Details

sample19.0ms

Algorithm

intervals

Results

9.0ms

269×

body

valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	7
1	36	7
2	48	7
3	66	7
4	72	7
5	72	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.1b

localize9.0ms

Local error

Found 2 expressions with local error:

0.7b	(- (* b c) (* a d))
25.6b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`pow1` `flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

2 → 44

Calls

2 calls:

3.0ms	(- (* b c) (* a d))
8.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series124.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(- (* b c) (* a d))
87.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify102.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	251	464
1	938	427
2	3504	426
3	5001	426

prune144.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 25.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (* b c) (* a d))
17.4b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
29.0b	(sqrt (+ (* c c) (* d d)))
29.0b	(sqrt (+ (* c c) (* d d)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 86

Calls

4 calls:

3.0ms	(- (* b c) (* a d))
13.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
4.0ms	(sqrt (+ (* c c) (* d d)))
3.0ms	(sqrt (+ (* c c) (* d d)))

series224.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (* b c) (* a d))
117.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
34.0ms	(sqrt (+ (* c c) (* d d)))
35.0ms	(sqrt (+ (* c c) (* d d)))

simplify93.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	304	910
1	990	857
2	3354	845
3	5001	845

prune293.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 22.9b

localize18.0ms

Local error

Found 4 expressions with local error:

9.6b	(/ (- (* b c) (* a d)) (sqrt (sqrt (+ (* c c) (* d d)))))
29.0b	(sqrt (+ (* c c) (* d d)))
29.0b	(sqrt (+ (* c c) (* d d)))
29.0b	(sqrt (+ (* c c) (* d d)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

45×	`sqrt-prod`
32×	`add-sqr-sqrt`
29×	`add-cube-cbrt` `*-un-lft-identity`
27×	`times-frac`
10×	`sqrt-div`
9×	`associate-/r*`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
4×	`flip3-+` `flip-+` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l*`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-sub` `div-exp` `clear-num` `flip--` `div-inv`

Counts

4 → 101

Calls

4 calls:

10.0ms	(/ (- (* b c) (* a d)) (sqrt (sqrt (+ (* c c) (* d d)))))
4.0ms	(sqrt (+ (* c c) (* d d)))
3.0ms	(sqrt (+ (* c c) (* d d)))
3.0ms	(sqrt (+ (* c c) (* d d)))

series307.0ms

Counts

4 → 12

Calls

4 calls:

200.0ms	(/ (- (* b c) (* a d)) (sqrt (sqrt (+ (* c c) (* d d)))))
34.0ms	(sqrt (+ (* c c) (* d d)))
38.0ms	(sqrt (+ (* c c) (* d d)))
34.0ms	(sqrt (+ (* c c) (* d d)))

simplify86.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	328	1241
1	1033	1183
2	3129	1158
3	5001	1158

prune377.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 22.9b

localize11.0ms

Local error

Found 3 expressions with local error:

0.4b	(/ 1 (+ (* c c) (* d d)))
0.7b	(- (* b c) (* a d))
25.5b	(* (- (* b c) (* a d)) (/ 1 (+ (* c c) (* d d))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `times-frac`
19×	`add-cube-cbrt`
16×	`add-exp-log`
15×	`associate-r`
10×	`add-cbrt-cube`
6×	`pow1`
5×	`add-log-exp`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`flip3--` `associate-l` `associate-/r` `flip--` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `flip3-+` `1-exp` `associate-*l/` `cbrt-unprod` `flip-+` `div-inv`
1×	`sub-neg` `pow-flip` `frac-2neg` `diff-log` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

3 → 87

Calls

3 calls:

5.0ms	(/ 1 (+ (* c c) (* d d)))
3.0ms	(- (* b c) (* a d))
12.0ms	(* (- (* b c) (* a d)) (/ 1 (+ (* c c) (* d d))))

series166.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(/ 1 (+ (* c c) (* d d)))
39.0ms	(- (* b c) (* a d))
87.0ms	(* (- (* b c) (* a d)) (/ 1 (+ (* c c) (* d d))))

simplify44.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	343	780
1	1563	687
2	5002	659

prune199.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 22.9b

regimes211.0ms

Accuracy

13.3% (2.5b remaining)

Error of 25.6b against oracle of 23.1b and baseline of 26.0b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	25
1	21	25

end0.0ms

sample497.0ms

Algorithm

intervals

Results

293.0ms

8467×

body

valid