Details

sample43.0ms

Algorithm

intervals

Results

10.0ms	196×	body	80	valid
6.0ms	19×	body	2560	valid
5.0ms	256×	pre	80	true
4.0ms	17×	body	1280	valid
2.0ms	12×	body	640	valid
1.0ms	6×	body	320	valid
1.0ms	6×	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: 12.8b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
1.4b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
16.3b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

13.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 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)))))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series473.0ms

Counts

4 → 12

Calls

4 calls:

283.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
57.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
74.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify88.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 3 (71.0ms)

Iter	Nodes	Cost
0	297	948
1	884	898
2	2732	885
3	5001	883

prune318.0ms

Filtered

104 candidates to 82 candidates (78.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	91	13	104
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	92	13	105

Merged error: 12.5b

Counts

105 → 13

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
0.2b	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.3b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
16.3b	(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`
15×	`sqrt-prod`
13×	`add-exp-log`
10×	`pow1`
9×	`add-cbrt-cube`
6×	`sqrt-div` `add-log-exp`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `flip3-+` `prod-exp` `flip-+` `log1p-expm1-u`
3×	`fma-def` `sqrt-pow1` `associate-r/` `associate-l*`
2×	`pow1/2` `div-exp` `pow-prod-down` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `rec-exp` `1-exp` `sum-log` `un-div-inv` `*-commutative` `div-inv`

Counts

4 → 99

Calls

4 calls:

4.0ms	(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 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)))

series484.0ms

Counts

4 → 12

Calls

4 calls:

287.0ms	(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
60.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
75.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
61.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify56.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	407	966
1	1757	881
2	5001	845

prune298.0ms

Filtered

111 candidates to 81 candidates (73.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	106	5	111
Fresh	7	5	12
Picked	1	0	1
Done	0	0	0
Total	114	10	124

Merged error: 12.5b

Counts

124 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.7b	(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
3.3b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
16.3b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

15.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (* 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)))

series490.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
287.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
82.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
62.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify47.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	416	1032
1	1721	918
2	5001	881

prune375.0ms

Filtered

114 candidates to 87 candidates (76.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	106	8	114
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	111	13	124

Merged error: 12.5b

Counts

124 → 13

localize25.0ms

Local error

Found 4 expressions with local error:

1.3b	(log (log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))
2.7b	(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
3.3b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
16.3b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

3.0ms	(log (log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))
2.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
3.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
6.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series861.0ms

Counts

4 → 12

Calls

4 calls:

385.0ms	(log (log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))
338.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
81.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
57.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify75.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 3 (66.0ms)

Iter	Nodes	Cost
0	284	938
1	800	817
2	2882	815
3	5002	804

prune297.0ms

Filtered

82 candidates to 70 candidates (85.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	78	4	82
Fresh	7	5	12
Picked	1	0	1
Done	0	0	0
Total	86	9	95

Merged error: 8.0b

Counts

95 → 9

regimes210.0ms

Accuracy

77.6% (1.4b remaining)

Error of 8.5b against oracle of 7.1b and baseline of 13.3b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	28
1	39	28

end0.0ms

sample1.2s

Algorithm

intervals

Results

320.0ms	6040×	body	80	valid
254.0ms	780×	body	2560	valid
163.0ms	621×	body	1280	valid
149.0ms	8000×	pre	80	true
63.0ms	308×	body	640	valid
25.0ms	159×	body	320	valid
9.0ms	92×	body	160	valid