Details

sample39.0ms

Algorithm

intervals

Results

7.0ms	193×	body	80	valid
6.0ms	31×	body	1280	valid
4.0ms	256×	pre	80	true
4.0ms	17×	body	2560	valid
1.0ms	7×	body	640	valid
0.0ms	4×	body	320	valid
0.0ms	4×	body	160	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: 14.5b

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))))
1.2b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
16.7b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite65.0ms

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	(+ (* (* 4.0 p) p) (* x x))
13.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
31.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
11.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series231.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ (* (* 4.0 p) p) (* x x))
61.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
79.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
57.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify157.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 3 (147.0ms)

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

prune508.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 14.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
1.2b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
1.2b	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
16.7b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

14.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
27.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
106.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
13.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series265.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
77.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
78.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
57.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify76.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 3 (61.0ms)

Iter	Nodes	Cost
0	286	956
1	875	889
2	2480	876
3	5002	874

prune393.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 14.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.2b	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.1b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
16.7b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
40×	`times-frac`
37×	`*-un-lft-identity`
35×	`add-cube-cbrt`
26×	`sqrt-prod`
24×	`associate-r`
17×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`pow1`
6×	`sqrt-div` `associate-/r*` `add-log-exp`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `flip3-+` `div-exp` `prod-exp` `associate-/r/` `flip-+` `log1p-expm1-u`
3×	`pow-flip` `fma-def` `associate-l` `associate-/l*`
2×	`cbrt-undiv` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 133

Calls

4 calls:

15.0ms	(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
36.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
11.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series261.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
61.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
78.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
59.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify57.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	384	1258
1	1724	1133
2	5001	1063

prune363.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 14.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
8.4b	(+ 1.0 (* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
16.7b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
16.7b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

39×	`sqrt-prod`
27×	`associate-r`
23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
11×	`pow1`
10×	`sqrt-div`
9×	`add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u`
3×	`fma-def` `associate-*r/` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/`
1×	`+-commutative` `frac-times` `associate-l` `associate-l/` `sum-log` `-commutative` `div-inv`

Counts

4 → 97

Calls

4 calls:

83.0ms	(* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
3.0ms	(+ 1.0 (* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
11.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series256.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
80.0ms	(+ 1.0 (* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
61.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
56.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify54.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	401	1399
1	1578	1211
2	5002	1134

prune357.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 14.2b

regimes191.0ms

Accuracy

0% (0.2b remaining)

Error of 13.6b against oracle of 13.3b and baseline of 13.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	11
1	21	11

end0.0ms

sample923.0ms

Algorithm

intervals

Results

235.0ms	5989×	body	80	valid
194.0ms	807×	body	2560	valid
122.0ms	647×	body	1280	valid
121.0ms	8000×	pre	80	true
48.0ms	323×	body	640	valid
18.0ms	161×	body	320	valid
5.0ms	73×	body	160	valid