Details

sample43.0ms

Algorithm

intervals

Results

28.0ms

256×

body

valid

simplify87.0ms

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: 30.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ x y) z)
0.9b	(+ (* (+ x y) z) (* (+ t y) a))
2.9b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
29.0b	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

rewrite144.0ms

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:

10.0ms	(* (+ x y) z)
8.0ms	(+ (* (+ x y) z) (* (+ t y) a))
40.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
83.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

series820.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (+ x y) z)
53.0ms	(+ (* (+ x y) z) (* (+ t y) a))
108.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
637.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

simplify86.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (69.0ms)

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

prune460.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 9.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (fma x z (* z y)) (* (+ t y) a))
1.0b	(fma x z (* z y))
2.9b	(- (+ (fma x z (* z y)) (* (+ t y) a)) (* y b))
29.0b	(/ (- (+ (fma x z (* z y)) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

rewrite62.0ms

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:

3.0ms	(+ (fma x z (* z y)) (* (+ t y) a))
0.0ms	(fma x z (* z y))
15.0ms	(- (+ (fma x z (* z y)) (* (+ t y) a)) (* y b))
41.0ms	(/ (- (+ (fma x z (* z y)) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

series479.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(+ (fma x z (* z y)) (* (+ t y) a))
40.0ms	(fma x z (* z y))
116.0ms	(- (+ (fma x z (* z y)) (* (+ t y) a)) (* y b))
266.0ms	(/ (- (+ (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 (47.0ms)

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

prune362.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 9.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (fma x z (* z y)) (* (+ t y) a))
1.0b	(fma x z (* z y))
2.9b	(- (+ (fma x z (* z y)) (* (+ t y) a)) (* y b))
29.1b	(* (- (+ (fma x z (* z y)) (* (+ t y) a)) (* y b)) (/ 1 (+ (+ x t) y)))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

33×	`*-un-lft-identity`
24×	`add-sqr-sqrt`
21×	`associate-r`
17×	`add-cube-cbrt` `times-frac`
13×	`add-exp-log`
11×	`add-log-exp`
9×	`add-cbrt-cube` `distribute-lft-out`
6×	`pow1`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u`
3×	`flip3--` `fma-def` `fma-neg` `associate-l` `prod-diff` `flip--` `unswap-sqr`
2×	`frac-times` `flip3-+` `diff-log` `div-exp` `associate-*l/` `sum-log` `associate-/r/` `cbrt-unprod` `flip-+` `fma-udef`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rec-exp` `associate-+l+` `1-exp` `associate-r/` `pow-prod-down` `associate--l+` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 99

Calls

4 calls:

3.0ms	(+ (fma x z (* z y)) (* (+ t y) a))
0.0ms	(fma x z (* z y))
17.0ms	(- (+ (fma x z (* z y)) (* (+ t y) a)) (* y b))
75.0ms	(* (- (+ (fma x z (* z y)) (* (+ t y) a)) (* y b)) (/ 1 (+ (+ x t) y)))

series461.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(+ (fma x z (* z y)) (* (+ t y) a))
39.0ms	(fma x z (* z y))
113.0ms	(- (+ (fma x z (* z y)) (* (+ t y) a)) (* y b))
253.0ms	(* (- (+ (fma x z (* z y)) (* (+ t y) a)) (* y b)) (/ 1 (+ (+ x t) y)))

simplify70.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	451	1109
1	2290	979
2	5003	949

prune394.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 9.1b

localize21.0ms

Local error

Found 4 expressions with local error:

1.0b	(fma x z (* z y))
2.9b	(- (+ (fma x z (* z y)) (* (+ t y) a)) (* y b))
9.2b	(* (/ (- (+ (fma x z (* z y)) (* (+ t y) a)) (* y b)) (* (cbrt (+ (+ x t) y)) (cbrt (+ (+ x t) y)))) (/ (cbrt 1) (cbrt (+ (+ x t) y))))
19.7b	(/ (- (+ (fma x z (* z y)) (* (+ t y) a)) (* y b)) (* (cbrt (+ (+ x t) y)) (cbrt (+ (+ x t) y))))

rewrite244.0ms

Algorithm

rewrite-expression-head

Rules

75×	`add-sqr-sqrt`
73×	`*-un-lft-identity` `times-frac`
68×	`cbrt-prod`
54×	`associate-r`
39×	`add-cube-cbrt`
30×	`add-exp-log`
26×	`cbrt-div`
18×	`associate-/r/` `add-cbrt-cube` `distribute-lft-out`
15×	`associate-l`
14×	`unswap-sqr`
13×	`flip3-+` `flip-+`
9×	`cbrt-undiv` `frac-times` `div-exp` `prod-exp` `cbrt-unprod` `add-log-exp`
6×	`pow1`
5×	`associate-r/` `associate-l/`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `prod-diff` `div-inv` `associate-/l*`
2×	`flip3--` `diff-log` `flip--` `associate-/l/`
1×	`sub-neg` `frac-2neg` `div-sub` `pow-prod-down` `associate--l+` `clear-num` `associate-/r` `sum-log` `-commutative` `fma-udef`

Counts

4 → 175

Calls

4 calls:

0.0ms	(fma x z (* z y))
15.0ms	(- (+ (fma x z (* z y)) (* (+ t y) a)) (* y b))
169.0ms	(* (/ (- (+ (fma x z (* z y)) (* (+ t y) a)) (* y b)) (* (cbrt (+ (+ x t) y)) (cbrt (+ (+ x t) y)))) (/ (cbrt 1) (cbrt (+ (+ x t) y))))
48.0ms	(/ (- (+ (fma x z (* z y)) (* (+ t y) a)) (* y b)) (* (cbrt (+ (+ x t) y)) (cbrt (+ (+ x t) y))))

series4.0s

Counts

4 → 12

Calls

4 calls:

34.0ms	(fma x z (* z y))
114.0ms	(- (+ (fma x z (* z y)) (* (+ t y) a)) (* y b))
297.0ms	(* (/ (- (+ (fma x z (* z y)) (* (+ t y) a)) (* y b)) (* (cbrt (+ (+ x t) y)) (cbrt (+ (+ x t) y)))) (/ (cbrt 1) (cbrt (+ (+ x t) y))))
3.6s	(/ (- (+ (fma x z (* z y)) (* (+ t y) a)) (* y b)) (* (cbrt (+ (+ x t) y)) (cbrt (+ (+ x t) y))))

simplify151.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 2 (115.0ms)

Iter	Nodes	Cost
0	1021	3858
1	4812	3474
2	5001	3469

prune840.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 9.1b

regimes488.0ms

Accuracy

19.5% (14.7b remaining)

Error of 23.1b against oracle of 8.4b and baseline of 26.6b

bsearch219.0ms

Steps

Iters	Range		Point
7	6.559931041703192e+145	2.000287750443077e+147	1.9123949505361042e+146
5	1.2719413066342094e-246	3.0299120629582616e-246	1.293616190882518e-246
10	-3.320139054429188e-298	3.519047225537398e-303	2.5768960874769005e-303
8	-3.739307379384431e+110	-1.120612400025049e+108	-1.323428910747886e+109

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	20
1	35	20

end0.0ms

sample1.1s

Algorithm

intervals

Results

779.0ms	7999×	body	80	valid
0.0ms	1×	body	1280	valid