Details

sample31.0ms

Algorithm

intervals

Results

14.0ms

264×

body

valid

simplify134.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	24	8
1	43	8
2	75	8
3	120	8
4	156	8
5	189	8
6	265	8
7	451	8
8	1023	8
9	3632	8
10	5001	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x y) (* z (- t a)))
0.0b	(* z (- b y))
0.0b	(* z (- t a))
20.9b	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
54×	`prod-diff`
52×	`add-cube-cbrt`
33×	`distribute-rgt-in` `distribute-lft-in`
22×	`associate-+r+`
10×	`add-exp-log` `associate-r` `add-cbrt-cube`
9×	`times-frac`
8×	`pow1`
6×	`sub-neg` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`flip3--` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `flip--` `cbrt-unprod` `associate-/l/` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `fma-def` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 161

Calls

4 calls:

9.0ms	(+ (* x y) (* z (- t a)))
11.0ms	(* z (- b y))
12.0ms	(* z (- t a))
11.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

series409.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(+ (* x y) (* z (- t a)))
34.0ms	(* z (- b y))
38.0ms	(* z (- t a))
296.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

simplify79.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	623	1398
1	2536	1029
2	5002	1026

prune443.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 21.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- b y))
0.0b	(* z (- t a))
0.4b	(/ 1 (/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a)))))
20.8b	(/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

92×	`add-sqr-sqrt`
90×	`times-frac`
88×	`*-un-lft-identity`
84×	`add-cube-cbrt`
36×	`prod-diff`
22×	`distribute-rgt-in` `distribute-lft-in`
21×	`add-exp-log`
18×	`associate-/r*`
15×	`add-cbrt-cube`
11×	`associate-/r/`
10×	`associate-r`
9×	`pow1`
8×	`div-exp`
6×	`flip3-+` `associate-l` `flip-+` `div-inv` `associate-/l*`
4×	`cbrt-undiv` `expm1-log1p-u` `sub-neg` `associate-*r/` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `flip3--` `frac-2neg` `1-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `flip--` `cbrt-unprod` `associate-/l/` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
1×	`pow-flip` `inv-pow`

Counts

4 → 211

Calls

4 calls:

11.0ms	(* z (- b y))
11.0ms	(* z (- t a))
10.0ms	(/ 1 (/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a)))))
11.0ms	(/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a))))

series1.3s

Counts

4 → 12

Calls

4 calls:

37.0ms	(* z (- b y))
34.0ms	(* z (- t a))
957.0ms	(/ 1 (/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a)))))
255.0ms	(/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a))))

simplify107.0ms

Algorithm

egg-herbie

Counts

223 → 223

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	799	2569
1	3770	2096
2	5001	2079

prune511.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 21.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- b y) z)
0.0b	(* z (- t a))
0.4b	(/ 1 (/ (+ y (* (- b y) z)) (+ (* x y) (* z (- t a)))))
20.8b	(/ (+ y (* (- b y) z)) (+ (* x y) (* z (- t a))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
80×	`add-sqr-sqrt`
76×	`*-un-lft-identity`
72×	`add-cube-cbrt`
21×	`add-exp-log`
18×	`prod-diff` `associate-/r*`
15×	`add-cbrt-cube`
11×	`distribute-rgt-in` `distribute-lft-in` `associate-/r/`
9×	`pow1`
8×	`div-exp` `associate-r` `associate-l`
6×	`flip3-+` `flip-+` `div-inv` `associate-/l*`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`sub-neg` `rec-exp` `flip3--` `frac-2neg` `1-exp` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `*-commutative` `flip--` `cbrt-unprod` `associate-/l/` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
1×	`pow-flip` `inv-pow`

Counts

4 → 189

Calls

4 calls:

12.0ms	(* (- b y) z)
12.0ms	(* z (- t a))
10.0ms	(/ 1 (/ (+ y (* (- b y) z)) (+ (* x y) (* z (- t a)))))
11.0ms	(/ (+ y (* (- b y) z)) (+ (* x y) (* z (- t a))))

series862.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (- b y) z)
34.0ms	(* z (- t a))
655.0ms	(/ 1 (/ (+ y (* (- b y) z)) (+ (* x y) (* z (- t a)))))
142.0ms	(/ (+ y (* (- b y) z)) (+ (* x y) (* z (- t a))))

simplify91.0ms

Algorithm

egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	723	2305
1	3453	1958
2	5001	1859

prune445.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 21.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x y) (* z (- t a)))
0.0b	(* z (- t a))
0.7b	(/ 1 (fma z (- b y) y))
20.1b	(* (/ 1 (fma z (- b y) y)) (+ (* x y) (* z (- t a))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt`
49×	`*-un-lft-identity`
46×	`add-cube-cbrt`
36×	`prod-diff`
23×	`distribute-rgt-in` `distribute-lft-in`
22×	`associate-+r+`
20×	`times-frac`
19×	`add-exp-log`
16×	`associate-l`
13×	`add-cbrt-cube`
9×	`pow1`
8×	`associate-r`
6×	`add-log-exp`
5×	`prod-exp`
4×	`expm1-log1p-u` `sub-neg` `associate-*r/` `div-exp` `log1p-expm1-u` `unswap-sqr`
3×	`flip3-+` `associate-/r` `cbrt-unprod` `flip-+` `associate-/l`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`+-commutative` `flip3--` `pow-flip` `fma-def` `frac-2neg` `associate-*l/` `clear-num` `sum-log` `flip--` `distribute-lft-out--` `inv-pow` `difference-of-squares`

Counts

4 → 158

Calls

4 calls:

6.0ms	(+ (* x y) (* z (- t a)))
11.0ms	(* z (- t a))
2.0ms	(/ 1 (fma z (- b y) y))
14.0ms	(* (/ 1 (fma z (- b y) y)) (+ (* x y) (* z (- t a))))

series583.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(+ (* x y) (* z (- t a)))
34.0ms	(* z (- t a))
57.0ms	(/ 1 (fma z (- b y) y))
448.0ms	(* (/ 1 (fma z (- b y) y)) (+ (* x y) (* z (- t a))))

simplify80.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	635	1268
1	3093	982
2	5001	957

prune398.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 7.7b

regimes402.0ms

Accuracy

26.5% (9.0b remaining)

Error of 20.1b against oracle of 11.1b and baseline of 23.3b

bsearch90.0ms

Steps

Iters	Range		Point
9	2.5703553510780522e+39	3.6963524777395996e+46	3.6434322402537893e+46
8	-9.151471596316372e+71	-2.3660077477016814e+69	-4.2825952014482863e+70

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	11
1	33	11

end0.0ms

sample616.0ms

Algorithm

intervals

Results

336.0ms

8391×

body

valid