Details

sample32.0ms

Algorithm

intervals

Results

18.0ms	112×	body	1280	valid
3.0ms	109×	body	80	valid
2.0ms	19×	body	640	valid
1.0ms	9×	body	320	valid
0.0ms	7×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	6
1	26	6
2	33	6
3	35	6
4	41	6
5	44	6
6	44	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.4b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(hypot 1.0 x)
2.5b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
21×	`add-cube-cbrt`
12×	`prod-diff`
9×	`times-frac`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def` `fma-neg` `associate-/r` `sqrt-prod` `associate-/l`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `hypot-udef` `flip3--` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `sum-log` `flip--` `flip-+` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 87

Calls

4 calls:

6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
2.0ms	(/ 1.0 (hypot 1.0 x))
0.0ms	(hypot 1.0 x)
4.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series609.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
105.0ms	(/ 1.0 (hypot 1.0 x))
53.0ms	(hypot 1.0 x)
347.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify56.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	539	998
1	2059	745
2	5001	742

prune258.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 14.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
2.1b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

2.0ms	(/ 1.0 (hypot 1.0 x))
2.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

series677.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ 1.0 (hypot 1.0 x))
100.0ms	(/ 1.0 (hypot 1.0 x))
316.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
153.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify47.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	430	681
1	1662	625
2	5001	623

prune342.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
2.1b	(log (exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))
2.1b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

2.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
2.0ms	(log (exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))
0.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

series723.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ 1.0 (hypot 1.0 x))
318.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
152.0ms	(log (exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))
152.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify46.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	466	707
1	1745	637
2	5001	636

prune337.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.6b	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
2.1b	(log (exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))
2.1b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
8×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `cbrt-div` `log-prod` `log-pow` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`exp-prod`
2×	`flip3-+` `pow1/3` `flip-+` `fma-udef` `distribute-lft-out`
1×	`rem-log-exp` `exp-sum`

Counts

4 → 60

Calls

4 calls:

2.0ms	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
2.0ms	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.0ms	(log (exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))
0.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

series2.8s

Counts

4 → 12

Calls

4 calls:

1.2s	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.2s	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
153.0ms	(log (exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))
155.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify60.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	455	1151
1	1729	1050
2	5002	1042

prune378.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

regimes211.0ms

Accuracy

99.8% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 15.1b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	37
1	44	37

end0.0ms

sample796.0ms

Algorithm

intervals

Results

446.0ms	2799×	body	1280	valid
116.0ms	4031×	body	80	valid
90.0ms	666×	body	640	valid
29.0ms	336×	body	320	valid
9.0ms	168×	body	160	valid