Details

sample25.0ms

Algorithm

intervals

Results

12.0ms

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: 25.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ x y) z)
1.0b	(+ (* (+ x y) z) (* (+ t y) a))
2.0b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
24.0b	(/ (- (+ (* (+ 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)
6.0ms	(+ (* (+ x y) z) (* (+ t y) a))
40.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
85.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

series746.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (+ x y) z)
48.0ms	(+ (* (+ x y) z) (* (+ t y) a))
94.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
584.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

simplify70.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (56.0ms)

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

prune377.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y)) (/ (* y b) (+ (+ x t) y)))
1.0b	(fma (+ x y) z (* (+ t y) a))
8.8b	(/ (* y b) (+ (+ x t) y))
20.7b	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

rewrite392.0ms

Algorithm

rewrite-expression-head

Rules

2010×	`*-un-lft-identity`
1804×	`times-frac`
804×	`add-sqr-sqrt`
792×	`add-cube-cbrt`
781×	`prod-diff`
729×	`distribute-lft-out`
174×	`associate-/r/`
153×	`div-inv`
87×	`flip3-+` `flip-+`
71×	`fma-neg`
16×	`add-exp-log`
14×	`add-cbrt-cube` `associate-/l*`
10×	`associate-/r*`
7×	`div-exp`
6×	`add-log-exp`
5×	`cbrt-undiv`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `difference-of-squares`
3×	`distribute-rgt-out--`
2×	`frac-2neg` `clear-num`
1×	`sub-neg` `flip3--` `diff-log` `1-exp` `prod-exp` `frac-sub` `flip--` `cbrt-unprod` `fma-udef` `associate-/l/` `distribute-lft-out--` `sub-div`

Counts

4 → 1018

Calls

4 calls:

230.0ms	(- (/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y)) (/ (* y b) (+ (+ x t) y)))
0.0ms	(fma (+ x y) z (* (+ t y) a))
21.0ms	(/ (* y b) (+ (+ x t) y))
23.0ms	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

series945.0ms

Counts

4 → 12

Calls

4 calls:

614.0ms	(- (/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y)) (/ (* y b) (+ (+ x t) y)))
49.0ms	(fma (+ x y) z (* (+ t y) a))
71.0ms	(/ (* y b) (+ (+ x t) y))
211.0ms	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

simplify424.0ms

Algorithm

egg-herbie

Counts

1030 → 1030

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1572	39498
1	4928	29750
2	5001	29750

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (+ x t) y) b)
1.0b	(fma (+ x y) z (* (+ t y) a))
8.8b	(/ y (/ (+ (+ x t) y) b))
20.7b	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

276×	`*-un-lft-identity`
251×	`times-frac`
126×	`add-sqr-sqrt` `add-cube-cbrt`
90×	`distribute-lft-out`
27×	`associate-/r*`
21×	`associate-/l*`
18×	`add-exp-log`
16×	`add-cbrt-cube`
13×	`div-inv`
9×	`div-exp`
7×	`cbrt-undiv`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num` `associate-/r/` `associate-/l/`
2×	`flip3-+` `flip-+`
1×	`1-exp` `fma-udef`

Counts

4 → 248

Calls

4 calls:

37.0ms	(/ (+ (+ x t) y) b)
0.0ms	(fma (+ x y) z (* (+ t y) a))
21.0ms	(/ y (/ (+ (+ x t) y) b))
22.0ms	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

series430.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ (+ (+ x t) y) b)
51.0ms	(fma (+ x y) z (* (+ t y) a))
139.0ms	(/ y (/ (+ (+ x t) y) b))
217.0ms	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

simplify85.0ms

Algorithm

egg-herbie

Counts

260 → 260

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	750	2668
1	3198	2487
2	5001	2386

prune614.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ b (+ (+ x t) y))
1.0b	(fma (+ x y) z (* (+ t y) a))
8.1b	(* y (/ b (+ (+ x t) y)))
20.7b	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

rewrite95.0ms

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:

18.0ms	(/ b (+ (+ x t) y))
0.0ms	(fma (+ x y) z (* (+ t y) a))
45.0ms	(* y (/ b (+ (+ x t) y)))
22.0ms	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

series375.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ b (+ (+ x t) y))
46.0ms	(fma (+ x y) z (* (+ t y) a))
73.0ms	(* y (/ b (+ (+ x t) y)))
219.0ms	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

simplify71.0ms

Algorithm

egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 2 (44.0ms)

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

prune439.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.2b

regimes392.0ms

Accuracy

8% (20.2b remaining)

Error of 23.1b against oracle of 2.9b and baseline of 24.9b

bsearch327.0ms

Steps

Iters	Range		Point
7	9.527769158271123e+230	6.307412931937878e+232	9.710984417321525e+230
7	2.2403849999126312e-203	5.336812281805387e-201	6.764295827651096e-203
8	-3.60492936257594e-271	-1.3606216317788122e-275	-2.8607533668137723e-271
8	-2.9487660899258344e-168	-1.0891363728484868e-171	-6.687658727110805e-170
7	-1571706.2701315084	-6296.219699052463	-485115.4001107813
8	-2.02871990001622e+135	-4.08314403078979e+130	-1.5070868377098019e+134
7	-1.2429840927979902e+173	-1.4860138911190977e+171	-1.510420172746674e+171

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	65
1	65	65
2	65	65

end0.0ms

sample632.0ms

Algorithm

intervals

Results

370.0ms	7997×	body	80	valid
0.0ms	3×	body	320	valid