Details

sample46.0ms

Algorithm

intervals

Results

13.0ms	197×	body	80	valid
8.0ms	27×	body	2560	valid
5.0ms	256×	pre	80	true
5.0ms	19×	body	1280	valid
1.0ms	5×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	3×	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: 10.9b

Counts

2 → 1

localize12.0ms

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))))
0.9b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.3b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite32.0ms

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))
7.0ms	(/ 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)))

series227.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(+ (* (* 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)))))
57.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify156.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 3 (146.0ms)

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

prune283.0ms

Filtered

103 candidates to 79 candidates (76.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	95	8	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	96	8	104

Merged error: 10.7b

Counts

104 → 8

localize17.0ms

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)))))
2.6b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
13.3b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite30.0ms

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))
14.0ms	(* 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)))

series224.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ (* (* 4.0 p) p) (* x x))
58.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
72.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
60.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify63.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (47.0ms)

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

prune264.0ms

Filtered

110 candidates to 79 candidates (71.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	108	2	110
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	111	7	118

Merged error: 10.7b

Counts

118 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
7.7b	(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
13.3b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.3b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite25.0ms

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:

9.0ms	(/ 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)))

series349.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
86.0ms	(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
55.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
61.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify52.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	359	1350
1	1263	1258
2	5001	1226

prune369.0ms

Filtered

117 candidates to 88 candidates (75.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	114	3	117
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	115	9	124

Merged error: 10.7b

Counts

124 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x)))))
5.8b	(+ 1.0 (* x (/ 1 (* (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x))))))))
14.1b	(cbrt (+ (* (* 4.0 p) p) (* x x)))
14.1b	(cbrt (+ (* (* 4.0 p) p) (* x x)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`cbrt-prod`
9×	`associate-r`
8×	`sqrt-prod`
6×	`pow1` `add-exp-log` `cbrt-div` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u`
3×	`fma-def` `associate-l` `unswap-sqr`
2×	`pow1/3` `sqrt-div` `associate-*r/`
1×	`+-commutative` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod`

Counts

4 → 76

Calls

4 calls:

10.0ms	(* (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x)))))
3.0ms	(+ 1.0 (* x (/ 1 (* (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)))

series602.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(* (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x)))))
180.0ms	(+ 1.0 (* x (/ 1 (* (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x))))))))
127.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))
133.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))

simplify63.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	460	1258
1	1850	1149
2	5001	1129

prune363.0ms

Filtered

88 candidates to 80 candidates (90.9%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	86	2	88
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	86	11	97

Merged error: 10.7b

Counts

97 → 11

regimes177.0ms

Accuracy

0% (0.4b 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

sample1.1s

Algorithm

intervals

Results

313.0ms	6042×	body	80	valid
247.0ms	796×	body	2560	valid
154.0ms	609×	body	1280	valid
153.0ms	8000×	pre	80	true
63.0ms	309×	body	640	valid
24.0ms	164×	body	320	valid
8.0ms	80×	body	160	valid