x 0.5) (log x)) (+ 0.91893853320467 (- (/ (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) x) x)))
17.0ms	(/ (+ (* 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

prune248.0ms

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

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
6.2b	(/ (+ (* 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)

series86.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(cbrt x)
22.0ms	(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 (43.0ms)

Iter	Nodes	Cost
0	4947	766
1	4947	766

prune139.0ms

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

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (log x) (- x 0.5))
0.1b	(* (log x) (- x 0.5))
0.5b	(* (sqrt (* (log x) (- x 0.5))) (sqrt (* (log x) (- x 0.5))))
6.2b	(/ (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) x)

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 136

Calls

4 calls:

6.0ms	(* (log x) (- x 0.5))
6.0ms	(* (log x) (- x 0.5))
13.0ms	(* (sqrt (* (log x) (- x 0.5))) (sqrt (* (log x) (- x 0.5))))
11.0ms	(/ (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) x)

series101.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (log x) (- x 0.5))
22.0ms	(* (log x) (- x 0.5))
37.0ms	(* (sqrt (* (log x) (- x 0.5))) (sqrt (* (log x) (- x 0.5))))
18.0ms	(/ (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) x)

simplify36.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5522	1943

prune281.0ms

Filtered

95 candidates to 148 candidates (-55.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	147	1	148
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	149	8	157

Merged error: 0.0b

Counts

157 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 0.0007936500793651 (/ z (/ x z)))
0.2b	(/ z (/ x z))
0.2b	(* 0.0027777777777778 (/ z x))
0.5b	(* (sqrt (* (log x) (- x 0.5))) (sqrt (* (log x) (- x 0.5))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

154×	`times-frac`
110×	`add-sqr-sqrt`
94×	`add-cube-cbrt` `*-un-lft-identity`
61×	`associate-r`
57×	`pow1`
28×	`sqrt-pow1`
25×	`add-exp-log` `add-cbrt-cube`
22×	`pow-prod-down`
16×	`associate-*r/`
13×	`associate-/r*`
12×	`sqrt-div`
10×	`pow1/2` `associate-l` `pow-prod-up` `div-inv`
7×	`cbrt-undiv` `div-exp`
6×	`flip3--` `prod-exp` `pow-sqr` `flip--` `cbrt-unprod` `unswap-sqr`
4×	`frac-times` `swap-sqr` `sqrt-prod` `add-log-exp`
3×	`-commutative` `associate-/l`
2×	`associate-*l/` `associate-/r/`
1×	`pow2` `frac-2neg` `pow-plus` `sqrt-unprod` `clear-num` `rem-square-sqrt`

Counts

4 → 225

Calls

4 calls:

14.0ms	(* 0.0007936500793651 (/ z (/ x z)))
6.0ms	(/ z (/ x z))
7.0ms	(* 0.0027777777777778 (/ z x))
16.0ms	(* (sqrt (* (log x) (- x 0.5))) (sqrt (* (log x) (- x 0.5))))

series52.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* 0.0007936500793651 (/ z (/ x z)))
3.0ms	(/ z (/ x z))
3.0ms	(* 0.0027777777777778 (/ z x))
41.0ms	(* (sqrt (* (log x) (- x 0.5))) (sqrt (* (log x) (- x 0.5))))

simplify48.0ms

Algorithm

egg-herbie

Counts

237 → 237

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5527	2429

prune396.0ms

Filtered

161 candidates to 237 candidates (-47.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	236	1	237
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	236	9	245

Merged error: 0.0b

Counts

245 → 9

regimes318.0ms

Accuracy

96.8% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 6.9b

bsearch245.0ms

Steps

Iters	Range		Point
9	13036833251855.12	2.199061599096176e+21	2246989294872715.0

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	56
1	50	56

end0.0ms

analyze439.0ms

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

sample878.0ms

Algorithm

intervals

Results

545.0ms	8000×	body	80	valid
83.0ms	1222×	body	80	invalid
43.0ms	726×	body	80	nan

Details

analyze443.0ms

sample31.0ms

simplify5.0ms

prune9.0ms

localize19.0ms

rewrite50.0ms

series81.0ms

simplify59.0ms

prune248.0ms

localize26.0ms

rewrite16.0ms

series86.0ms

simplify49.0ms

prune139.0ms

localize19.0ms

rewrite42.0ms

series101.0ms

simplify36.0ms

prune281.0ms

localize20.0ms

rewrite53.0ms

series52.0ms

simplify48.0ms

prune396.0ms

regimes318.0ms

bsearch245.0ms

simplify1.0ms

end0.0ms

analyze439.0ms

sample878.0ms

Profiling