Details

analyze77.0ms

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
12.5%	87.4%	0.1%	4
25%	74.9%	0.1%	5
31.2%	68.7%	0.1%	6
67.1%	32.8%	0.1%	7
71%	28.9%	0.1%	8
82.3%	17.6%	0.1%	9
84.9%	15%	0.1%	10
90.8%	9.1%	0.1%	11
92.2%	7.7%	0.1%	12
95.3%	4.6%	0.1%	13
96%	3.9%	0.1%	14

sample20.0ms

Algorithm

intervals

Results

6.0ms	189×	body	80	valid
3.0ms	25×	body	640	valid
2.0ms	11×	body	1280	valid
1.0ms	17×	body	320	valid
1.0ms	14×	body	160	valid

simplify242.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (240.0ms)

Iter	Nodes	Cost
0	5206	11

prune8.0ms

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: 15.3b

Counts

2 → 2

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x 1.0) (+ 1.0 y))
0.1b	(* y (/ (- x 1.0) (+ 1.0 y)))
5.7b	(+ 1.0 (* y (/ (- x 1.0) (+ 1.0 y))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

65×	`*-un-lft-identity`
48×	`add-sqr-sqrt`
41×	`times-frac`
26×	`associate-r`
25×	`add-cube-cbrt`
11×	`distribute-lft-out`
10×	`add-exp-log` `add-cbrt-cube`
9×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1` `associate-/l*` `add-log-exp`
4×	`associate-/r*` `associate-/r/`
3×	`flip3-+` `associate-l` `flip-+`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `flip3--` `frac-2neg` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip--`

Counts

3 → 102

Calls

3 calls:

7.0ms	(/ (- x 1.0) (+ 1.0 y))
12.0ms	(* y (/ (- x 1.0) (+ 1.0 y)))
3.0ms	(+ 1.0 (* y (/ (- x 1.0) (+ 1.0 y))))

series21.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(/ (- x 1.0) (+ 1.0 y))
5.0ms	(* y (/ (- x 1.0) (+ 1.0 y)))
10.0ms	(+ 1.0 (* y (/ (- x 1.0) (+ 1.0 y))))

simplify57.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	6163	1269

prune187.0ms

Filtered

76 candidates to 111 candidates (-46.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	98	13	111
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	99	14	113

Merged error: 8.3b

Counts

113 → 14

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ 1.0 y))
0.3b	(cbrt (+ 1.0 y))
0.3b	(cbrt (+ 1.0 y))
10.6b	(+ 1.0 (* (/ y (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))) (/ (- x 1.0) (cbrt (+ 1.0 y)))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
3×	`pow1/3` `distribute-lft-out`
1×	`+-commutative` `sum-log`

Counts

4 → 53

Calls

4 calls:

3.0ms	(cbrt (+ 1.0 y))
3.0ms	(cbrt (+ 1.0 y))
3.0ms	(cbrt (+ 1.0 y))
4.0ms	(+ 1.0 (* (/ y (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))) (/ (- x 1.0) (cbrt (+ 1.0 y)))))

series29.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(cbrt (+ 1.0 y))
6.0ms	(cbrt (+ 1.0 y))
6.0ms	(cbrt (+ 1.0 y))
11.0ms	(+ 1.0 (* (/ y (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))) (/ (- x 1.0) (cbrt (+ 1.0 y)))))

simplify72.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4914	683
1	4914	683

prune164.0ms

Filtered

50 candidates to 65 candidates (-30.0%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	61	4	65
Fresh	2	11	13
Picked	0	1	1
Done	0	0	0
Total	63	16	79

Merged error: 8.3b

Counts

79 → 16

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ 1.0 y))
0.3b	(cbrt (+ 1.0 y))
0.3b	(cbrt (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y))))
11.3b	(+ 1.0 (* (/ y (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))) (/ (- x 1.0) (* (cbrt (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))) (cbrt (cbrt (+ 1.0 y)))))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

24×	`cbrt-div`
10×	`*-un-lft-identity`
9×	`cbrt-prod` `flip3-+` `flip-+`
6×	`add-sqr-sqrt` `add-cube-cbrt` `add-log-exp`
4×	`pow1` `add-exp-log` `frac-times` `add-cbrt-cube`
3×	`pow1/3`
2×	`associate-r/` `associate-l/` `distribute-lft-out`
1×	`+-commutative` `sum-log`

