Details

sample37.0ms

Algorithm

intervals

Results

7.0ms	202×	body	80	valid
7.0ms	30×	body	2560	valid
6.0ms	13×	body	1280	valid
4.0ms	256×	pre	80	true
1.0ms	9×	body	640	valid
0.0ms	1×	body	320	valid
0.0ms	1×	body	160	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	28	9
1	40	9
2	48	9
3	50	9
4	52	9
5	53	9
6	53	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: 9.8b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.0b	(+ (* (* 4.0 p) p) (* x x))
0.2b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
21×	`add-cube-cbrt`
18×	`times-frac`
15×	`sqrt-prod`
8×	`add-log-exp`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `fma-def` `flip3-+` `sqrt-div` `flip-+` `log1p-expm1-u`
3×	`associate-/l*`
2×	`+-commutative` `sum-log` `associate-/r/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv` `distribute-lft-out`

Counts

4 → 91

Calls

4 calls:

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

series244.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
35.0ms	(+ (* (* 4.0 p) p) (* x x))
83.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
64.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify154.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 3 (143.0ms)

Iter	Nodes	Cost
0	296	867
1	1081	815
2	4584	798
3	5001	795

prune296.0ms

Filtered

103 candidates to 79 candidates (76.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	93	10	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	94	10	104

Merged error: 9.7b

Counts

104 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.2b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
0.2b	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
15.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `add-log-exp`
6×	`pow1`
5×	`log-pow`
4×	`add-exp-log` `expm1-log1p-u` `log-prod` `exp-prod` `fma-def` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3-+` `sqrt-prod` `flip-+`
2×	`+-commutative` `sqrt-div` `sum-log` `distribute-lft-out`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp` `exp-sum`

Counts

4 → 67

Calls

4 calls:

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

series261.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (* (* 4.0 p) p) (* x x))
82.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
83.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
64.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify90.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 3 (83.0ms)

Iter	Nodes	Cost
0	249	589
1	926	533
2	3159	528
3	5001	524

prune248.0ms

Filtered

79 candidates to 65 candidates (82.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	78	1	79
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	80	9	89

Merged error: 9.7b

Counts

89 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
0.3b	(* (sqrt (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
15.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

32×	`sqrt-prod`
31×	`*-un-lft-identity`
29×	`add-sqr-sqrt`
21×	`pow1`
16×	`sqrt-div`
15×	`add-cube-cbrt`
11×	`swap-sqr`
10×	`sqrt-pow1` `pow1/2`
9×	`flip3-+` `flip-+`
7×	`associate-r` `associate-l` `distribute-lft-out`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u` `unswap-sqr`
3×	`fma-def` `pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`+-commutative` `pow2` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 115

Calls

4 calls:

17.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
29.0ms	(* (sqrt (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (+ 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)))

series281.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
82.0ms	(* (sqrt (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
62.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
56.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify205.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	270	1313
1	959	1197
2	4777	1151
3	5001	1151

prune346.0ms

Filtered

127 candidates to 83 candidates (65.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	127	9	136

Merged error: 9.7b

Counts

136 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.3b	(* (sqrt (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
15.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
22×	`sqrt-prod`
19×	`*-un-lft-identity`
13×	`add-cube-cbrt`
12×	`pow1`
11×	`associate-r`
10×	`log-pow`
8×	`exp-prod`
7×	`associate-l`
6×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
4×	`expm1-log1p-u` `log-prod` `sqrt-pow1` `pow1/2` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`flip3-+` `pow-prod-down` `flip-+` `distribute-lft-out`
2×	`rem-sqrt-square` `associate-*l/`
1×	`sqrt-unprod` `rem-log-exp` `exp-sum` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 93

Calls

4 calls:

13.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
34.0ms	(* (sqrt (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (log (exp (+ 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)))

series283.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
83.0ms	(* (sqrt (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
63.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify65.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	252	1148
1	721	956
2	2012	890
3	5001	890

prune341.0ms

Filtered

105 candidates to 81 candidates (77.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	104	1	105
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	104	10	114

Merged error: 9.7b

Counts

114 → 10

regimes229.0ms

Accuracy

0% (0.3b remaining)

Error of 13.2b against oracle of 13.0b and baseline of 13.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	33
1	27	33

end0.0ms

sample879.0ms

Algorithm

intervals

Results

226.0ms	6024×	body	80	valid
190.0ms	803×	body	2560	valid
117.0ms	600×	body	1280	valid
110.0ms	8000×	pre	80	true
49.0ms	327×	body	640	valid
19.0ms	170×	body	320	valid
5.0ms	76×	body	160	valid