Details

sample26.0ms

Algorithm

intervals

Results

10.0ms

256×

body

valid

simplify79.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ x y) z)
1.3b	(+ (* (+ x y) z) (* (+ t y) a))
2.2b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
22.3b	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

rewrite283.0ms

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:

19.0ms	(* (+ x y) z)
14.0ms	(+ (* (+ x y) z) (* (+ t y) a))
83.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
163.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

series718.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (+ x y) z)
47.0ms	(+ (* (+ x y) z) (* (+ t y) a))
93.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
558.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

simplify76.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	568	1186
1	2526	1087
2	5001	1076

prune426.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 8.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.8b	(fma x z (* z y))
1.3b	(+ (fma x z (* z y)) (* (+ t y) a))
2.2b	(- (+ (fma x z (* z y)) (* (+ t y) a)) (* y b))
22.3b	(/ (- (+ (fma x z (* z y)) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
17×	`add-sqr-sqrt` `add-cube-cbrt`
15×	`times-frac`
12×	`distribute-lft-out`
11×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`associate-/r*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def` `fma-neg` `prod-diff` `associate-/l*`
2×	`flip3--` `flip3-+` `diff-log` `sum-log` `associate-/r/` `flip--` `flip-+` `fma-udef` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `associate-+l+` `frac-2neg` `div-sub` `div-exp` `associate--l+` `clear-num` `div-inv`

Counts

4 → 91

Calls

4 calls:

0.0ms	(fma x z (* z y))
6.0ms	(+ (fma x z (* z y)) (* (+ t y) a))
34.0ms	(- (+ (fma x z (* z y)) (* (+ t y) a)) (* y b))
81.0ms	(/ (- (+ (fma x z (* z y)) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

series401.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(fma x z (* z y))
52.0ms	(+ (fma x z (* z y)) (* (+ t y) a))
98.0ms	(- (+ (fma x z (* z y)) (* (+ t y) a)) (* y b))
222.0ms	(/ (- (+ (fma x z (* z y)) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

simplify58.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	368	1067
1	1651	987
2	5001	975

prune344.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b)))))
1.4b	(- (* (+ t y) a) (* y b))
1.8b	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
22.3b	(/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b))))

rewrite129.0ms

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:

37.0ms	(/ 1 (/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b)))))
14.0ms	(- (* (+ t y) a) (* y b))
0.0ms	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
69.0ms	(/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b))))

series768.0ms

Counts

4 → 12

Calls

4 calls:

552.0ms	(/ 1 (/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b)))))
27.0ms	(- (* (+ t y) a) (* y b))
93.0ms	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
96.0ms	(/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b))))

simplify71.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 2 (48.0ms)

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

prune412.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (+ x t) y))
1.4b	(- (* (+ t y) a) (* y b))
1.8b	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
22.4b	(* (/ 1 (+ (+ x t) y)) (fma z (+ x y) (- (* (+ t y) a) (* y b))))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

60×	`*-un-lft-identity`
32×	`times-frac`
31×	`add-sqr-sqrt`
24×	`add-cube-cbrt`
21×	`associate-l` `distribute-lft-out`
17×	`add-exp-log`
11×	`add-cbrt-cube`
7×	`pow1`
6×	`add-log-exp`
5×	`associate-/r*`
4×	`expm1-log1p-u` `div-exp` `prod-exp` `associate-/r/` `log1p-expm1-u`
3×	`associate-r` `fma-udef` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `flip3-+` `1-exp` `cbrt-unprod` `flip-+` `div-inv`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `pow-flip` `frac-2neg` `distribute-lft-in` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `flip--` `inv-pow`

Counts

4 → 116

Calls

4 calls:

33.0ms	(/ 1 (+ (+ x t) y))
14.0ms	(- (* (+ t y) a) (* y b))
0.0ms	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
77.0ms	(* (/ 1 (+ (+ x t) y)) (fma z (+ x y) (- (* (+ t y) a) (* y b))))

series725.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ 1 (+ (+ x t) y))
27.0ms	(- (* (+ t y) a) (* y b))
92.0ms	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
550.0ms	(* (/ 1 (+ (+ x t) y)) (fma z (+ x y) (- (* (+ t y) a) (* y b))))

simplify53.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	397	1050
1	1754	922
2	5003	881

prune321.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 5.6b

regimes554.0ms

Accuracy

84.1% (3.5b remaining)

Error of 8.4b against oracle of 4.9b and baseline of 27.2b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	32
1	43	32

end0.0ms

sample676.0ms

Algorithm

intervals

Results

323.0ms	7993×	body	80	valid
0.0ms	3×	body	640	valid
0.0ms	2×	body	1280	valid
0.0ms	2×	body	320	valid