Details

sample36.0ms

Algorithm

intervals

Results

8.0ms	197×	body	80	valid
6.0ms	24×	body	2560	valid
4.0ms	23×	body	1280	valid
4.0ms	256×	pre	80	true
1.0ms	8×	body	640	valid
0.0ms	3×	body	320	valid
0.0ms	1×	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: 12.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.6b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
16.8b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite46.0ms

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:

8.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
13.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
16.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
6.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series468.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
281.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
77.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
56.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify82.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 3 (72.0ms)

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

prune333.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.4b

localize13.0ms

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)))))
3.7b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
16.8b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite33.0ms

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))))))))
17.0ms	(* 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)))

series463.0ms

Counts

4 → 12

Calls

4 calls:

274.0ms	(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
55.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
77.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
56.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify50.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (39.0ms)

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

prune329.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.6b	(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
3.7b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
16.8b	(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))))))
6.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series461.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
274.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
73.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
60.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify53.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	416	1033
1	1736	917
2	5001	881

prune398.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.4b

localize19.0ms

Local error

Found 4 expressions with local error:

1.7b	(log (log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))
3.6b	(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
3.7b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
16.8b	(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)))

series785.0ms

Counts

4 → 12

Calls

4 calls:

373.0ms	(log (log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))
275.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
77.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
59.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify79.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 3 (69.0ms)

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

prune323.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.0b

regimes373.0ms

Accuracy

79.8% (1.3b remaining)

Error of 8.4b against oracle of 7.1b and baseline of 13.6b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	28
1	39	28

end0.0ms

sample897.0ms

Algorithm

intervals

Results

228.0ms	6003×	body	80	valid
195.0ms	821×	body	2560	valid
119.0ms	613×	body	1280	valid
117.0ms	8000×	pre	80	true
54.0ms	341×	body	640	valid
17.0ms	152×	body	320	valid
5.0ms	70×	body	160	valid