Details

sample46.0ms

Algorithm

intervals

Results

10.0ms	200×	body	80	valid
6.0ms	23×	body	1280	valid
6.0ms	19×	body	2560	valid
4.0ms	256×	pre	80	true
1.0ms	7×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	2×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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 (100.0%)

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: 12.2b

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))))
0.5b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite39.0ms

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:

12.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
7.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
11.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series57.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
9.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
12.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
7.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify72.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (62.0ms)

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

prune205.0ms

Filtered

93 candidates to 71 candidates (23.7%)

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: 12.0b

Counts

94 → 13

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
0.5b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
0.5b	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
15.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

13.0ms	(exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
12.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
12.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series55.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
16.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
11.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
7.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify110.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	202	567
1	613	507
2	1609	506
3	3883	506
4	5001	506

prune174.0ms

Filtered

70 candidates to 56 candidates (20.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	68	2	70
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	70	13	83

Merged error: 12.0b

Counts

83 → 13

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.5b	(+ 1.0 (log (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
2.5b	(log (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
15.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
36×	`add-sqr-sqrt` `times-frac`
35×	`add-cube-cbrt`
26×	`log-pow`
24×	`exp-prod` `sqrt-prod`
7×	`pow1`
6×	`add-exp-log` `log-prod` `sqrt-div` `associate-/r*` `add-cbrt-cube`
5×	`add-log-exp`
4×	`flip3-+` `associate-/r/` `flip-+`
3×	`associate-+r+` `associate-/l*`
2×	`div-inv` `distribute-lft-out`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `rem-log-exp` `clear-num` `sum-log`

Counts

4 → 108

Calls

4 calls:

9.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
16.0ms	(+ 1.0 (log (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
9.0ms	(log (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series37.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
12.0ms	(+ 1.0 (log (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
9.0ms	(log (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify69.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 3 (57.0ms)

Iter	Nodes	Cost
0	308	1094
1	803	1021
2	2268	1001
3	5002	998

prune259.0ms

Filtered

120 candidates to 87 candidates (27.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	117	3	120
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	120	13	133

Merged error: 12.0b

Counts

133 → 13

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
0.2b	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
1.4b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
15.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
24×	`associate-r`
22×	`times-frac`
21×	`*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`sqrt-prod`
13×	`add-exp-log`
10×	`pow1`
9×	`add-cbrt-cube`
6×	`sqrt-div` `add-log-exp`
5×	`unswap-sqr`
4×	`flip3-+` `prod-exp` `flip-+`
3×	`sqrt-pow1` `associate-r/` `associate-l*`
2×	`pow1/2` `div-exp` `pow-prod-down` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `rec-exp` `1-exp` `sum-log` `un-div-inv` `*-commutative` `div-inv`

Counts

4 → 88

Calls

4 calls:

3.0ms	(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
13.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series61.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
9.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
12.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify46.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	390	900
1	1684	818
2	5001	784

prune156.0ms

Filtered

100 candidates to 72 candidates (28.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	95	5	100
Fresh	9	3	12
Picked	1	0	1
Done	0	0	0
Total	105	8	113

Merged error: 12.0b

Counts

113 → 8

regimes242.0ms

Accuracy

0% (1.2b remaining)

Error of 14.4b against oracle of 13.2b and baseline of 14.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	19
1	27	19

end0.0ms

sample1.2s

Algorithm

intervals

Results

308.0ms	5984×	body	80	valid
256.0ms	811×	body	2560	valid
173.0ms	688×	body	1280	valid
133.0ms	8000×	pre	80	true
56.0ms	280×	body	640	valid
23.0ms	154×	body	320	valid
8.0ms	83×	body	160	valid

Details

sample46.0ms

simplify8.0ms

prune3.0ms

localize12.0ms

rewrite39.0ms

series57.0ms

simplify72.0ms

prune205.0ms

localize18.0ms

rewrite43.0ms

series55.0ms

simplify110.0ms

prune174.0ms

localize15.0ms

rewrite42.0ms

series37.0ms

simplify69.0ms

prune259.0ms

localize13.0ms

rewrite27.0ms

series61.0ms

simplify46.0ms

prune156.0ms

regimes242.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.2s

Profiling