Counts

4 → 56

Calls

4 calls:

3.0ms	(cbrt (+ 1.0 y))
3.0ms	(cbrt (+ 1.0 y))
8.0ms	(cbrt (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y))))
4.0ms	(+ 1.0 (* (/ y (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))) (/ (- x 1.0) (* (cbrt (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))) (cbrt (cbrt (+ 1.0 y)))))))

series31.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(cbrt (+ 1.0 y))
6.0ms	(cbrt (+ 1.0 y))
7.0ms	(cbrt (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y))))
11.0ms	(+ 1.0 (* (/ y (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))) (/ (- x 1.0) (* (cbrt (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))) (cbrt (cbrt (+ 1.0 y)))))))

simplify75.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4885	1245
1	4885	1245

prune257.0ms

Filtered

51 candidates to 68 candidates (-33.3%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	64	4	68
Fresh	4	10	14
Picked	1	0	1
Done	0	1	1
Total	69	15	84

Merged error: 8.2b

Counts

84 → 15

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ 1.0 y))
0.3b	(cbrt (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y))))
0.3b	(cbrt (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y))))
12.5b	(+ 1.0 (* (/ y (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))) (/ (- x 1.0) (* (* (sqrt (cbrt (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y))))) (sqrt (cbrt (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))))) (cbrt (cbrt (+ 1.0 y)))))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

42×	`cbrt-div`
14×	`flip3-+` `flip-+`
8×	`frac-times`
7×	`*-un-lft-identity`
6×	`cbrt-prod` `add-log-exp`
5×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`pow1` `add-exp-log` `associate-r/` `associate-l/` `add-cbrt-cube`
3×	`pow1/3`
1×	`+-commutative` `sum-log` `distribute-lft-out`

Counts

4 → 59

Calls

4 calls:

3.0ms	(cbrt (+ 1.0 y))
11.0ms	(cbrt (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y))))
9.0ms	(cbrt (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y))))
4.0ms	(+ 1.0 (* (/ y (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))) (/ (- x 1.0) (* (* (sqrt (cbrt (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y))))) (sqrt (cbrt (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))))) (cbrt (cbrt (+ 1.0 y)))))))

series32.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(cbrt (+ 1.0 y))
7.0ms	(cbrt (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y))))
7.0ms	(cbrt (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y))))
12.0ms	(+ 1.0 (* (/ y (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))) (/ (- x 1.0) (* (* (sqrt (cbrt (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y))))) (sqrt (cbrt (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))))) (cbrt (cbrt (+ 1.0 y)))))))

simplify92.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4945	1477
1	4945	1477

prune256.0ms

Filtered

51 candidates to 71 candidates (-39.2%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	13	13
Picked	0	1	1
Done	0	1	1
Total	71	15	86

Merged error: 8.2b

Counts

86 → 15

regimes516.0ms

Accuracy

97.3% (0.2b remaining)

Error of 7.3b against oracle of 7.1b and baseline of 14.9b

bsearch23.0ms

Steps

Iters	Range		Point
7	1.296962845559342e+23	9.721480850484785e+24	2.9017319871335257e+23
6	-53632592433846.13	-11883060582780.744	-53035177634780.61

simplify7.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	331	31
1	331	31

end0.0ms

sample526.0ms

Algorithm

intervals

Results

192.0ms	6076×	body	80	valid
84.0ms	745×	body	640	valid
60.0ms	391×	body	1280	valid
42.0ms	494×	body	320	valid
17.0ms	294×	body	160	valid

Details

analyze77.0ms

sample20.0ms

simplify242.0ms

prune8.0ms

localize10.0ms

rewrite27.0ms

series21.0ms

simplify57.0ms

prune187.0ms

localize11.0ms

rewrite14.0ms

series29.0ms

simplify72.0ms

prune164.0ms

localize17.0ms

rewrite20.0ms

series31.0ms

simplify75.0ms

prune257.0ms

localize18.0ms

rewrite29.0ms

series32.0ms

simplify92.0ms

prune256.0ms

regimes516.0ms

bsearch23.0ms

simplify7.0ms

end0.0ms

sample526.0ms

Profiling