Details

sample30.0ms

Algorithm

intervals

Results

13.0ms

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: 28.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ t y) a)
1.6b	(+ (* (+ x y) z) (* (+ t y) a))
3.1b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
27.1b	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

rewrite281.0ms

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:

20.0ms	(* (+ t y) a)
14.0ms	(+ (* (+ x y) z) (* (+ t y) a))
82.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
161.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

series695.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (+ t y) a)
44.0ms	(+ (* (+ x y) z) (* (+ t y) a))
90.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
540.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

simplify73.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (61.0ms)

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

prune383.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 10.5b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ t y) a)
1.3b	(fma (+ x y) z (* (+ t y) a))
11.9b	(/ (* y b) (+ (+ x t) y))
23.1b	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 165

Calls

4 calls:

19.0ms	(* (+ t y) a)
0.0ms	(fma (+ x y) z (* (+ t y) a))
38.0ms	(/ (* y b) (+ (+ x t) y))
38.0ms	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

series333.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (+ t y) a)
47.0ms	(fma (+ x y) z (* (+ t y) a))
63.0ms	(/ (* y b) (+ (+ x t) y))
204.0ms	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

simplify67.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	588	1846
1	2585	1673
2	5001	1572

prune412.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ b (+ (+ x t) y))
1.3b	(fma (+ x y) z (* (+ t y) a))
7.8b	(* y (/ b (+ (+ x t) y)))
23.1b	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

rewrite156.0ms

Algorithm

rewrite-expression-head

Rules

185×	`*-un-lft-identity`
150×	`times-frac`
85×	`add-sqr-sqrt`
80×	`add-cube-cbrt`
63×	`distribute-lft-out`
21×	`associate-r`
18×	`add-exp-log`
16×	`add-cbrt-cube` `associate-/l*`
10×	`associate-/r*`
9×	`div-inv`
7×	`div-exp`
6×	`pow1` `associate-/r/`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `associate-l` `flip-+`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `unswap-sqr`
1×	`1-exp` `associate-r/` `pow-prod-down` `-commutative` `fma-udef` `associate-/l/`

Counts

4 → 194

Calls

4 calls:

33.0ms	(/ b (+ (+ x t) y))
0.0ms	(fma (+ x y) z (* (+ t y) a))
71.0ms	(* y (/ b (+ (+ x t) y)))
41.0ms	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

series346.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ b (+ (+ x t) y))
43.0ms	(fma (+ x y) z (* (+ t y) a))
67.0ms	(* y (/ b (+ (+ x t) y)))
202.0ms	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

simplify73.0ms

Algorithm

egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	572	2047
1	2448	1871
2	5001	1770

prune471.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ b (+ (+ x t) y))
1.3b	(fma (+ x y) z (* (+ t y) a))
7.8b	(* y (/ b (+ (+ x t) y)))
23.2b	(* (/ (fma (+ x y) z (* (+ t y) a)) 1) (/ 1 (+ (+ x t) y)))

rewrite196.0ms

Algorithm

rewrite-expression-head

Rules

96×	`*-un-lft-identity`
69×	`add-sqr-sqrt`
67×	`times-frac`
42×	`add-exp-log` `associate-r`
40×	`add-cube-cbrt`
30×	`distribute-lft-out`
23×	`add-cbrt-cube`
16×	`div-exp` `associate-l`
14×	`prod-exp`
11×	`unswap-sqr`
8×	`pow1`
7×	`1-exp`
6×	`cbrt-undiv` `associate-/r/` `cbrt-unprod`
5×	`associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`rec-exp` `flip3-+` `flip-+` `associate-/l*`
2×	`associate-r/` `pow-prod-down` `-commutative`
1×	`frac-times` `frac-2neg` `associate-*l/` `clear-num` `un-div-inv` `fma-udef`

Counts

4 → 165

Calls

4 calls:

33.0ms	(/ b (+ (+ x t) y))
0.0ms	(fma (+ x y) z (* (+ t y) a))
71.0ms	(* y (/ b (+ (+ x t) y)))
85.0ms	(* (/ (fma (+ x y) z (* (+ t y) a)) 1) (/ 1 (+ (+ x t) y)))

series349.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ b (+ (+ x t) y))
43.0ms	(fma (+ x y) z (* (+ t y) a))
67.0ms	(* y (/ b (+ (+ x t) y)))
201.0ms	(* (/ (fma (+ x y) z (* (+ t y) a)) 1) (/ 1 (+ (+ x t) y)))

simplify69.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	631	1366
1	2944	1176
2	5003	1150

prune440.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.5b

regimes452.0ms

Accuracy

19.5% (17.3b remaining)

Error of 20.4b against oracle of 3.1b and baseline of 24.6b

bsearch257.0ms

Steps

Iters	Range		Point
11	2.348694069630382e+90	1.4532198707101622e+111	2.0498830344811778e+97
10	1.6037472448008606e-27	6.48928639058972e-13	3.5472576759436823e-19
9	-3.9119777043664893e+64	-5.703231889576933e+55	-1.0718899043330679e+63
10	-4.13860978481725e+123	-1.1326817453204279e+108	-7.346408580041242e+109
5	-6.917380919692286e+169	-2.219369699985109e+169	-4.66003709328808e+169

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	53
1	51	53

end0.0ms

sample708.0ms

Algorithm

intervals

Results

340.0ms	7999×	body	80	valid
0.0ms	1×	body	160	valid