Details

sample41.0ms

Algorithm

intervals

Results

23.0ms	104×	body	1280	valid
5.0ms	116×	body	80	valid
4.0ms	22×	body	640	valid
1.0ms	9×	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	24	6
2	28	6
3	30	6
4	35	6
5	37	6
6	37	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: 16.8b

Counts

2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

4.0ms	(/ 1.0 (hypot 1.0 x))
7.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
9.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
4.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series191.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ 1.0 (hypot 1.0 x))
74.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
26.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
85.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify70.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	221	492
1	697	465
2	2323	463
3	5001	463

prune137.0ms

Filtered

78 candidates to 55 candidates (70.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	76	2	78
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	77	2	79

Merged error: 16.4b

Counts

79 → 2

localize13.0ms

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))))))
0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
1.0b	(- (* 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`
12×	`add-sqr-sqrt` `add-cube-cbrt`
10×	`add-log-exp`
9×	`times-frac`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `associate-*r/` `associate--l+`
3×	`sub-neg` `associate-/r` `associate-/l`
2×	`+-commutative` `distribute-rgt-in` `flip3--` `distribute-lft-in` `flip3-+` `sum-log` `frac-sub` `flip--` `flip-+` `distribute-lft-out`
1×	`cbrt-undiv` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

4 → 69

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 (hypot 1.0 x)))
6.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series149.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ 1.0 (hypot 1.0 x))
80.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
26.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
37.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify41.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	350	554
1	1241	510
2	5001	506

prune172.0ms

Filtered

81 candidates to 57 candidates (70.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	79	2	81
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	80	3	83

Merged error: 16.4b

Counts

83 → 3

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

3.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
15.0ms	(/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))) (* (+ 1.0 0.5) (hypot 1.0 x)))
6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
7.0ms	(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

series209.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
64.0ms	(/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))) (* (+ 1.0 0.5) (hypot 1.0 x)))
27.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
37.0ms	(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

simplify84.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	614	1108
1	3011	926
2	5001	926

prune254.0ms

Filtered

83 candidates to 60 candidates (72.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	82	4	86

Merged error: 16.3b

Counts

86 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

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

series174.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
26.0ms	(+ 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))))))

simplify50.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	329	627
1	1028	560
2	5002	557

prune161.0ms

Filtered

76 candidates to 51 candidates (67.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	76	4	80

Merged error: 16.3b

Counts

80 → 4

regimes135.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	15
1	21	15

end0.0ms

sample1.1s

Algorithm

intervals

Results

626.0ms	2845×	body	1280	valid
167.0ms	4046×	body	80	valid
108.0ms	625×	body	640	valid
38.0ms	314×	body	320	valid
13.0ms	170×	body	160	valid