Details

sample29.0ms

Algorithm

intervals

Results

14.0ms

256×

body

valid

simplify74.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	33	10
1	79	10
2	210	10
3	483	10
4	910	10
5	1516	10
6	2818	10
7	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: 24.0b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ t y) a)
1.5b	(+ (* (+ x y) z) (* (+ t y) a))
2.1b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
22.4b	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

40×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
18×	`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×	`expm1-log1p-u` `associate-l` `frac-add` `log1p-expm1-u`
3×	`fma-neg` `associate-r` `prod-diff` `associate-/l*`
2×	`flip3--` `diff-log` `sum-log` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `fma-def` `frac-2neg` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `associate--l+` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 105

Calls

4 calls:

6.0ms	(* (+ t y) a)
7.0ms	(+ (* (+ x y) z) (* (+ t y) a))
10.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
20.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

series821.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (+ t y) a)
48.0ms	(+ (* (+ x y) z) (* (+ t y) a))
104.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
642.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

simplify74.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	564	1186
1	2509	1087
2	5002	1077

prune400.0ms

Filtered

117 candidates to 93 candidates (79.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	105	12	117
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	106	12	118

Merged error: 6.6b

Counts

118 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ x y) z)
0.5b	(fma y (- a b) (* a t))
2.7b	(+ (* (+ x y) z) (fma y (- a b) (* a t)))
22.4b	(/ (+ (* (+ x y) z) (fma y (- a b) (* a t))) (+ (+ x t) y))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
18×	`add-sqr-sqrt`
16×	`add-cube-cbrt`
15×	`times-frac`
13×	`distribute-lft-out`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `add-log-exp`
5×	`associate-/r*`
4×	`expm1-log1p-u` `flip3-+` `associate-l` `flip-+` `log1p-expm1-u`
3×	`associate-r` `associate-/l*`
2×	`associate-*l/` `associate-/r/` `fma-udef` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+r+` `fma-def` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `sum-log` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 89

Calls

4 calls:

6.0ms	(* (+ x y) z)
1.0ms	(fma y (- a b) (* a t))
6.0ms	(+ (* (+ x y) z) (fma y (- a b) (* a t)))
17.0ms	(/ (+ (* (+ x y) z) (fma y (- a b) (* a t))) (+ (+ x t) y))

series436.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (+ x y) z)
31.0ms	(fma y (- a b) (* a t))
106.0ms	(+ (* (+ x y) z) (fma y (- a b) (* a t)))
277.0ms	(/ (+ (* (+ x y) z) (fma y (- a b) (* a t))) (+ (+ x t) y))

simplify50.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	334	876
1	1269	814
2	5002	814

prune302.0ms

Filtered

101 candidates to 75 candidates (74.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	98	3	101
Fresh	3	8	11
Picked	0	1	1
Done	0	0	0
Total	101	12	113

Merged error: 6.6b

Counts

113 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b)))))
0.9b	(- (* (+ t y) a) (* y b))
1.0b	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
22.5b	(/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

150×	`*-un-lft-identity`
132×	`times-frac`
70×	`add-sqr-sqrt` `add-cube-cbrt`
48×	`distribute-lft-out`
22×	`associate-/r*`
17×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`div-exp` `associate-/l*`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `associate-/l/`
1×	`sub-neg` `flip3--` `pow-flip` `flip3-+` `fma-neg` `diff-log` `prod-diff` `associate-/r/` `flip--` `flip-+` `fma-udef` `inv-pow`

Counts

4 → 167

Calls

4 calls:

14.0ms	(/ 1 (/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b)))))
6.0ms	(- (* (+ t y) a) (* y b))
1.0ms	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
8.0ms	(/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b))))

series872.0ms

Counts

4 → 12

Calls

4 calls:

627.0ms	(/ 1 (/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b)))))
31.0ms	(- (* (+ t y) a) (* y b))
106.0ms	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
108.0ms	(/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b))))

simplify74.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	496	2605
1	2228	2401
2	5002	2286

prune365.0ms

Filtered

179 candidates to 92 candidates (51.4%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	177	2	179
Fresh	1	9	10
Picked	0	1	1
Done	0	1	1
Total	178	13	191

Merged error: 4.6b

Counts

191 → 13

localize17.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (* (+ t y) a) (* y b))
0.9b	(/ 1 (fma z (+ x y) (- (* (+ t y) a) (* y b))))
1.0b	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
21.4b	(/ (/ 1 (+ (+ x t) y)) (/ 1 (fma z (+ x y) (- (* (+ t y) a) (* y b)))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

690×	`times-frac`
502×	`*-un-lft-identity`
292×	`add-sqr-sqrt` `add-cube-cbrt`
126×	`distribute-lft-out`
48×	`add-exp-log`
38×	`div-inv`
34×	`div-exp`
29×	`associate-/r/`
24×	`associate-/l*`
18×	`add-cbrt-cube`
16×	`associate-/r*`
14×	`flip3-+` `flip-+`
9×	`cbrt-undiv` `rec-exp` `1-exp`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`frac-2neg` `clear-num`
1×	`sub-neg` `flip3--` `pow-flip` `fma-neg` `diff-log` `prod-diff` `flip--` `fma-udef` `associate-/l/` `inv-pow`

Counts

4 → 400

Calls

4 calls:

6.0ms	(- (* (+ t y) a) (* y b))
3.0ms	(/ 1 (fma z (+ x y) (- (* (+ t y) a) (* y b))))
1.0ms	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
24.0ms	(/ (/ 1 (+ (+ x t) y)) (/ 1 (fma z (+ x y) (- (* (+ t y) a) (* y b)))))

series830.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- (* (+ t y) a) (* y b))
66.0ms	(/ 1 (fma z (+ x y) (- (* (+ t y) a) (* y b))))
103.0ms	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
630.0ms	(/ (/ 1 (+ (+ x t) y)) (/ 1 (fma z (+ x y) (- (* (+ t y) a) (* y b)))))

simplify112.0ms

Algorithm

egg-herbie

Counts

412 → 412

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1514	8420
1	5001	7758

prune653.0ms

Filtered

412 candidates to 162 candidates (39.3%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	411	1	412
Fresh	0	10	10
Picked	1	0	1
Done	0	2	2
Total	412	13	425

Merged error: 4.6b

Counts

425 → 13

regimes618.0ms

Accuracy

84.4% (3.5b remaining)

Error of 8.0b against oracle of 4.5b and baseline of 27.0b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	31
1	43	31

end0.0ms

sample728.0ms

Algorithm

intervals

Results

451.0ms	7998×	body	80	valid
0.0ms	1×	body	320	valid
0.0ms	1×	body	160	valid