Details

sample36.0ms

Algorithm

intervals

Results

18.0ms

256×

body

valid

simplify100.0ms

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: 27.5b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ t y) a)
2.0b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
2.1b	(+ (* (+ x y) z) (* (+ t y) a))
25.7b	(/ (- (+ (* (+ 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	(* (+ t y) a)
9.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
7.0ms	(+ (* (+ x y) z) (* (+ t y) a))
18.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

series743.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (+ t y) a)
95.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
46.0ms	(+ (* (+ x y) z) (* (+ t y) a))
578.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

simplify67.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	520	1087
1	2308	1025
2	5003	1025

prune306.0ms

Filtered

102 candidates to 76 candidates (74.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	92	10	102
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	93	10	103

Merged error: 9.1b

Counts

103 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (+ (+ x t) y) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))))
2.0b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
2.1b	(+ (* (+ x y) z) (* (+ t y) a))
25.7b	(/ (+ (+ x t) y) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

152×	`*-un-lft-identity`
138×	`times-frac`
72×	`add-sqr-sqrt` `add-cube-cbrt`
48×	`distribute-lft-out`
24×	`associate-/r*`
17×	`add-exp-log`
11×	`associate-/r/` `add-cbrt-cube` `add-log-exp`
8×	`div-exp` `associate-l/` `associate-/l`
6×	`flip3--` `flip3-+` `flip--` `flip-+` `div-inv`
5×	`pow1`
4×	`cbrt-undiv` `frac-add`
2×	`rec-exp` `frac-2neg` `diff-log` `1-exp` `clear-num` `sum-log` `associate-/l/`
1×	`+-commutative` `sub-neg` `pow-flip` `associate--l+` `inv-pow`

Counts

4 → 176

Calls

4 calls:

21.0ms	(/ 1 (/ (+ (+ x t) y) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))))
10.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
7.0ms	(+ (* (+ x y) z) (* (+ t y) a))
15.0ms	(/ (+ (+ x t) y) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))

series810.0ms

Counts

4 → 12

Calls

4 calls:

570.0ms	(/ 1 (/ (+ (+ x t) y) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))))
96.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
47.0ms	(+ (* (+ x y) z) (* (+ t y) a))
97.0ms	(/ (+ (+ x t) y) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))

simplify95.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	703	3190
1	3355	2979
2	5002	2861

prune333.0ms

Filtered

188 candidates to 94 candidates (50.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	187	1	188
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	188	10	198

Merged error: 6.1b

Counts

198 → 10

localize25.0ms

Local error

Found 4 expressions with local error:

10.6b	(/ (* (cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))) (cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))) (* (cbrt (+ (+ x t) y)) (cbrt (+ (+ x t) y))))
26.5b	(cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))
26.5b	(cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))
26.5b	(cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

30×	`cbrt-div`
16×	`add-exp-log`
9×	`cbrt-prod` `flip3--` `flip--`
8×	`frac-times` `associate-/r/` `add-cbrt-cube` `associate-/l/`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`flip3-+` `flip-+`
4×	`pow1` `cbrt-undiv` `associate-r/` `div-exp` `associate-l/` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`pow1/3`
1×	`frac-2neg` `times-frac` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 76

Calls

4 calls:

33.0ms	(/ (* (cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))) (cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))) (* (cbrt (+ (+ x t) y)) (cbrt (+ (+ x t) y))))
9.0ms	(cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))
9.0ms	(cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))
9.0ms	(cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))

series1.5s

Counts

4 → 12

Calls

4 calls:

612.0ms	(/ (* (cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))) (cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))) (* (cbrt (+ (+ x t) y)) (cbrt (+ (+ x t) y))))
294.0ms	(cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))
290.0ms	(cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))
304.0ms	(cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))

simplify48.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	425	1797
1	1415	1558
2	5002	1512

prune375.0ms

Filtered

88 candidates to 75 candidates (85.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	87	11	98

Merged error: 6.1b

Counts

98 → 11

localize32.0ms

Local error

Found 4 expressions with local error:

26.5b	(cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))
26.5b	(cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))
26.5b	(cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))
26.5b	(cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `cbrt-div` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `flip3--` `pow1/3` `add-cbrt-cube` `flip--` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

9.0ms	(cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))
9.0ms	(cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))
9.0ms	(cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))
9.0ms	(cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))

series1.2s

Counts

4 → 12

Calls

4 calls:

288.0ms	(cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))
291.0ms	(cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))
286.0ms	(cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))
293.0ms	(cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))

simplify57.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 3 (49.0ms)

Iter	Nodes	Cost
0	157	884
1	462	816
2	1970	784
3	5001	780

prune325.0ms

Filtered

64 candidates to 60 candidates (93.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	63	1	64
Fresh	0	8	8
Picked	1	0	1
Done	0	2	2
Total	64	11	75

Merged error: 6.1b

Counts

75 → 11

regimes515.0ms

Accuracy

85.4% (3.2b remaining)

Error of 7.9b against oracle of 4.6b and baseline of 26.9b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	33
1	41	33

end0.0ms

sample606.0ms

Algorithm

intervals

Results

348.0ms	7997×	body	80	valid
0.0ms	2×	body	1280	valid
0.0ms	1×	body	320	valid