Details

sample29.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
9.0ms	258×	body	80	nan

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	21	7
1	39	7
2	61	7
3	80	7
4	105	7
5	114	7
6	114	7

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: 0.1b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x 1.0) (* 4.0 (sqrt x)))
0.0b	(* 6.0 (- x 1.0))
0.1b	(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 64

Calls

3 calls:

5.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
9.0ms	(* 6.0 (- x 1.0))
11.0ms	(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))

series161.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
40.0ms	(* 6.0 (- x 1.0))
80.0ms	(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))

simplify45.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	377	495
1	1642	421
2	5001	420

prune128.0ms

Filtered

73 candidates to 53 candidates (72.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	69	4	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	4	74

Merged error: 0b

Counts

74 → 4

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x 1.0) (* 4.0 (sqrt x)))
0.0b	(* 6.0 (/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x)))))
0.0b	(/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
31×	`times-frac`
23×	`add-cube-cbrt`
21×	`associate-r`
10×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1` `associate-/l*`
4×	`associate-/r/`
3×	`flip3-+` `associate-l` `associate-/r*` `sum-log` `flip-+`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `associate-+l+` `flip3--` `frac-2neg` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `flip--`

Counts

3 → 93

Calls

3 calls:

5.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
13.0ms	(* 6.0 (/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x)))))
9.0ms	(/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x))))

series190.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
81.0ms	(* 6.0 (/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x)))))
74.0ms	(/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x))))

simplify57.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	439	987
1	1809	895
2	5001	893

prune182.0ms

Filtered

102 candidates to 76 candidates (74.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	102	4	106

Merged error: 0b

Counts

106 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))
0.2b	(* (/ 6.0 (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))) (/ (- x 1.0) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))))
0.2b	(/ 6.0 (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))))
0.3b	(/ (- x 1.0) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

126×	`add-sqr-sqrt`
108×	`times-frac`
95×	`*-un-lft-identity`
69×	`add-cube-cbrt`
63×	`sqrt-prod`
36×	`associate-r`
24×	`associate-l`
20×	`add-exp-log` `add-cbrt-cube`
13×	`distribute-lft-out--` `difference-of-squares`
12×	`associate-/r*`
10×	`sqrt-div`
9×	`unswap-sqr`
8×	`associate-/r/` `associate-/l*`
7×	`pow1`
6×	`cbrt-undiv` `div-exp`
5×	`flip3-+` `flip-+`
4×	`prod-exp` `cbrt-unprod` `div-inv` `add-log-exp`
2×	`frac-2neg` `clear-num` `associate-/l/`
1×	`frac-times` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `flip--`

Counts

4 → 203

Calls

4 calls:

5.0ms	(sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))
31.0ms	(* (/ 6.0 (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))) (/ (- x 1.0) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))))
7.0ms	(/ 6.0 (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))))
11.0ms	(/ (- x 1.0) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))))

series599.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))
266.0ms	(* (/ 6.0 (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))) (/ (- x 1.0) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))))
117.0ms	(/ 6.0 (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))))
142.0ms	(/ (- x 1.0) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))))

simplify97.0ms

Algorithm

egg-herbie

Counts

215 → 215

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	772	3129
1	3369	2865
2	5002	2758

prune399.0ms

Filtered

215 candidates to 140 candidates (65.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	215	0	215
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	215	4	219

Merged error: 0b

Counts

219 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ x 1.0) (+ x 1.0))
0.1b	(/ (* 6.0 (- x 1.0)) (/ (+ (* (neg (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0))) (- (+ x 1.0) (* 4.0 (sqrt x)))))
0.2b	(+ (* (neg (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0)))
14.1b	(/ (+ (* (neg (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0))) (- (+ x 1.0) (* 4.0 (sqrt x))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

44×	`*-un-lft-identity`
42×	`times-frac`
32×	`add-sqr-sqrt`
30×	`add-cube-cbrt`
20×	`add-exp-log` `add-cbrt-cube`
18×	`associate-/r*`
11×	`pow1`
8×	`flip3-+` `flip-+`
7×	`cbrt-undiv` `div-exp` `associate-/r/`
6×	`swap-sqr` `distribute-lft-out` `add-log-exp`
4×	`frac-times` `flip3--` `associate-r/` `associate-r` `associate-l` `flip--` `div-inv` `associate-/l/` `associate-/l`
3×	`prod-exp` `cbrt-unprod`
2×	`distribute-rgt-in` `associate-+r+` `frac-2neg` `distribute-lft-in` `associate-*l/` `clear-num`
1×	`+-commutative` `pow2` `pow-plus` `pow-prod-down` `sum-log` `pow-sqr` `*-commutative` `pow-prod-up` `unswap-sqr`

Counts

4 → 136

Calls

4 calls:

12.0ms	(* (+ x 1.0) (+ x 1.0))
14.0ms	(/ (* 6.0 (- x 1.0)) (/ (+ (* (neg (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0))) (- (+ x 1.0) (* 4.0 (sqrt x)))))
5.0ms	(+ (* (neg (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0)))
11.0ms	(/ (+ (* (neg (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0))) (- (+ x 1.0) (* 4.0 (sqrt x))))

series249.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (+ x 1.0) (+ x 1.0))
120.0ms	(/ (* 6.0 (- x 1.0)) (/ (+ (* (neg (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0))) (- (+ x 1.0) (* 4.0 (sqrt x)))))
25.0ms	(+ (* (neg (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0)))
86.0ms	(/ (+ (* (neg (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0))) (- (+ x 1.0) (* 4.0 (sqrt x))))

simplify126.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 2 (94.0ms)

Iter	Nodes	Cost
0	770	2181
1	3910	1922
2	5001	1898

prune313.0ms

Filtered

148 candidates to 106 candidates (71.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	148	0	148
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	148	4	152

Merged error: 0b

Counts

152 → 4

regimes20.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	7
1	15	7

end0.0ms

sample844.0ms

Algorithm

intervals

Results

348.0ms	8000×	body	80	valid
301.0ms	7956×	body	80	nan

Details

sample29.0ms

simplify13.0ms

prune2.0ms

localize9.0ms

rewrite27.0ms

series161.0ms

simplify45.0ms

prune128.0ms

localize9.0ms

rewrite32.0ms

series190.0ms

simplify57.0ms

prune182.0ms

localize16.0ms

rewrite64.0ms

series599.0ms

simplify97.0ms

prune399.0ms

localize15.0ms

rewrite47.0ms

series249.0ms

simplify126.0ms

prune313.0ms

regimes20.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample844.0ms

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