Details

sample44.0ms

Algorithm

intervals

Results

10.0ms	191×	body	80	valid
8.0ms	25×	body	2560	valid
6.0ms	24×	body	1280	valid
5.0ms	256×	pre	80	true
2.0ms	9×	body	640	valid
1.0ms	7×	body	320	valid

simplify11.0ms

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

prune2.0ms

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: 13.6b

Counts

2 → 1

localize16.0ms

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))
0.3b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.6b	(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:

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)))

series221.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
31.0ms	(+ (* (* 4.0 p) p) (* x x))
75.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
59.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify149.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 3 (139.0ms)

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

prune446.0ms

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: 13.3b

Counts

104 → 12

localize18.0ms

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)))))
2.5b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
14.6b	(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)))

series217.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ (* (* 4.0 p) p) (* x x))
55.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
71.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify59.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (46.0ms)

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

prune263.0ms

Filtered

110 candidates to 81 candidates (73.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	106	4	110
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	111	11	122

Merged error: 13.3b

Counts

122 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (* 4.0 p) p (* x x))
0.2b	(* x (/ 1 (sqrt (fma (* 4.0 p) p (* x x)))))
2.5b	(+ 1.0 (* x (/ 1 (sqrt (fma (* 4.0 p) p (* x x))))))
14.6b	(sqrt (fma (* 4.0 p) p (* x x)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

1.0ms	(fma (* 4.0 p) p (* x x))
10.0ms	(* x (/ 1 (sqrt (fma (* 4.0 p) p (* x x)))))
3.0ms	(+ 1.0 (* x (/ 1 (sqrt (fma (* 4.0 p) p (* x x))))))
2.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

series228.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(fma (* 4.0 p) p (* x x))
55.0ms	(* x (/ 1 (sqrt (fma (* 4.0 p) p (* x x)))))
74.0ms	(+ 1.0 (* x (/ 1 (sqrt (fma (* 4.0 p) p (* x x))))))
62.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

simplify42.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	320	682
1	1447	608
2	5002	574

prune241.0ms

Filtered

102 candidates to 75 candidates (73.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	98	4	102
Fresh	4	6	10
Picked	0	1	1
Done	0	0	0
Total	102	11	113

Merged error: 13.3b

Counts

113 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.3b	(+ 1.0 (log (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
2.5b	(log (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
14.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

26×	`log-pow`
24×	`exp-prod` `*-un-lft-identity`
22×	`add-sqr-sqrt`
21×	`add-cube-cbrt`
18×	`times-frac`
12×	`sqrt-prod`
7×	`pow1` `add-log-exp`
6×	`log-prod`
4×	`add-exp-log` `expm1-log1p-u` `fma-def` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
3×	`associate-+r+`
2×	`+-commutative` `sum-log` `associate-/r/` `distribute-lft-out`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp` `div-inv`

Counts

4 → 90

Calls

4 calls:

5.0ms	(+ (* (* 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))))))
7.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series211.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ (* (* 4.0 p) p) (* x x))
72.0ms	(+ 1.0 (log (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
50.0ms	(log (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
55.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify102.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 3 (93.0ms)

Iter	Nodes	Cost
0	321	789
1	1023	727
2	3716	703
3	5001	699

prune247.0ms

Filtered

102 candidates to 81 candidates (79.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	102	11	113

Merged error: 13.3b

Counts

113 → 11

regimes216.0ms

Accuracy

0% (0.4b remaining)

Error of 13.4b against oracle of 13.0b and baseline of 13.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	9
1	21	9

end0.0ms

sample1.2s

Algorithm

intervals

Results

332.0ms	6021×	body	80	valid
266.0ms	785×	body	2560	valid
183.0ms	641×	body	1280	valid
151.0ms	8000×	pre	80	true
69.0ms	314×	body	640	valid
25.0ms	143×	body	320	valid
10.0ms	96×	body	160	valid