Details

sample38.0ms

Algorithm

intervals

Results

22.0ms	256×	body	80	valid
6.0ms	256×	pre	80	true

simplify68.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	6
1	52	6
2	117	6
3	240	6
4	478	6
5	947	6
6	1844	6
7	5001	6

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 19.2b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
19.3b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

8×	`associate-/l/`
7×	`add-exp-log` `add-cbrt-cube`
5×	`flip3-+` `flip-+`
4×	`add-sqr-sqrt` `frac-times` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
3×	`flip3--` `times-frac` `associate-/r*` `flip--`
2×	`pow1` `cbrt-undiv` `expm1-log1p-u` `associate-r/` `div-exp` `associate-l/` `associate-/r/` `log1p-expm1-u`
1×	`+-commutative` `fma-def` `frac-2neg` `prod-exp` `clear-num` `sum-log` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

2 → 47

Calls

2 calls:

2.0ms	(+ (* x x) (* y y))
12.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series87.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(+ (* x x) (* y y))
61.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify45.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	322	380
1	1875	324
2	5001	308

prune129.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(log1p (expm1 (/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))))
0.3b	(expm1 (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))))
19.3b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/l/`
6×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
5×	`flip3-+` `flip-+` `log1p-expm1-u`
4×	`pow1` `expm1-log1p-u` `frac-times`
3×	`flip3--` `times-frac` `associate-/r*` `flip--`
2×	`cbrt-undiv` `associate-r/` `div-exp` `associate-l/` `associate-/r/`
1×	`+-commutative` `log1p-udef` `expm1-log1p` `fma-def` `frac-2neg` `log1p-expm1` `prod-exp` `clear-num` `sum-log` `cbrt-unprod` `div-inv` `associate-/l*` `expm1-udef`

Counts

4 → 69

Calls

4 calls:

3.0ms	(+ (* x x) (* y y))
0.0ms	(log1p (expm1 (/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))))
0.0ms	(expm1 (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))))
11.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series282.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* x x) (* y y))
106.0ms	(log1p (expm1 (/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))))
89.0ms	(expm1 (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))))
61.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify47.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	353	600
1	1923	513
2	5002	494

prune210.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (+ 1 (expm1 (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))))))
0.3b	(+ 1 (expm1 (/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))))
0.3b	(expm1 (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))))
19.3b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

2.0ms	(log (+ 1 (expm1 (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))))))
2.0ms	(+ 1 (expm1 (/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))))
0.0ms	(expm1 (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))))
14.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series341.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(log (+ 1 (expm1 (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))))))
86.0ms	(+ 1 (expm1 (/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))))
88.0ms	(expm1 (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))))
59.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify47.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	378	852
1	1881	741
2	5001	722

prune241.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (- x y) (hypot x y)) (/ (/ (+ x y) 1) (hypot x y)))
0.0b	(/ (- x y) (hypot x y))
0.3b	(+ 1 (expm1 (* (/ (- x y) (hypot x y)) (/ (/ (+ x y) 1) (hypot x y)))))
0.3b	(expm1 (* (/ (- x y) (hypot x y)) (/ (/ (+ x y) 1) (hypot x y))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

128×	`times-frac`
107×	`add-sqr-sqrt`
101×	`*-un-lft-identity`
65×	`add-cube-cbrt`
52×	`associate-r`
34×	`add-exp-log`
27×	`add-cbrt-cube`
19×	`associate-l`
15×	`div-exp`
10×	`cbrt-undiv` `distribute-lft-out`
8×	`prod-exp` `unswap-sqr`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1` `cbrt-unprod` `div-inv` `add-log-exp`
5×	`log1p-expm1-u` `associate-/l*`
4×	`expm1-log1p-u`
3×	`fma-def` `associate-/r*`
2×	`1-exp` `associate-/l/` `expm1-udef`
1×	`+-commutative` `frac-times` `associate-+r-` `expm1-log1p` `flip3--` `frac-2neg` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `sum-log` `*-commutative` `flip--` `flip-+`

Counts

4 → 176

Calls

4 calls:

47.0ms	(* (/ (- x y) (hypot x y)) (/ (/ (+ x y) 1) (hypot x y)))
8.0ms	(/ (- x y) (hypot x y))
2.0ms	(+ 1 (expm1 (* (/ (- x y) (hypot x y)) (/ (/ (+ x y) 1) (hypot x y)))))
0.0ms	(expm1 (* (/ (- x y) (hypot x y)) (/ (/ (+ x y) 1) (hypot x y))))

series406.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* (/ (- x y) (hypot x y)) (/ (/ (+ x y) 1) (hypot x y)))
90.0ms	(/ (- x y) (hypot x y))
113.0ms	(+ 1 (expm1 (* (/ (- x y) (hypot x y)) (/ (/ (+ x y) 1) (hypot x y)))))
116.0ms	(expm1 (* (/ (- x y) (hypot x y)) (/ (/ (+ x y) 1) (hypot x y))))

simplify69.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	882	1793
1	4152	1549
2	5001	1527

prune480.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes65.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	9
1	12	9

end0.0ms

sample924.0ms

Algorithm

intervals

Results

585.0ms	8000×	body	80	valid
189.0ms	8000×	pre	80	true