Details

sample35.0ms

Algorithm

intervals

Results

19.0ms	97×	body	1280	valid
4.0ms	132×	body	80	valid
2.0ms	16×	body	640	valid
1.0ms	9×	body	320	valid
0.0ms	2×	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: 14.8b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(hypot 1.0 x)
0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
1.8b	(- 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:

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

series640.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ 1.0 (hypot 1.0 x))
57.0ms	(hypot 1.0 x)
113.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
360.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify57.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (47.0ms)

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

prune255.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 14.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 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)))))))
0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
1.3b	(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))
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)))))))
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))

series1.9s

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ 1.0 (hypot 1.0 x))
1.3s	(/ (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)))))))
325.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
162.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify94.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	867	1615
1	3960	1498
2	5001	1488

prune413.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (log (exp (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)))))))
0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
1.3b	(log (exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))
1.3b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

9.0ms	(/ (log (exp (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)))))))
3.0ms	(+ 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))

series2.1s

Counts

4 → 12

Calls

4 calls:

1.4s	(/ (log (exp (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)))))))
340.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
165.0ms	(log (exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))
154.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify97.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	812	2187
1	3535	2009
2	5002	1995

prune411.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (/ (log (exp (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))))))) 3)
0.5b	(cbrt (pow (/ (log (exp (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))))))) 3))
1.3b	(log (exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))
1.3b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

128×	`*-un-lft-identity`
112×	`times-frac`
74×	`cbrt-prod`
72×	`add-sqr-sqrt` `add-cube-cbrt`
68×	`unpow-prod-down` `cube-prod` `log-pow`
51×	`exp-prod`
28×	`distribute-lft-out`
22×	`pow1`
8×	`associate-/r/`
7×	`add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log-prod` `flip3-+` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow-unpow`
2×	`cube-div` `cube-mult` `unpow3` `pow-exp` `fma-udef` `rem-cube-cbrt` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `cbrt-div` `pow-pow` `pow1/3` `div-exp` `rem-log-exp` `exp-sum` `rem-cbrt-cube`

Counts

4 → 204

Calls

4 calls:

12.0ms	(pow (/ (log (exp (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))))))) 3)
17.0ms	(cbrt (pow (/ (log (exp (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))))))) 3))
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))

series5.8s

Counts

4 → 12

Calls

4 calls:

4.2s	(pow (/ (log (exp (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))))))) 3)
1.2s	(cbrt (pow (/ (log (exp (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))))))) 3))
159.0ms	(log (exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))
160.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify87.0ms

Algorithm

egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1667	6107
1	5001	5740

prune571.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

regimes346.0ms

Accuracy

99.8% (0.0b remaining)

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

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	37
1	44	37

end0.0ms

sample840.0ms

Algorithm

intervals

Results

491.0ms	2884×	body	1280	valid
122.0ms	4073×	body	80	valid
80.0ms	599×	body	640	valid
28.0ms	302×	body	320	valid
9.0ms	142×	body	160	valid