Details

sample34.0ms

Algorithm

intervals

Results

7.0ms	197×	body	80	valid
5.0ms	22×	body	2560	valid
4.0ms	256×	pre	80	true
4.0ms	20×	body	1280	valid
1.0ms	8×	body	640	valid
1.0ms	7×	body	160	valid
0.0ms	2×	body	320	valid

simplify13.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.2b

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))))
1.6b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
17.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite59.0ms

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:

6.0ms	(+ (* (* 4.0 p) p) (* x x))
12.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
28.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
11.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series222.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (* (* 4.0 p) p) (* x x))
56.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
73.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
59.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify154.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 3 (141.0ms)

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

prune316.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
1.6b	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
1.6b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
17.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite229.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

96.0ms	(exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
96.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
25.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series360.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
76.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
75.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
53.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify119.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (46.0ms)

Iter	Nodes	Cost
0	219	628
1	680	566
2	1814	565
3	4609	564
4	5001	564

prune304.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3)
1.6b	(log (exp (cbrt (pow (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3))))
1.6b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
17.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite276.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

47.0ms	(pow (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3)
192.0ms	(log (exp (cbrt (pow (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3))))
24.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series394.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(pow (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3)
80.0ms	(log (exp (cbrt (pow (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3))))
81.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify45.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	324	918
1	1178	848
2	5001	843

prune407.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.9b

localize21.0ms

Local error

Found 4 expressions with local error:

1.5b	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
2.1b	(/ x (fma (* 4.0 p) p (* x x)))
17.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
17.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
17×	`add-cube-cbrt`
12×	`fma-def`
9×	`times-frac`
7×	`unpow-prod-down` `cube-prod`
6×	`pow1` `add-exp-log` `sqrt-prod` `add-cbrt-cube` `add-log-exp`
5×	`distribute-lft-out`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`cbrt-undiv` `+-commutative` `cube-mult` `frac-2neg` `unpow3` `div-exp` `clear-num` `sum-log` `sum-cubes` `div-inv` `sqr-pow`

Counts

4 → 94

Calls

4 calls:

73.0ms	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
2.0ms	(/ x (fma (* 4.0 p) p (* x x)))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series247.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
56.0ms	(/ x (fma (* 4.0 p) p (* x x)))
52.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
57.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify39.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	285	751
1	1103	692
2	5001	688

prune497.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.9b

regimes230.0ms

Accuracy

0% (0.2b remaining)

Error of 13.4b against oracle of 13.2b and baseline of 13.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	27
1	31	27

end0.0ms

sample845.0ms

Algorithm

intervals

Results

205.0ms	5986×	body	80	valid
196.0ms	882×	body	2560	valid
113.0ms	625×	body	1280	valid
110.0ms	8000×	pre	80	true
40.0ms	288×	body	640	valid
18.0ms	144×	body	320	valid
5.0ms	75×	body	160	valid