Details

sample38.0ms

Algorithm

intervals

Results

7.0ms	193×	body	80	valid
6.0ms	25×	body	2560	valid
4.0ms	9×	body	640	valid
4.0ms	21×	body	1280	valid
4.0ms	256×	pre	80	true
1.0ms	6×	body	320	valid
0.0ms	2×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 12.3b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
1.2b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.8b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite34.0ms

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:

5.0ms	(+ (* (* 4.0 p) p) (* x x))
8.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
13.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
6.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series228.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(+ (* (* 4.0 p) p) (* x x))
53.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
77.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
59.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify152.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 3 (142.0ms)

Iter	Nodes	Cost
0	296	868
1	1081	815
2	4584	798
3	5001	795

prune287.0ms

Filtered

103 candidates to 79 candidates (76.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	89	14	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	90	14	104

Merged error: 12.0b

Counts

104 → 14

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (log1p (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.3b	(log1p (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
1.2b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.8b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

1.0ms	(expm1 (log1p (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
1.0ms	(log1p (+ 1.0 (/ x (sqrt (+ (* (* 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)))

series486.0ms

Counts

4 → 12

Calls

4 calls:

204.0ms	(expm1 (log1p (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
149.0ms	(log1p (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
75.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
57.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify109.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 4 (103.0ms)

Iter	Nodes	Cost
0	207	515
1	578	462
2	1519	461
3	4020	460
4	5001	452

prune219.0ms

Filtered

68 candidates to 61 candidates (89.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	7	6	13
Picked	1	0	1
Done	0	0	0
Total	74	8	82

Merged error: 12.0b

Counts

82 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (pow (log1p (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))) 3))
0.9b	(pow (log1p (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))) 3)
1.2b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.8b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
13×	`add-sqr-sqrt`
12×	`cbrt-prod` `add-cube-cbrt`
6×	`pow1` `unpow-prod-down` `cube-prod` `add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `fma-def` `sqrt-prod`
2×	`cube-mult` `flip3-+` `sqrt-div` `unpow3` `flip-+` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `pow1/3` `pow-exp` `sum-log` `rem-cbrt-cube` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 82

Calls

4 calls:

2.0ms	(cbrt (pow (log1p (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))) 3))
2.0ms	(pow (log1p (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))) 3)
13.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series670.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(cbrt (pow (log1p (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))) 3))
378.0ms	(pow (log1p (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))) 3)
78.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
60.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify177.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 3 (166.0ms)

Iter	Nodes	Cost
0	280	947
1	923	870
2	4278	863
3	5001	862

prune306.0ms

Filtered

94 candidates to 67 candidates (71.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	90	4	94
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	91	11	102

Merged error: 12.0b

Counts

102 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.2b	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
4.9b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
13.8b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
40×	`times-frac`
37×	`*-un-lft-identity`
35×	`add-cube-cbrt`
26×	`sqrt-prod`
24×	`associate-r`
17×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`pow1`
6×	`sqrt-div` `associate-/r*` `add-log-exp`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `flip3-+` `div-exp` `prod-exp` `associate-/r/` `flip-+` `log1p-expm1-u`
3×	`pow-flip` `fma-def` `associate-l` `associate-/l*`
2×	`cbrt-undiv` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 133

Calls

4 calls:

13.0ms	(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
18.0ms	(* 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)))

series260.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
52.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
82.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify60.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	384	1256
1	1710	1134
2	5001	1063

prune262.0ms

Filtered

145 candidates to 91 candidates (62.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	144	1	145
Fresh	3	6	9
Picked	0	1	1
Done	1	0	1
Total	148	8	156

Merged error: 12.0b

Counts

156 → 8

regimes129.0ms

Accuracy

0% (0.5b remaining)

Error of 13.3b against oracle of 12.9b and baseline of 13.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	10
1	24	10

end0.0ms

sample834.0ms

Algorithm

intervals

Results

212.0ms	6052×	body	80	valid
175.0ms	765×	body	2560	valid
119.0ms	652×	body	1280	valid
103.0ms	8000×	pre	80	true
44.0ms	314×	body	640	valid
21.0ms	151×	body	320	valid
5.0ms	66×	body	160	valid