Details

sample36.0ms

Algorithm

intervals

Results

8.0ms	197×	body	80	valid
5.0ms	21×	body	2560	valid
4.0ms	22×	body	1280	valid
3.0ms	256×	pre	80	true
1.0ms	9×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	2×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.5b

localize16.0ms

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)))))))
0.5b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.5b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite166.0ms

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:

28.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
56.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
55.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
24.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series441.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
261.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
75.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
56.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify84.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 3 (68.0ms)

Iter	Nodes	Cost
0	297	951
1	884	898
2	2732	885
3	5001	883

prune533.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.2b

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)))))
2.2b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
14.5b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite114.0ms

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:

7.0ms	(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
72.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
6.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
26.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series444.0ms

Counts

4 → 12

Calls

4 calls:

264.0ms	(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
50.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
73.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify49.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (39.0ms)

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

prune539.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.0b	(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
2.2b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
14.5b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite111.0ms

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:

76.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
6.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
23.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series441.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
261.0ms	(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))))))
52.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify49.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (38.0ms)

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

prune622.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.2b

localize19.0ms

Local error

Found 4 expressions with local error:

1.2b	(log (log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))
2.0b	(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
2.2b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
14.5b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite219.0ms

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)))))))))))
3.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
188.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
22.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series695.0ms

Counts

4 → 12

Calls

4 calls:

332.0ms	(log (log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))))
246.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
68.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
49.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify76.0ms

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

prune459.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.6b

regimes533.0ms

Accuracy

78% (1.3b remaining)

Error of 8.7b against oracle of 7.4b and baseline of 13.5b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	28
1	40	28

end0.0ms

sample884.0ms

Algorithm

intervals

Results

241.0ms	6026×	body	80	valid
203.0ms	800×	body	2560	valid
118.0ms	605×	body	1280	valid
89.0ms	8000×	pre	80	true
48.0ms	314×	body	640	valid
23.0ms	165×	body	320	valid
7.0ms	90×	body	160	valid