Details

sample52.0ms

Algorithm

intervals

Results

26.0ms	82×	body	1280	valid
8.0ms	129×	body	80	valid
7.0ms	26×	body	640	valid
3.0ms	14×	body	320	valid
1.0ms	5×	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: 17.1b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(/ 1.0 (hypot 1.0 x))
1.5b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite23.0ms

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`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `sqrt-prod` `log1p-expm1-u`
3×	`fma-def` `fma-neg` `associate-/r` `associate-/l`
2×	`sqrt-pow1` `flip3-+` `sqrt-div` `associate-*r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `flip3--` `frac-2neg` `pow1/2` `diff-log` `div-exp` `pow-prod-down` `clear-num` `sum-log` `flip--` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 92

Calls

4 calls:

9.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
7.0ms	(sqrt (* 0.5 (+ 1.0 (/ 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))))))

series886.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
290.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
109.0ms	(/ 1.0 (hypot 1.0 x))
378.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify61.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	533	1129
1	2036	878
2	5001	876

prune475.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 16.3b

localize13.0ms

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

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

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))))))
6.0ms	(/ (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (+ 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))

series1.8s

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ 1.0 (hypot 1.0 x))
328.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
1.2s	(/ (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
160.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify108.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	867	1615
1	3961	1498
2	5001	1488

prune400.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

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

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

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))))))
8.0ms	(/ (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (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))

series1.6s

Counts

4 → 12

Calls

4 calls:

108.0ms	(/ 1.0 (hypot 1.0 x))
334.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
971.0ms	(/ (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)))
165.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify96.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	820	1494
1	3621	1388
2	5002	1385

prune391.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

378×	`times-frac`
303×	`*-un-lft-identity`
224×	`sqrt-prod`
189×	`add-sqr-sqrt` `add-cube-cbrt`
57×	`distribute-lft-out`
34×	`associate-/r*`
20×	`sqrt-div`
19×	`associate-/r/`
11×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
10×	`div-inv` `associate-/l*`
6×	`add-log-exp`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`fma-def`
2×	`frac-2neg` `clear-num` `associate-/l/`
1×	`+-commutative` `sum-log` `fma-udef`

Counts

4 → 316

Calls

4 calls:

3.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
20.0ms	(/ (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (/ (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
11.0ms	(/ (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (sqrt (+ 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))

series3.4s

Counts

4 → 12

Calls

4 calls:

347.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
1.0s	(/ (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (/ (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
1.8s	(/ (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
170.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify137.0ms

Algorithm

egg-herbie

Counts

328 → 328

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1510	11813
1	5002	11035

prune920.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

regimes252.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 14.7b

bsearch160.0ms

Steps

Iters	Range		Point
9	4.4231300544851e-09	0.003211336228265424	7.9648613263332e-05
8	-1.3862719480695398	-4.2961337728369966e-05	-0.0014344305208084957

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	58
1	50	58

end0.0ms

sample1.5s

Algorithm

intervals

Results

926.0ms	2892×	body	1280	valid
247.0ms	4011×	body	80	valid
164.0ms	650×	body	640	valid
55.0ms	304×	body	320	valid
17.0ms	143×	body	160	valid