Details

sample37.0ms

Algorithm

intervals

Results

24.0ms

256×

body

valid

simplify77.0ms

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: 27.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ t y) a)
1.4b	(+ (* (+ x y) z) (* (+ t y) a))
2.4b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
25.7b	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

rewrite138.0ms

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	(* (+ t y) a)
6.0ms	(+ (* (+ x y) z) (* (+ t y) a))
39.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
81.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

series744.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (+ t y) a)
48.0ms	(+ (* (+ x y) z) (* (+ t y) a))
97.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
579.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

simplify72.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (61.0ms)

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

prune425.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 8.4b

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)))))
0.8b	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
2.2b	(- (* (+ t y) a) (* y b))
25.8b	(/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b))))

rewrite70.0ms

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:

21.0ms	(/ 1 (/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b)))))
0.0ms	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
6.0ms	(- (* (+ t y) a) (* y b))
35.0ms	(/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b))))

series807.0ms

Counts

4 → 12

Calls

4 calls:

578.0ms	(/ 1 (/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b)))))
96.0ms	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
31.0ms	(- (* (+ t y) a) (* y b))
102.0ms	(/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b))))

simplify67.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 2 (45.0ms)

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

prune377.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ 1 (/ (fma z (+ x y) (- (* (+ t y) a) (* y b))) (+ (+ x t) y))))
0.8b	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
2.2b	(- (* (+ t y) a) (* y b))
25.7b	(/ (fma z (+ x y) (- (* (+ t y) a) (* y b))) (+ (+ x t) y))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

651×	`times-frac`
479×	`*-un-lft-identity`
279×	`add-sqr-sqrt` `add-cube-cbrt`
120×	`distribute-lft-out`
73×	`associate-/r*`
49×	`add-exp-log`
36×	`div-exp`
31×	`associate-/r/`
18×	`div-inv`
15×	`add-cbrt-cube`
13×	`rec-exp` `flip3-+` `1-exp` `flip-+`
7×	`cbrt-undiv`
6×	`pow1` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `pow-flip` `log1p-expm1-u`
2×	`frac-2neg` `clear-num` `inv-pow`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `prod-diff` `flip--` `fma-udef` `remove-double-div`

Counts

4 → 382

Calls

4 calls:

36.0ms	(/ 1 (/ 1 (/ (fma z (+ x y) (- (* (+ t y) a) (* y b))) (+ (+ x t) y))))
0.0ms	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
6.0ms	(- (* (+ t y) a) (* y b))
17.0ms	(/ (fma z (+ x y) (- (* (+ t y) a) (* y b))) (+ (+ x t) y))

series916.0ms

Counts

4 → 12

Calls

4 calls:

391.0ms	(/ 1 (/ 1 (/ (fma z (+ x y) (- (* (+ t y) a) (* y b))) (+ (+ x t) y))))
97.0ms	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
31.0ms	(- (* (+ t y) a) (* y b))
397.0ms	(/ (fma z (+ x y) (- (* (+ t y) a) (* y b))) (+ (+ x t) y))

simplify91.0ms

Algorithm

egg-herbie

Counts

394 → 394

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1216	7298
1	5001	6213

prune674.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 3.6b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ t y) a)
0.8b	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
2.2b	(- (* (+ t y) a) (* y b))
25.8b	(* (/ (fma z (+ x y) (- (* (+ t y) a) (* y b))) (* (cbrt 1) (cbrt 1))) (/ (/ 1 (+ (+ x t) y)) (cbrt 1)))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

259×	`times-frac`
209×	`*-un-lft-identity`
165×	`add-sqr-sqrt`
133×	`associate-r`
105×	`add-cube-cbrt`
75×	`cbrt-prod`
66×	`add-exp-log`
55×	`distribute-lft-out`
30×	`add-cbrt-cube`
28×	`div-exp`
21×	`prod-exp` `unswap-sqr`
15×	`cbrt-undiv`
13×	`cbrt-unprod`
12×	`associate-/r/`
11×	`associate-l`
8×	`pow1` `div-inv`
7×	`flip3-+` `flip-+`
6×	`add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`rec-exp` `1-exp` `associate-*l/`
2×	`pow-prod-down` `*-commutative`
1×	`frac-times` `sub-neg` `flip3--` `fma-neg` `diff-log` `associate-*r/` `prod-diff` `flip--` `fma-udef`

Counts

4 → 244

Calls

4 calls:

9.0ms	(* (+ t y) a)
0.0ms	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
6.0ms	(- (* (+ t y) a) (* y b))
96.0ms	(* (/ (fma z (+ x y) (- (* (+ t y) a) (* y b))) (* (cbrt 1) (cbrt 1))) (/ (/ 1 (+ (+ x t) y)) (cbrt 1)))

series540.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (+ t y) a)
94.0ms	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
31.0ms	(- (* (+ t y) a) (* y b))
395.0ms	(* (/ (fma z (+ x y) (- (* (+ t y) a) (* y b))) (* (cbrt 1) (cbrt 1))) (/ (/ 1 (+ (+ x t) y)) (cbrt 1)))

simplify67.0ms

Algorithm

egg-herbie

Counts

256 → 256

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1344	4298
1	5002	3860

prune768.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 3.6b

regimes586.0ms

Accuracy

40.2% (13.2b remaining)

Error of 17.7b against oracle of 4.4b and baseline of 26.5b

bsearch123.0ms

Steps

Iters	Range		Point
10	3.3097163651926868e+38	9.405842079080587e+56	2.8337340625170535e+50
9	-2.668986491918808e-85	-2.310852153833226e-93	-2.60154563186859e-85

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	13
1	38	13

end0.0ms

sample1.0s

Algorithm

intervals

Results

737.0ms	7996×	body	80	valid
1.0ms	3×	body	640	valid
0.0ms	1×	body	1280	valid