Details

sample30.0ms

Algorithm

intervals

Results

15.0ms	93×	body	1280	valid
4.0ms	127×	body	80	valid
2.0ms	18×	body	640	valid
1.0ms	13×	body	320	valid
0.0ms	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 17.1b

Counts

2 → 1

localize8.0ms

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)))
2.4b	(- 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))))))

series627.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(hypot 1.0 x)
103.0ms	(/ 1.0 (hypot 1.0 x))
106.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
359.0ms	(- 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

prune218.0ms

Filtered

99 candidates to 81 candidates (81.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	95	4	99
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	96	4	100

Merged error: 16.3b

Counts

100 → 4

localize16.0ms

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	(/ 1.0 (hypot 1.0 x))
1.9b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite15.0ms

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:

6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
3.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(/ 1.0 (hypot 1.0 x))
1.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

series492.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
106.0ms	(/ 1.0 (hypot 1.0 x))
105.0ms	(/ 1.0 (hypot 1.0 x))
153.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify45.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	319	561
1	1141	522
2	5001	520

prune295.0ms

Filtered

97 candidates to 85 candidates (87.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	94	3	97
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	96	5	101

Merged error: 0.3b

Counts

101 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
1.9b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))
1.9b	(log (exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

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

series656.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ 1.0 (hypot 1.0 x))
233.0ms	(/ 1.0 (hypot 1.0 x))
156.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))
159.0ms	(log (exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))

simplify163.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 3 (154.0ms)

Iter	Nodes	Cost
0	279	665
1	931	600
2	4763	594
3	5001	592

prune327.0ms

Filtered

98 candidates to 85 candidates (86.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	97	1	98
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	97	6	103

Merged error: 0.3b

Counts

103 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(/ (- (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)) (fma 1.0 1.0 (fma 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
0.5b	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
1.8b	(- (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

239×	`add-sqr-sqrt`
171×	`*-un-lft-identity`
168×	`prod-diff`
157×	`unpow-prod-down` `cube-prod`
119×	`add-cube-cbrt`
80×	`difference-of-squares`
75×	`times-frac`
68×	`sqr-pow`
28×	`cube-mult` `unpow3`
26×	`sqrt-prod`
25×	`associate-/l*` `distribute-lft-out--`
12×	`fma-neg`
8×	`pow1` `add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
5×	`difference-cubes`
4×	`expm1-log1p-u` `pow-pow` `log1p-expm1-u`
3×	`pow-unpow` `fma-def` `associate-/r*`
2×	`cube-div` `flip3--` `sqrt-pow1` `flip3-+` `sqrt-div` `associate-*r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `sub-neg` `frac-2neg` `pow1/2` `diff-log` `div-sub` `div-exp` `pow-prod-down` `pow-exp` `clear-num` `sum-log` `sqrt-pow2` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 386

Calls

4 calls:

6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
29.0ms	(/ (- (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)) (fma 1.0 1.0 (fma 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
9.0ms	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
16.0ms	(- (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))

series7.5s

Counts

4 → 12

Calls

4 calls:

105.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
5.5s	(/ (- (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)) (fma 1.0 1.0 (fma 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
661.0ms	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
1.2s	(- (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))

simplify171.0ms

Algorithm

egg-herbie

Counts

398 → 398

Iterations

Useful iterations: 1 (49.0ms)

Iter	Nodes	Cost
0	2397	11917
1	5003	10786

prune970.0ms

Filtered

398 candidates to 148 candidates (37.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	394	4	398
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	397	7	404

Merged error: 0.3b

Counts

404 → 7

regimes270.0ms

Accuracy

99.8% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 14.9b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	37
1	44	37

end0.0ms

sample834.0ms

Algorithm

intervals

Results

488.0ms	2863×	body	1280	valid
118.0ms	4043×	body	80	valid
81.0ms	624×	body	640	valid
29.0ms	317×	body	320	valid
9.0ms	153×	body	160	valid