Details

sample26.0ms

Algorithm

intervals

Results

13.0ms

256×

body

valid

simplify106.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	32	10
1	71	10
2	184	10
3	381	10
4	682	10
5	1102	10
6	2122	10
7	4337	10
8	5001	10

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: 28.5b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ x y) z)
2.1b	(+ (* (+ x y) z) (* (+ t y) a))
2.7b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
26.7b	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

6.0ms	(* (+ x y) z)
7.0ms	(+ (* (+ x y) z) (* (+ t y) a))
10.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
17.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

series754.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (+ x y) z)
46.0ms	(+ (* (+ x y) z) (* (+ t y) a))
94.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
592.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

simplify65.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	523	1089
1	2308	1025
2	5001	1025

prune285.0ms

Filtered

102 candidates to 74 candidates (72.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	90	12	102
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	91	12	103

Merged error: 9.9b

Counts

103 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (+ (* (+ x y) z) (* (+ t y) a)) (+ (+ x t) y)) (/ (* y b) (+ (+ x t) y)))
2.1b	(+ (* (+ x y) z) (* (+ t y) a))
8.9b	(/ (* y b) (+ (+ x t) y))
23.2b	(/ (+ (* (+ x y) z) (* (+ t y) a)) (+ (+ x t) y))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

31.0ms	(- (/ (+ (* (+ x y) z) (* (+ t y) a)) (+ (+ x t) y)) (/ (* y b) (+ (+ x t) y)))
7.0ms	(+ (* (+ x y) z) (* (+ t y) a))
8.0ms	(/ (* y b) (+ (+ x t) y))
14.0ms	(/ (+ (* (+ x y) z) (* (+ t y) a)) (+ (+ x t) y))

series1.1s

Counts

4 → 12

Calls

4 calls:

710.0ms	(- (/ (+ (* (+ x y) z) (* (+ t y) a)) (+ (+ x t) y)) (/ (* y b) (+ (+ x t) y)))
49.0ms	(+ (* (+ x y) z) (* (+ t y) a))
73.0ms	(/ (* y b) (+ (+ x t) y))
220.0ms	(/ (+ (* (+ x y) z) (* (+ t y) a)) (+ (+ x t) y))

simplify76.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	562	1293
1	2674	1218
2	5003	1218

prune324.0ms

Filtered

117 candidates to 84 candidates (71.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	113	4	117
Fresh	3	8	11
Picked	0	1	1
Done	0	0	0
Total	116	13	129

Merged error: 6.3b

Counts

129 → 13

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (+ x t) y) b)
2.1b	(+ (* (+ x y) z) (* (+ t y) a))
7.4b	(/ y (/ (+ (+ x t) y) b))
23.2b	(/ (+ (* (+ x y) z) (* (+ t y) a)) (+ (+ x t) y))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

180×	`*-un-lft-identity`
147×	`times-frac`
80×	`add-sqr-sqrt` `add-cube-cbrt`
60×	`distribute-lft-out`
27×	`associate-/r*`
16×	`associate-*l/`
13×	`add-exp-log` `add-cbrt-cube`
12×	`flip3-+` `flip-+`
11×	`associate-/l*`
8×	`frac-add` `associate-/l/`
7×	`div-inv`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`pow1`
3×	`frac-2neg` `clear-num` `associate-/r/`
1×	`+-commutative` `sum-log`

Counts

4 → 189

Calls

4 calls:

8.0ms	(/ (+ (+ x t) y) b)
7.0ms	(+ (* (+ x y) z) (* (+ t y) a))
10.0ms	(/ y (/ (+ (+ x t) y) b))
14.0ms	(/ (+ (* (+ x y) z) (* (+ t y) a)) (+ (+ x t) y))

series434.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ (+ (+ x t) y) b)
47.0ms	(+ (* (+ x y) z) (* (+ t y) a))
149.0ms	(/ y (/ (+ (+ x t) y) b))
214.0ms	(/ (+ (* (+ x y) z) (* (+ t y) a)) (+ (+ x t) y))

simplify99.0ms

Algorithm

egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	726	1823
1	3478	1734
2	5001	1733

prune506.0ms

Filtered

201 candidates to 133 candidates (66.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	198	3	201
Fresh	2	9	11
Picked	1	0	1
Done	0	1	1
Total	201	13	214

Merged error: 4.5b

Counts

214 → 13

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 1 (/ (/ (+ (+ x t) y) b) y))
2.1b	(+ (* (+ x y) z) (* (+ t y) a))
7.4b	(/ (/ (+ (+ x t) y) b) y)
23.2b	(/ (+ (* (+ x y) z) (* (+ t y) a)) (+ (+ x t) y))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

723×	`times-frac`
580×	`*-un-lft-identity`
320×	`add-sqr-sqrt` `add-cube-cbrt`
156×	`distribute-lft-out`
69×	`associate-/r*`
32×	`add-exp-log`
25×	`associate-/l*`
23×	`div-inv`
20×	`add-cbrt-cube`
19×	`div-exp`
16×	`associate-*l/`
11×	`flip3-+` `flip-+`
10×	`cbrt-undiv`
8×	`frac-add`
7×	`associate-/l/`
6×	`add-log-exp`
5×	`pow1`
3×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `associate-/r/`
1×	`+-commutative` `pow-flip` `sum-log` `inv-pow`

Counts

4 → 424

Calls

4 calls:

19.0ms	(/ 1 (/ (/ (+ (+ x t) y) b) y))
7.0ms	(+ (* (+ x y) z) (* (+ t y) a))
15.0ms	(/ (/ (+ (+ x t) y) b) y)
15.0ms	(/ (+ (* (+ x y) z) (* (+ t y) a)) (+ (+ x t) y))

series469.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(/ 1 (/ (/ (+ (+ x t) y) b) y))
51.0ms	(+ (* (+ x y) z) (* (+ t y) a))
33.0ms	(/ (/ (+ (+ x t) y) b) y)
220.0ms	(/ (+ (* (+ x y) z) (* (+ t y) a)) (+ (+ x t) y))

simplify80.0ms

Algorithm

egg-herbie

Counts

436 → 436

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1383	4958
1	5001	4462

prune921.0ms

Filtered

436 candidates to 237 candidates (54.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	435	1	436
Fresh	1	10	11
Picked	1	0	1
Done	0	1	1
Total	437	12	449

Merged error: 4.5b

Counts

449 → 12

Details

sample26.0ms

simplify106.0ms

prune3.0ms

localize15.0ms

rewrite43.0ms

series754.0ms

simplify65.0ms

prune285.0ms

localize15.0ms

rewrite64.0ms

series1.1s

simplify76.0ms

prune324.0ms

localize15.0ms

rewrite50.0ms

series434.0ms

simplify99.0ms

prune506.0ms

localize16.0ms

rewrite92.0ms

series469.0ms

simplify80.0ms

prune921.0ms

regimes550.0ms

bsearch3.0ms

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