Details

sample29.0ms

Algorithm

intervals

Results

14.0ms

256×

body

valid

simplify84.0ms

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))

rewrite43.0ms

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)
8.0ms	(+ (* (+ x y) z) (* (+ t y) a))
10.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
16.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

series777.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (+ t y) a)
51.0ms	(+ (* (+ x y) z) (* (+ t y) a))
102.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
602.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

simplify72.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (60.0ms)

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

prune376.0ms

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

localize13.0ms

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))

rewrite27.0ms

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)))
12.0ms	(/ (+ (* (+ x y) z) (fma y (- a b) (* a t))) (+ (+ x t) y))

series417.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (+ x y) z)
30.0ms	(fma y (- a b) (* a t))
101.0ms	(+ (* (+ x y) z) (fma y (- a b) (* a t)))
260.0ms	(/ (+ (* (+ x y) z) (fma y (- a b) (* a t))) (+ (+ x t) y))

simplify47.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 1 (11.0ms)

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

prune274.0ms

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

localize18.0ms

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))))

rewrite32.0ms

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:

10.0ms	(/ 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))))

series832.0ms

Counts

4 → 12

Calls

4 calls:

597.0ms	(/ 1 (/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b)))))
34.0ms	(- (* (+ t y) a) (* y b))
99.0ms	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
103.0ms	(/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b))))

simplify77.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 2 (48.0ms)

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

prune342.0ms

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

localize20.0ms

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)))))

rewrite63.0ms

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)))
19.0ms	(/ (/ 1 (+ (+ x t) y)) (/ 1 (fma z (+ x y) (- (* (+ t y) a) (* y b)))))

series787.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(- (* (+ t y) a) (* y b))
63.0ms	(/ 1 (fma z (+ x y) (- (* (+ t y) a) (* y b))))
100.0ms	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
594.0ms	(/ (/ 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 (36.0ms)

Iter	Nodes	Cost
0	1514	8420
1	5001	7758

prune651.0ms

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

regimes604.0ms

Accuracy

84.4% (3.5b remaining)

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

bsearch3.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	31
1	43	31

end0.0ms

sample653.0ms

Algorithm

intervals

Results

362.0ms	7998×	body	80	valid
0.0ms	1×	body	320	valid
0.0ms	1×	body	160	valid

Details

sample29.0ms

simplify84.0ms

prune3.0ms

localize14.0ms

rewrite43.0ms

series777.0ms

simplify72.0ms

prune376.0ms

localize13.0ms

rewrite27.0ms

series417.0ms

simplify47.0ms

prune274.0ms

localize18.0ms

rewrite32.0ms

series832.0ms

simplify77.0ms

prune342.0ms

localize20.0ms

rewrite63.0ms

series787.0ms

simplify112.0ms

prune651.0ms

regimes604.0ms

bsearch3.0ms

simplify2.0ms

end0.0ms

sample653.0ms

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