Details

sample37.0ms

Algorithm

intervals

Results

19.0ms	89×	body	1280	valid
6.0ms	137×	body	80	valid
3.0ms	18×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	4×	body	160	valid

simplify20.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	442	12
1	442	12

prune6.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 13.7b

Counts

2 → 1

localize8.0ms

Local error

Found 3 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)))))
2.1b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

7×	`*-un-lft-identity` `add-log-exp`
6×	`pow1`
5×	`add-sqr-sqrt`
3×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
2×	`sqrt-pow1` `flip3-+` `sqrt-div` `associate-*r/` `flip-+`
1×	`+-commutative` `sub-neg` `flip3--` `pow1/2` `diff-log` `pow-prod-down` `sum-log` `sqrt-prod` `flip--` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 39

Calls

3 calls:

6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
7.0ms	(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))))))

series37.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
16.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
15.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify57.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4960	618
1	4960	618

prune86.0ms

Filtered

33 candidates to 48 candidates (-45.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	45	3	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	3	49

Merged error: 13.1b

Counts

49 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
11×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`add-cube-cbrt` `times-frac` `associate-*r/` `distribute-lft-out`
5×	`associate-/r*`
4×	`flip3--` `sqrt-prod` `frac-sub` `flip--` `associate-/l/`
3×	`flip3-+` `diff-log` `flip-+` `distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `sqrt-pow1` `sqrt-div` `div-exp` `associate--l+` `associate-/r/` `difference-of-squares`
1×	`+-commutative` `associate--l-` `frac-2neg` `pow1/2` `pow-prod-down` `prod-exp` `clear-num` `sum-log` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 79

Calls

4 calls:

3.0ms	(+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))))
15.0ms	(/ (* 1.0 (- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))))))
7.0ms	(sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))))
12.0ms	(- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))

series73.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))))
39.0ms	(/ (* 1.0 (- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))))))
14.0ms	(sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))))
6.0ms	(- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))

simplify43.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	6015	1628

prune203.0ms

Filtered

65 candidates to 91 candidates (-40.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	88	3	91
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	90	4	94

Merged error: 13.1b

Counts

94 → 4

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* 1.0 (/ (* (+ 1.0 0.5) (- (* (- 1.0 0.5) (hypot 1.0 x)) 0.5)) (* (hypot 1.0 x) (+ 1.0 0.5)))) (+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))))))
0.0b	(sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))))
0.0b	(* (+ 1.0 0.5) (- (* (- 1.0 0.5) (hypot 1.0 x)) 0.5))
1.6b	(- (* (- 1.0 0.5) (hypot 1.0 x)) 0.5)

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log` `add-cbrt-cube`
14×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
10×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
9×	`pow1`
8×	`add-cube-cbrt`
6×	`add-log-exp`
5×	`flip3-+` `times-frac` `associate-r/` `associate-/r` `flip-+` `distribute-lft-out`
4×	`frac-times` `flip3--` `associate-l` `flip--`
3×	`sub-neg` `associate-r` `sqrt-prod`
2×	`distribute-rgt-in` `distribute-lft-in` `sqrt-pow1` `sqrt-div` `pow-prod-down` `associate-*l/` `associate-/r/`
1×	`frac-2neg` `pow1/2` `diff-log` `clear-num` `-commutative` `div-inv` `associate-/l/` `associate-/l` `unswap-sqr`

Counts

4 → 92

Calls

4 calls:

18.0ms	(/ (* 1.0 (/ (* (+ 1.0 0.5) (- (* (- 1.0 0.5) (hypot 1.0 x)) 0.5)) (* (hypot 1.0 x) (+ 1.0 0.5)))) (+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))))))
7.0ms	(sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))))
12.0ms	(* (+ 1.0 0.5) (- (* (- 1.0 0.5) (hypot 1.0 x)) 0.5))
6.0ms	(- (* (- 1.0 0.5) (hypot 1.0 x)) 0.5)

series64.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ (* 1.0 (/ (* (+ 1.0 0.5) (- (* (- 1.0 0.5) (hypot 1.0 x)) 0.5)) (* (hypot 1.0 x) (+ 1.0 0.5)))) (+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))))))
15.0ms	(sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))))
5.0ms	(* (+ 1.0 0.5) (- (* (- 1.0 0.5) (hypot 1.0 x)) 0.5))
3.0ms	(- (* (- 1.0 0.5) (hypot 1.0 x)) 0.5)

simplify50.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5073	2222

prune267.0ms

Filtered

70 candidates to 104 candidates (-48.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	104	4	108

