Details

sample44.0ms

Algorithm

intervals

Results

10.0ms	193×	body	80	valid
8.0ms	26×	body	2560	valid
5.0ms	256×	pre	80	true
5.0ms	19×	body	1280	valid
2.0ms	11×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	1×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	27	9
1	34	9
2	38	9
3	40	9
4	41	9
5	41	9

prune3.0ms

Filtered

1 candidates to 0 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: 14.0b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.4b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.5b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
21×	`add-sqr-sqrt`
20×	`add-cube-cbrt`
18×	`times-frac`
16×	`sqrt-prod`
8×	`pow1`
6×	`add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube` `add-log-exp`
4×	`flip3-+` `flip-+`
3×	`sqrt-pow1` `associate-/l*`
2×	`pow1/2` `associate-*r/` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `div-exp` `pow-prod-down` `clear-num` `sum-log` `div-inv` `distribute-lft-out`

Counts

4 → 81

Calls

4 calls:

13.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
8.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
18.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series492.0ms

Counts

4 → 12

Calls

4 calls:

293.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
60.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
81.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
57.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify77.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (66.0ms)

Iter	Nodes	Cost
0	280	888
1	816	840
2	2486	828
3	5001	827

prune271.0ms

Filtered

93 candidates to 71 candidates (76.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	80	13	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	13	94

Merged error: 13.8b

Counts

94 → 13

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.4b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.4b	(log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
13.5b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `log-prod`
7×	`pow1`
6×	`add-log-exp`
5×	`add-exp-log`
4×	`log-div` `exp-prod` `flip3-+` `exp-sum` `add-cbrt-cube` `flip-+`
3×	`sqrt-prod` `distribute-lft-out`
2×	`exp-diff` `sqrt-div` `log-pow`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp` `sum-log` `rem-exp-log`

Counts

4 → 60

Calls

4 calls:

14.0ms	(exp (log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
15.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.0ms	(log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series422.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(exp (log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
84.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
192.0ms	(log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
63.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify116.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (44.0ms)

Iter	Nodes	Cost
0	230	707
1	588	645
2	1449	625
3	3630	619
4	5001	619

prune220.0ms

Filtered

72 candidates to 56 candidates (77.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	77	8	85

Merged error: 9.6b

Counts

85 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))) (cbrt (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
13.5b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.5b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.5b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
20×	`cbrt-prod`
18×	`sqrt-div`
15×	`add-cube-cbrt` `*-un-lft-identity`
14×	`pow1` `associate-*r/`
13×	`sqrt-prod`
12×	`cbrt-div`
9×	`flip3-+` `flip-+`
7×	`swap-sqr` `associate-r` `associate-l`
6×	`add-exp-log` `pow1/3`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`pow-prod-down` `associate-*l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 96

Calls

4 calls:

9.0ms	(* (cbrt (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))) (cbrt (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series856.0ms

Counts

4 → 12

Calls

4 calls:

675.0ms	(* (cbrt (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))) (cbrt (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
55.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
63.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
63.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify123.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 3 (107.0ms)

Iter	Nodes	Cost
0	305	1729
1	949	1628
2	3976	1523
3	5001	1511

prune389.0ms

Filtered

108 candidates to 81 candidates (75.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	108	8	116

Merged error: 9.6b

Counts

116 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ x (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))))
6.0b	(+ 1.0 (/ (/ x (fabs (cbrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x))))))
14.4b	(cbrt (+ (* (* 4.0 p) p) (* x x)))
14.4b	(cbrt (+ (* (* 4.0 p) p) (* x x)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

3.0ms	(/ x (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))))
37.0ms	(+ 1.0 (/ (/ x (fabs (cbrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x))))))
5.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))

series492.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ x (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))))
177.0ms	(+ 1.0 (/ (/ x (fabs (cbrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x))))))
144.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))
138.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))

simplify48.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	388	1007
1	1398	923
2	5001	915

prune289.0ms

Filtered

77 candidates to 69 candidates (89.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	75	2	77
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	76	9	85

Merged error: 9.6b

Counts

85 → 9

regimes314.0ms

Accuracy

65.7% (1.3b remaining)

Error of 11.0b against oracle of 9.7b and baseline of 13.6b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	35
1	47	35

end0.0ms

sample1.1s

Algorithm

intervals

Results

325.0ms	6057×	body	80	valid
246.0ms	801×	body	2560	valid
149.0ms	603×	body	1280	valid
142.0ms	8000×	pre	80	true
62.0ms	312×	body	640	valid
21.0ms	139×	body	320	valid
9.0ms	88×	body	160	valid

Details

sample44.0ms

simplify11.0ms

prune3.0ms

localize12.0ms

rewrite47.0ms

series492.0ms

simplify77.0ms

prune271.0ms

localize18.0ms

rewrite49.0ms

series422.0ms

simplify116.0ms

prune220.0ms

localize16.0ms

rewrite28.0ms

series856.0ms

simplify123.0ms

prune389.0ms

localize14.0ms

rewrite52.0ms

series492.0ms

simplify48.0ms

prune289.0ms

regimes314.0ms

bsearch2.0ms

simplify1.0ms

end0.0ms

sample1.1s

Profiling