Details

sample41.0ms

Algorithm

intervals

Results

22.0ms	106×	body	1280	valid
5.0ms	121×	body	80	valid
3.0ms	17×	body	640	valid
1.0ms	9×	body	320	valid
0.0ms	3×	body	160	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	6
1	24	6
2	28	6
3	30	6
4	35	6
5	37	6
6	37	6

prune3.0ms

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: 15.8b

Counts

2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(hypot 1.0 x)
2.2b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

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

series162.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
5.0ms	(/ 1.0 (hypot 1.0 x))
1.0ms	(hypot 1.0 x)
85.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify59.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	201	433
1	602	413
2	1986	411
3	5001	411

prune195.0ms

Filtered

73 candidates to 52 candidates (71.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	68	5	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	5	74

Merged error: 15.4b

Counts

74 → 5

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	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
1.8b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
20×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`associate-/r` `associate-/l`
4×	`pow1` `associate-*r/` `associate--l+`
3×	`sub-neg`
2×	`cbrt-undiv` `distribute-rgt-in` `flip3--` `frac-2neg` `distribute-lft-in` `div-exp` `clear-num` `frac-sub` `flip--` `div-inv`
1×	`+-commutative` `flip3-+` `diff-log` `sum-log` `flip-+` `distribute-lft-out`

Counts

4 → 84

Calls

4 calls:

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

series124.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ 1.0 (hypot 1.0 x))
8.0ms	(/ 1.0 (hypot 1.0 x))
74.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
37.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify147.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	306	616
1	1080	568
2	4837	560
3	5001	560

prune284.0ms

Filtered

96 candidates to 69 candidates (71.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	94	2	96
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	98	3	101

Merged error: 15.4b

Counts

101 → 3

localize19.0ms

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))))))
1.8b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))
1.8b	(log (exp (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

3.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
6.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))
6.0ms	(log (exp (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))))

series151.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ 1.0 (hypot 1.0 x))
77.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
37.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))
32.0ms	(log (exp (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))))

simplify43.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	349	684
1	1219	618
2	5002	615

prune288.0ms

Filtered

91 candidates to 63 candidates (69.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

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

Merged error: 15.4b

Counts

94 → 3

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (sqrt 0.5) (sqrt (+ (* 1.0 (/ 1 (hypot 1.0 x))) 1.0))) 1.0)
0.6b	(* (sqrt 0.5) (sqrt (+ (* 1.0 (/ 1 (hypot 1.0 x))) 1.0)))
1.8b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))
1.8b	(log (exp (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
9×	`pow1` `log-prod`
8×	`associate--l+` `add-log-exp`
6×	`add-exp-log` `sub-neg` `associate-r/` `associate-r` `associate-l*` `exp-sum` `add-cbrt-cube`
4×	`distribute-rgt-in` `distribute-lft-in` `log-pow` `unswap-sqr`
3×	`exp-prod` `pow-prod-down`
2×	`flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `frac-sub` `flip--` `flip-+`
1×	`+-commutative` `log-div` `exp-diff` `sqrt-unprod` `diff-log` `rem-log-exp` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod`

Counts

4 → 83

Calls

4 calls:

10.0ms	(+ (* (sqrt 0.5) (sqrt (+ (* 1.0 (/ 1 (hypot 1.0 x))) 1.0))) 1.0)
10.0ms	(* (sqrt 0.5) (sqrt (+ (* 1.0 (/ 1 (hypot 1.0 x))) 1.0)))
6.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))
6.0ms	(log (exp (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))))

series214.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(+ (* (sqrt 0.5) (sqrt (+ (* 1.0 (/ 1 (hypot 1.0 x))) 1.0))) 1.0)
71.0ms	(* (sqrt 0.5) (sqrt (+ (* 1.0 (/ 1 (hypot 1.0 x))) 1.0)))
31.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))
35.0ms	(log (exp (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))))

simplify50.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	367	879
1	1395	813
2	5001	803

prune307.0ms

Filtered

95 candidates to 61 candidates (64.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	0	1	1
Picked	1	0	1
Done	1	0	1
Total	96	2	98

Merged error: 15.4b

Counts

98 → 2

regimes62.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	25
1	31	25

end0.0ms

sample1.0s

Algorithm

intervals

Results

582.0ms	2905×	body	1280	valid
146.0ms	4037×	body	80	valid
99.0ms	630×	body	640	valid
32.0ms	292×	body	320	valid
10.0ms	136×	body	160	valid

Details

sample41.0ms

simplify9.0ms

prune3.0ms

localize8.0ms

rewrite15.0ms

series162.0ms

simplify59.0ms

prune195.0ms

localize13.0ms

rewrite17.0ms

series124.0ms

simplify147.0ms

prune284.0ms

localize19.0ms

rewrite20.0ms

series151.0ms

simplify43.0ms

prune288.0ms

localize19.0ms

rewrite35.0ms

series214.0ms

simplify50.0ms

prune307.0ms

regimes62.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.0s

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