Details

sample35.0ms

Algorithm

intervals

Results

7.0ms	186×	body	80	valid
7.0ms	29×	body	2560	valid
4.0ms	20×	body	1280	valid
4.0ms	256×	pre	80	true
1.0ms	9×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	4×	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: 14.6b

Counts

2 → 1

localize14.0ms

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))))
1.3b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.7b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite41.0ms

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)))))))
7.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
12.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
6.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series447.0ms

Counts

4 → 12

Calls

4 calls:

264.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
51.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
74.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
57.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify78.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 3 (68.0ms)

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

prune298.0ms

Filtered

104 candidates to 82 candidates (78.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	90	14	104
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	91	14	105

Merged error: 14.3b

Counts

105 → 14

localize12.0ms

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)))))
2.8b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
15.7b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite29.0ms

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))))))))
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)))

series441.0ms

Counts

4 → 12

Calls

4 calls:

262.0ms	(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
51.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
73.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
55.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify48.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	407	969
1	1772	880
2	5001	845

prune265.0ms

Filtered

111 candidates to 82 candidates (73.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	107	4	111
Fresh	5	8	13
Picked	1	0	1
Done	0	0	0
Total	113	12	125

Merged error: 14.3b

Counts

125 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.5b	(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
2.8b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
15.7b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite28.0ms

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:

14.0ms	(* 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)))

series446.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
260.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
74.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
57.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify49.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (37.0ms)

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

prune340.0ms

Filtered

114 candidates to 86 candidates (75.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	104	10	114
Fresh	8	3	11
Picked	1	0	1
Done	0	0	0
Total	113	13	126

Merged error: 14.3b

Counts

126 → 13

localize19.0ms

Local error

Found 4 expressions with local error:

0.7b	(log (log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))
2.5b	(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
2.8b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
15.7b	(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))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series755.0ms

Counts

4 → 12

Calls

4 calls:

357.0ms	(log (log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))
266.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
75.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
57.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify80.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 3 (67.0ms)

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

prune267.0ms

Filtered

82 candidates to 70 candidates (85.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	79	3	82
Fresh	7	5	12
Picked	0	1	1
Done	0	0	0
Total	86	9	95

Merged error: 8.9b

Counts

95 → 9

regimes161.0ms

Accuracy

-10.5% (6.7b remaining)

Error of 14.0b against oracle of 7.3b and baseline of 13.4b

bsearch274.0ms

Steps

Iters	Range		Point
9	-458620530.10775155	-5878.690365136192	-454354590.67968696
8	-4.483429892166135e+24	-1.207936976621e+20	-1.4053102055050533e+20
8	-7.83177520472042e+125	-2.1084671656053772e+122	-4.708638998895936e+125
6	-7.855319431460923e+138	-9.824461211299318e+137	-1.3486856894550456e+138

simplify6.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 2 (1.0ms)

Iter	Nodes	Cost
0	58	64
1	61	64
2	67	25
3	70	25
4	76	25
5	87	25
6	94	25
7	95	25
8	95	25

end0.0ms

sample855.0ms

Algorithm

intervals

Results

225.0ms	6033×	body	80	valid
191.0ms	819×	body	2560	valid
108.0ms	596×	body	1280	valid
104.0ms	8000×	pre	80	true
45.0ms	304×	body	640	valid
18.0ms	168×	body	320	valid
6.0ms	80×	body	160	valid