Details

sample32.0ms

Algorithm

intervals

Results

16.0ms	97×	body	1280	valid
4.0ms	29×	body	640	valid
3.0ms	121×	body	80	valid
1.0ms	4×	body	160	valid
0.0ms	5×	body	320	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 14.7b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot 1.0 x)
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
1.4b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite16.0ms

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:

1.0ms	(hypot 1.0 x)
3.0ms	(/ 1.0 (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))))))

series608.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(hypot 1.0 x)
99.0ms	(/ 1.0 (hypot 1.0 x))
102.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
350.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify59.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (48.0ms)

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

prune250.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 14.0b

localize13.0ms

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	(/ (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)))))))
0.9b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
30×	`times-frac`
29×	`add-sqr-sqrt` `add-cube-cbrt`
10×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
9×	`associate-/l*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
3×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`
2×	`associate-/r/`
1×	`flip3-+` `flip-+` `fma-udef`

Counts

4 → 103

Calls

4 calls:

3.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(/ 1.0 (hypot 1.0 x))
5.0ms	(/ (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)))))))
1.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

series1.6s

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ 1.0 (hypot 1.0 x))
103.0ms	(/ 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)))))))
151.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify92.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	764	1571
1	3539	1461
2	5001	1448

prune420.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ (fma (- 0.5) (+ 1.0 (log (exp (/ 1.0 (hypot 1.0 x))))) (* 1.0 1.0)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.9b	(fma (- 0.5) (+ 1.0 (log (exp (/ 1.0 (hypot 1.0 x))))) (* 1.0 1.0))
2.8b	(log (exp (/ 1.0 (hypot 1.0 x))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
30×	`times-frac`
29×	`add-sqr-sqrt` `add-cube-cbrt`
14×	`log-pow`
13×	`exp-prod`
8×	`add-exp-log` `add-cbrt-cube`
7×	`associate-/r*`
6×	`associate-/l*`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
3×	`log-prod` `div-inv`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `associate-/r/`
1×	`flip3-+` `rem-log-exp` `flip-+` `fma-udef`

Counts

4 → 101

Calls

4 calls:

3.0ms	(/ 1.0 (hypot 1.0 x))
5.0ms	(/ (fma (- 0.5) (+ 1.0 (log (exp (/ 1.0 (hypot 1.0 x))))) (* 1.0 1.0)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.0ms	(fma (- 0.5) (+ 1.0 (log (exp (/ 1.0 (hypot 1.0 x))))) (* 1.0 1.0))
5.0ms	(log (exp (/ 1.0 (hypot 1.0 x))))

series1.6s

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ 1.0 (hypot 1.0 x))
1.2s	(/ (fma (- 0.5) (+ 1.0 (log (exp (/ 1.0 (hypot 1.0 x))))) (* 1.0 1.0)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
158.0ms	(fma (- 0.5) (+ 1.0 (log (exp (/ 1.0 (hypot 1.0 x))))) (* 1.0 1.0))
101.0ms	(log (exp (/ 1.0 (hypot 1.0 x))))

simplify102.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	816	1673
1	3619	1535
2	5001	1516

prune437.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
0.9b	(fma (- 0.5) (+ 1.0 (log (exp (/ 1.0 (hypot 1.0 x))))) (* 1.0 1.0))
2.8b	(log (exp (/ 1.0 (hypot 1.0 x))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
27×	`times-frac`
14×	`log-pow`
13×	`exp-prod`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r` `associate-/l`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`log-prod` `div-inv`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`rem-log-exp` `fma-udef`

Counts

4 → 95

Calls

4 calls:

3.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(/ 1.0 (hypot 1.0 x))
1.0ms	(fma (- 0.5) (+ 1.0 (log (exp (/ 1.0 (hypot 1.0 x))))) (* 1.0 1.0))
5.0ms	(log (exp (/ 1.0 (hypot 1.0 x))))

series470.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ 1.0 (hypot 1.0 x))
107.0ms	(/ 1.0 (hypot 1.0 x))
155.0ms	(fma (- 0.5) (+ 1.0 (log (exp (/ 1.0 (hypot 1.0 x))))) (* 1.0 1.0))
105.0ms	(log (exp (/ 1.0 (hypot 1.0 x))))

simplify170.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 3 (154.0ms)

Iter	Nodes	Cost
0	290	639
1	922	581
2	4602	574
3	5001	567

prune419.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

regimes125.0ms

Accuracy

100% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 15.0b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	38
1	48	38

end0.0ms

sample819.0ms

Algorithm

intervals

Results

471.0ms	2849×	body	1280	valid
117.0ms	4082×	body	80	valid
88.0ms	645×	body	640	valid
28.0ms	283×	body	320	valid
8.0ms	141×	body	160	valid