Details

sample44.0ms

Algorithm

intervals

Results

10.0ms	189×	body	80	valid
9.0ms	29×	body	2560	valid
5.0ms	21×	body	1280	valid
5.0ms	256×	pre	80	true
2.0ms	11×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	2×	body	160	valid

simplify12.0ms

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: 14.0b

Counts

2 → 1

localize17.0ms

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))
0.4b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite31.0ms

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:

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

series241.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
34.0ms	(+ (* (* 4.0 p) p) (* x x))
82.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
63.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify163.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 3 (152.0ms)

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

prune297.0ms

Filtered

103 candidates to 79 candidates (76.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	91	12	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	92	12	104

Merged error: 13.7b

Counts

104 → 12

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.4b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
0.4b	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
15.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite38.0ms

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))
13.0ms	(+ 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)))

series256.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(+ (* (* 4.0 p) p) (* x x))
73.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
79.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
63.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify97.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 3 (89.0ms)

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

prune406.0ms

Filtered

79 candidates to 66 candidates (83.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	77	2	79
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	78	13	91

Merged error: 13.7b

Counts

91 → 13

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.2b	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.8b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
15.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
24×	`associate-r`
22×	`*-un-lft-identity` `times-frac`
20×	`add-cube-cbrt`
14×	`sqrt-prod`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `fma-def` `flip3-+` `sqrt-div` `prod-exp` `flip-+` `log1p-expm1-u`
3×	`associate-l`
2×	`+-commutative` `div-exp` `sum-log` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 98

Calls

4 calls:

5.0ms	(+ (* (* 4.0 p) p) (* x x))
15.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series228.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ (* (* 4.0 p) p) (* x x))
53.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
78.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
61.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify59.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	405	866
1	1987	780
2	5002	742

prune278.0ms

Filtered

110 candidates to 80 candidates (72.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	106	4	110
Fresh	6	5	11
Picked	1	0	1
Done	0	1	1
Total	113	10	123

Merged error: 13.7b

Counts

123 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
8.1b	(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
15.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

42×	`sqrt-prod`
31×	`add-sqr-sqrt`
29×	`add-cube-cbrt` `*-un-lft-identity`
27×	`times-frac`
9×	`associate-/r*`
8×	`sqrt-div`
6×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u`
3×	`fma-def` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 105

Calls

4 calls:

11.0ms	(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.0ms	(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (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)))

series336.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
82.0ms	(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
54.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify48.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	359	1348
1	1263	1258
2	5001	1226

prune318.0ms

Filtered

117 candidates to 88 candidates (75.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	115	2	117
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	115	12	127

Merged error: 13.7b

Counts

127 → 12

regimes268.0ms

Accuracy

0% (0.3b remaining)

Error of 13.5b against oracle of 13.3b and baseline of 13.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	11
1	21	11

end0.0ms

sample1.2s

Algorithm

intervals

Results

311.0ms	5985×	body	80	valid
265.0ms	838×	body	2560	valid
164.0ms	634×	body	1280	valid
149.0ms	8000×	pre	80	true
60.0ms	302×	body	640	valid
25.0ms	167×	body	320	valid
7.0ms	74×	body	160	valid