Merged error: 13.1b

Counts

108 → 4

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ 1.0 (+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))))) (* 1 (/ (- (* (- 1.0 0.5) (hypot 1.0 x)) 0.5) (hypot 1.0 x))))
0.0b	(sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))))
0.1b	(exp (log (* (/ 1.0 (+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))))) (* 1 (/ (- (* (- 1.0 0.5) (hypot 1.0 x)) 0.5) (hypot 1.0 x))))))
1.6b	(- (* (- 1.0 0.5) (hypot 1.0 x)) 0.5)

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-exp-log`
25×	`add-cbrt-cube`
21×	`associate-l`
20×	`*-un-lft-identity`
18×	`pow1` `prod-exp`
17×	`add-sqr-sqrt`
15×	`times-frac`
14×	`add-cube-cbrt`
10×	`cbrt-unprod`
9×	`div-exp`
8×	`associate-*r/`
7×	`pow-prod-down`
6×	`exp-prod` `distribute-lft-out` `add-log-exp`
5×	`cbrt-undiv`
4×	`1-exp` `sqrt-prod`
3×	`log-div` `exp-diff` `log-pow`
2×	`frac-times` `sqrt-pow1` `flip3-+` `sqrt-div` `associate-*l/` `associate-/r/` `flip-+`
1×	`sub-neg` `log-prod` `flip3--` `pow1/2` `diff-log` `associate-r` `exp-sum` `*-commutative` `flip--` `div-inv` `rem-exp-log`

Counts

4 → 94

Calls

4 calls:

16.0ms	(* (/ 1.0 (+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))))) (* 1 (/ (- (* (- 1.0 0.5) (hypot 1.0 x)) 0.5) (hypot 1.0 x))))
7.0ms	(sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))))
14.0ms	(exp (log (* (/ 1.0 (+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))))) (* 1 (/ (- (* (- 1.0 0.5) (hypot 1.0 x)) 0.5) (hypot 1.0 x))))))
6.0ms	(- (* (- 1.0 0.5) (hypot 1.0 x)) 0.5)

series101.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (/ 1.0 (+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))))) (* 1 (/ (- (* (- 1.0 0.5) (hypot 1.0 x)) 0.5) (hypot 1.0 x))))
13.0ms	(sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))))
42.0ms	(exp (log (* (/ 1.0 (+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))))) (* 1 (/ (- (* (- 1.0 0.5) (hypot 1.0 x)) 0.5) (hypot 1.0 x))))))
3.0ms	(- (* (- 1.0 0.5) (hypot 1.0 x)) 0.5)

simplify64.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5578	2298

prune251.0ms

Filtered

69 candidates to 106 candidates (-53.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	106	4	110

Merged error: 13.1b

Counts

110 → 4

regimes75.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	31
1	39	31

end0.0ms

sample1.1s

Algorithm

intervals

Results

652.0ms	2953×	body	1280	valid
159.0ms	3965×	body	80	valid
106.0ms	614×	body	640	valid
39.0ms	319×	body	320	valid
12.0ms	149×	body	160	valid

Details

sample37.0ms

simplify20.0ms

prune6.0ms

localize8.0ms

rewrite17.0ms

series37.0ms

simplify57.0ms

prune86.0ms

localize12.0ms

rewrite39.0ms

series73.0ms

simplify43.0ms

prune203.0ms

localize18.0ms

rewrite47.0ms

series64.0ms

simplify50.0ms

prune267.0ms

localize18.0ms

rewrite47.0ms

series101.0ms

simplify64.0ms

prune251.0ms

regimes75.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.1s

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