Details

sample35.0ms

Algorithm

intervals

Results

21.0ms

256×

body

valid

simplify83.0ms

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: 24.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ x y) z)
2.0b	(+ (* (+ x y) z) (* (+ t y) a))
2.2b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
23.0b	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

rewrite139.0ms

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:

9.0ms	(* (+ x y) z)
6.0ms	(+ (* (+ x y) z) (* (+ t y) a))
38.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
83.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

series755.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (+ x y) z)
49.0ms	(+ (* (+ x y) z) (* (+ t y) a))
97.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
588.0ms	(/ (- (+ (* (+ 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	568	1186
1	2526	1087
2	5001	1076

prune398.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ t y) a)
1.3b	(fma (+ x y) z (* (+ t y) a))
8.2b	(/ (* y b) (+ (+ x t) y))
19.7b	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

rewrite59.0ms

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:

9.0ms	(* (+ t y) a)
0.0ms	(fma (+ x y) z (* (+ t y) a))
21.0ms	(/ (* y b) (+ (+ x t) y))
21.0ms	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

series357.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (+ t y) a)
50.0ms	(fma (+ x y) z (* (+ t y) a))
73.0ms	(/ (* y b) (+ (+ x t) y))
214.0ms	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

simplify66.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	588	1849
1	2564	1673
2	5002	1573

prune419.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.8b

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (cbrt (+ (+ x t) y)) (cbrt (+ (+ x t) y)))
1.3b	(fma (+ x y) z (* (+ t y) a))
5.0b	(* (/ y (* (cbrt (+ (+ x t) y)) (cbrt (+ (+ x t) y)))) (/ b (cbrt (+ (+ x t) y))))
19.7b	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

rewrite242.0ms

Algorithm

rewrite-expression-head

Rules

214×	`*-un-lft-identity`
153×	`times-frac`
109×	`add-sqr-sqrt`
85×	`add-cube-cbrt`
75×	`distribute-lft-out`
53×	`cbrt-prod`
38×	`associate-r`
34×	`add-exp-log`
26×	`cbrt-div`
23×	`associate-l` `add-cbrt-cube`
14×	`flip3-+` `swap-sqr` `flip-+`
13×	`pow1` `associate-/l*`
12×	`div-exp` `associate-/r/`
10×	`cbrt-undiv` `unswap-sqr`
9×	`frac-times` `prod-exp` `cbrt-unprod` `div-inv`
6×	`pow1/3`
5×	`associate-r/` `associate-l/` `associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down`
2×	`pow-sqr` `*-commutative` `pow-prod-up`
1×	`pow2` `frac-2neg` `pow-plus` `1-exp` `clear-num` `fma-udef` `associate-/l/`

Counts

4 → 252

Calls

4 calls:

70.0ms	(* (cbrt (+ (+ x t) y)) (cbrt (+ (+ x t) y)))
0.0ms	(fma (+ x y) z (* (+ t y) a))
134.0ms	(* (/ y (* (cbrt (+ (+ x t) y)) (cbrt (+ (+ x t) y)))) (/ b (cbrt (+ (+ x t) y))))
24.0ms	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

series641.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(* (cbrt (+ (+ x t) y)) (cbrt (+ (+ x t) y)))
51.0ms	(fma (+ x y) z (* (+ t y) a))
177.0ms	(* (/ y (* (cbrt (+ (+ x t) y)) (cbrt (+ (+ x t) y)))) (/ b (cbrt (+ (+ x t) y))))
215.0ms	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

simplify126.0ms

Algorithm

egg-herbie

Counts

264 → 264

Iterations

Useful iterations: 2 (97.0ms)

Iter	Nodes	Cost
0	947	3451
1	4766	3144
2	5001	3143

prune813.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 2.7b

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
1.3b	(fma (+ x y) z (* (+ t y) a))
2.0b	(* (/ (* (cbrt y) (cbrt y)) (cbrt (+ (+ x t) y))) (* (/ (cbrt y) (cbrt (+ (+ x t) y))) (/ b (cbrt (+ (+ x t) y)))))
19.7b	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

139×	`*-un-lft-identity`
127×	`times-frac`
80×	`add-exp-log`
64×	`add-sqr-sqrt` `add-cube-cbrt`
45×	`distribute-lft-out`
40×	`add-cbrt-cube`
32×	`prod-exp` `cbrt-unprod`
27×	`div-exp`
25×	`cbrt-undiv`
14×	`associate-l`
13×	`associate-/l*`
9×	`pow1`
8×	`cbrt-prod` `div-inv`
5×	`frac-times` `associate-r/` `associate-/r`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `associate-*l/`
2×	`cbrt-div` `flip3-+` `flip-+`
1×	`frac-2neg` `pow1/3` `1-exp` `associate-r` `clear-num` `*-commutative` `fma-udef` `associate-/l/`

Counts

4 → 190

Calls

4 calls:

0.0ms	(cbrt y)
0.0ms	(fma (+ x y) z (* (+ t y) a))
123.0ms	(* (/ (* (cbrt y) (cbrt y)) (cbrt (+ (+ x t) y))) (* (/ (cbrt y) (cbrt (+ (+ x t) y))) (/ b (cbrt (+ (+ x t) y)))))
21.0ms	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

series576.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(cbrt y)
49.0ms	(fma (+ x y) z (* (+ t y) a))
139.0ms	(* (/ (* (cbrt y) (cbrt y)) (cbrt (+ (+ x t) y))) (* (/ (cbrt y) (cbrt (+ (+ x t) y))) (/ b (cbrt (+ (+ x t) y)))))
215.0ms	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

simplify106.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	850	3087
1	3676	2572
2	5001	2351

prune496.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.7b

regimes491.0ms

Accuracy

20.6% (16.8b remaining)

Error of 20.0b against oracle of 3.2b and baseline of 24.4b

bsearch215.0ms

Steps

Iters	Range		Point
6	4.6803077603340804e+57	1.9216128772820304e+58	9.184301226902076e+57
9	-1.4189253774345928e+82	-7.000917352149949e+75	-1.807389302035757e+81
5	-5.645335999683249e+164	-2.0283799556705056e+164	-2.5438150674675935e+164
9	-3.0218437262167455e+234	-2.0643612228683416e+228	-1.6180785068215594e+233

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	85
1	57	85

end0.0ms

sample934.0ms

Algorithm

intervals

Results

665.0ms	7999×	body	80	valid
0.0ms	1×	body	320	valid