Details

sample17.0ms

Algorithm

intervals

Results

5.0ms	198×	body	80	valid
2.0ms	25×	body	640	valid
1.0ms	11×	body	1280	valid
1.0ms	13×	body	320	valid
0.0ms	9×	body	160	valid

simplify67.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	16	5
1	35	5
2	74	5
3	128	5
4	252	5
5	374	5
6	514	5
7	642	5
8	777	5
9	1010	5
10	1686	5
11	5001	5

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: 20.5b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- 1.0 x) y)
2.9b	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
6.4b	(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 63

Calls

3 calls:

6.0ms	(* (- 1.0 x) y)
7.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
9.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

series147.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(* (- 1.0 x) y)
69.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
48.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

simplify48.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	338	401
1	1456	359
2	5001	359

prune132.0ms

Filtered

72 candidates to 51 candidates (70.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	67	5	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	5	73

Merged error: 0.2b

Counts

73 → 5

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ y (+ y 1.0))
0.0b	(* (- 1.0 x) (/ y (+ y 1.0)))
2.9b	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 88

Calls

3 calls:

5.0ms	(/ y (+ y 1.0))
17.0ms	(* (- 1.0 x) (/ y (+ y 1.0)))
3.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

series148.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(/ y (+ y 1.0))
47.0ms	(* (- 1.0 x) (/ y (+ y 1.0)))
67.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

simplify59.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	400	572
1	1790	526
2	5002	526

prune141.0ms

Filtered

97 candidates to 70 candidates (72.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	97	5	102

Merged error: 0.2b

Counts

102 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- 1.0 x) y)
0.1b	(* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0))
4.9b	(- 1.0 (* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0)))
16.0b	(/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

6.0ms	(* (- 1.0 x) y)
14.0ms	(* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0))
3.0ms	(- 1.0 (* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0)))
11.0ms	(/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0)))

series365.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* (- 1.0 x) y)
82.0ms	(* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0))
162.0ms	(- 1.0 (* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0)))
91.0ms	(/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0)))

simplify89.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	567	1027
1	3078	900
2	5001	900

prune192.0ms

Filtered

117 candidates to 82 candidates (70.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	116	1	117
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	118	4	122

Merged error: 0.2b

Counts

122 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* y (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))))
4.5b	(- 1.0 (* y (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0)))))
16.0b	(/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0)))
16.0b	(/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log` `add-cbrt-cube`
13×	`add-sqr-sqrt`
12×	`times-frac`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-r`
8×	`associate-/r*`
6×	`pow1` `cbrt-undiv` `flip3--` `div-exp` `prod-exp` `associate-/r/` `flip--` `cbrt-unprod` `add-log-exp`
5×	`difference-of-squares`
4×	`associate-*l/` `associate-/l/`
3×	`associate-l` `div-inv`
2×	`frac-2neg` `clear-num` `associate-/l*`
1×	`sub-neg` `diff-log` `associate-r/` `pow-prod-down` `-commutative` `unswap-sqr`

Counts

4 → 96

Calls

4 calls:

11.0ms	(* y (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))))
3.0ms	(- 1.0 (* y (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0)))))
13.0ms	(/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0)))
10.0ms	(/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0)))

series341.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* y (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))))
106.0ms	(- 1.0 (* y (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0)))))
90.0ms	(/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0)))
90.0ms	(/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0)))

simplify81.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	436	1007
1	2320	858
2	5002	858

prune220.0ms

Filtered

108 candidates to 83 candidates (76.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	104	4	108
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	106	6	112

Merged error: 0.0b

Counts

112 → 6

regimes125.0ms

Accuracy

99.1% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 14.4b

bsearch80.0ms

Steps

Iters	Range		Point
9	719.5386143167987	28642596122.821114	239490843.3230521
9	-937727910791.0848	-216561.7802280358	-132713451.24755439

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	10
1	29	10

end0.0ms

sample444.0ms

Algorithm

intervals

Results

151.0ms	6077×	body	80	valid
69.0ms	748×	body	640	valid
42.0ms	355×	body	1280	valid
37.0ms	492×	body	320	valid
15.0ms	328×	body	160	valid