Details

sample38.0ms

Algorithm

intervals

Results

19.0ms	89×	body	1280	valid
5.0ms	123×	body	80	valid
4.0ms	26×	body	640	valid
1.0ms	10×	body	320	valid
1.0ms	8×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	32	12
1	32	12

prune5.0ms

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: 15.3b

Counts

2 → 1

localize8.0ms

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	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.7b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite21.0ms

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:

6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
3.0ms	(/ 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))))))

series43.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
4.0ms	(/ 1.0 (hypot 1.0 x))
13.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
19.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify59.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5021	879

prune128.0ms

Filtered

54 candidates to 78 candidates (-44.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	75	3	78
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	3	79

Merged error: 14.8b

Counts

79 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 0.5 (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))))))
2.2b	(- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
25×	`add-sqr-sqrt`
20×	`add-cube-cbrt`
19×	`times-frac`
11×	`add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r` `associate-/l`
4×	`pow1`
3×	`diff-log` `distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `div-exp` `associate--l+` `clear-num` `frac-sub` `flip--` `div-inv` `difference-of-squares`
1×	`+-commutative` `associate--l-` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`

Counts

4 → 88

Calls

4 calls:

3.0ms	(/ 0.5 (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))))))
11.0ms	(- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))

series29.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(/ 0.5 (hypot 1.0 x))
4.0ms	(/ 1.0 (hypot 1.0 x))
14.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
7.0ms	(- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))

simplify68.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4964	1085
1	4964	1085

prune233.0ms

Filtered

74 candidates to 100 candidates (-35.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	95	5	100
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	97	6	103

Merged error: 14.5b

Counts

103 → 6

localize28.0ms

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 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
2.2b	(- (* (hypot 1.0 x) (- (pow 1.0 3) (pow 0.5 3))) (+ (pow 0.5 3) (* 0.5 (* 1.0 (+ 1.0 0.5)))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

3.0ms	(/ 1.0 (hypot 1.0 x))
6.0ms	(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))))))
22.0ms	(- (* (hypot 1.0 x) (- (pow 1.0 3) (pow 0.5 3))) (+ (pow 0.5 3) (* 0.5 (* 1.0 (+ 1.0 0.5)))))

series38.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(/ 1.0 (hypot 1.0 x))
16.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
14.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
3.0ms	(- (* (hypot 1.0 x) (- (pow 1.0 3) (pow 0.5 3))) (+ (pow 0.5 3) (* 0.5 (* 1.0 (+ 1.0 0.5)))))

simplify45.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5555	1547

prune361.0ms

Filtered

61 candidates to 86 candidates (-41.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	83	3	86
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	86	6	92

Merged error: 14.4b

Counts

92 → 6

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (pow (- 1.0 0.5) 3) (pow (/ 0.5 (hypot 1.0 x)) 3)) (+ (* (- 1.0 0.5) (- 1.0 0.5)) (* (/ 0.5 (hypot 1.0 x)) (+ (/ 0.5 (hypot 1.0 x)) (- 1.0 0.5)))))
0.0b	(* (/ 0.5 (hypot 1.0 x)) (+ (/ 0.5 (hypot 1.0 x)) (- 1.0 0.5)))
0.1b	(pow (/ 0.5 (hypot 1.0 x)) 3)
2.2b	(- (pow (- 1.0 0.5) 3) (pow (/ 0.5 (hypot 1.0 x)) 3))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

304×	`add-sqr-sqrt`
184×	`*-un-lft-identity`
179×	`times-frac`
123×	`unpow-prod-down` `cube-prod`
120×	`difference-of-squares`
108×	`frac-add`
76×	`flip3--` `flip--`
74×	`associate-/r/`
72×	`frac-times`
69×	`add-cube-cbrt`
66×	`distribute-lft-out--`
54×	`associate-*r/`
51×	`sqr-pow`
37×	`associate-/l*`
27×	`associate-*l/`
19×	`flip3-+` `flip-+`
14×	`add-exp-log` `add-cbrt-cube`
13×	`associate-l`
9×	`cube-div`
7×	`pow1`
6×	`add-log-exp`
5×	`difference-cubes` `associate-r`
4×	`frac-sub` `div-inv` `associate-/l/`
3×	`cbrt-undiv` `pow-unpow` `div-exp` `associate-/r*`
2×	`pow-exp` `prod-exp` `cbrt-unprod` `distribute-lft-out` `rem-cube-cbrt` `unswap-sqr`
1×	`distribute-rgt-in` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `distribute-lft-in` `diff-log` `unpow3` `div-sub` `pow-prod-down` `clear-num` `*-commutative`

Counts

4 → 380

Calls

4 calls:

48.0ms	(/ (- (pow (- 1.0 0.5) 3) (pow (/ 0.5 (hypot 1.0 x)) 3)) (+ (* (- 1.0 0.5) (- 1.0 0.5)) (* (/ 0.5 (hypot 1.0 x)) (+ (/ 0.5 (hypot 1.0 x)) (- 1.0 0.5)))))
19.0ms	(* (/ 0.5 (hypot 1.0 x)) (+ (/ 0.5 (hypot 1.0 x)) (- 1.0 0.5)))
5.0ms	(pow (/ 0.5 (hypot 1.0 x)) 3)
27.0ms	(- (pow (- 1.0 0.5) 3) (pow (/ 0.5 (hypot 1.0 x)) 3))

series96.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(/ (- (pow (- 1.0 0.5) 3) (pow (/ 0.5 (hypot 1.0 x)) 3)) (+ (* (- 1.0 0.5) (- 1.0 0.5)) (* (/ 0.5 (hypot 1.0 x)) (+ (/ 0.5 (hypot 1.0 x)) (- 1.0 0.5)))))
14.0ms	(* (/ 0.5 (hypot 1.0 x)) (+ (/ 0.5 (hypot 1.0 x)) (- 1.0 0.5)))
9.0ms	(pow (/ 0.5 (hypot 1.0 x)) 3)
15.0ms	(- (pow (- 1.0 0.5) 3) (pow (/ 0.5 (hypot 1.0 x)) 3))

simplify129.0ms

Algorithm

egg-herbie

Counts

392 → 392

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5397	18530

prune2.9s

Filtered

226 candidates to 392 candidates (-73.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	390	2	392
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	391	7	398

Merged error: 14.4b

Counts

398 → 7

regimes124.0ms

Accuracy

0% (0.3b remaining)

Error of 15.5b against oracle of 15.2b and baseline of 15.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	66
1	35	66

end0.0ms

sample1.1s

Algorithm

intervals

Results

638.0ms	2896×	body	1280	valid
154.0ms	3967×	body	80	valid
114.0ms	643×	body	640	valid
42.0ms	348×	body	320	valid
11.0ms	146×	body	160	valid

Details

sample38.0ms

simplify3.0ms

prune5.0ms

localize8.0ms

rewrite21.0ms

series43.0ms

simplify59.0ms

prune128.0ms

localize13.0ms

rewrite22.0ms

series29.0ms

simplify68.0ms

prune233.0ms

localize28.0ms

rewrite37.0ms

series38.0ms

simplify45.0ms

prune361.0ms

localize24.0ms

rewrite131.0ms

series96.0ms

simplify129.0ms

prune2.9s

regimes124.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.1s

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