Details

sample25.0ms

Algorithm

intervals

Results

11.0ms

265×

body

valid

simplify136.0ms

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: 24.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- b y))
0.0b	(* z (- t a))
1.3b	(+ (* x y) (* z (- t a)))
24.0b	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

rewrite52.0ms

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:

12.0ms	(* z (- b y))
15.0ms	(* z (- t a))
6.0ms	(+ (* x y) (* z (- t a)))
12.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

series501.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* z (- b y))
38.0ms	(* z (- t a))
53.0ms	(+ (* x y) (* z (- t a)))
369.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

simplify90.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (73.0ms)

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

prune486.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 24.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- b y))
0.5b	(fma x y (* t z))
0.9b	(+ (fma x y (* t z)) (* (- a) z))
24.0b	(/ (+ (fma x y (* t z)) (* (- a) z)) (+ y (* z (- b y))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
27×	`add-cube-cbrt`
18×	`prod-diff`
11×	`distribute-rgt-in` `distribute-lft-in`
9×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `add-log-exp`
5×	`associate-r`
4×	`distribute-lft-neg-out` `expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def` `flip3-+` `associate-l` `associate-/r` `flip-+` `associate-/l`
2×	`sub-neg` `div-sub` `associate-*r/` `unsub-neg` `associate-/r/` `fma-udef` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l+` `flip3--` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `div-inv` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 110

Calls

4 calls:

11.0ms	(* z (- b y))
0.0ms	(fma x y (* t z))
2.0ms	(+ (fma x y (* t z)) (* (- a) z))
10.0ms	(/ (+ (fma x y (* t z)) (* (- a) z)) (+ y (* z (- b y))))

series478.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* z (- b y))
48.0ms	(fma x y (* t z))
48.0ms	(+ (fma x y (* t z)) (* (- a) z))
342.0ms	(/ (+ (fma x y (* t z)) (* (- a) z)) (+ y (* z (- b y))))

simplify72.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	416	1024
1	1885	816
2	5001	797

prune382.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 22.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(fma x y (* t z))
0.9b	(+ (fma x y (* t z)) (* (- a) z))
1.3b	(+ (* z b) (* z (- y)))
24.0b	(/ (+ (fma x y (* t z)) (* (- a) z)) (+ y (+ (* z b) (* z (- y)))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
14×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`times-frac`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`distribute-lft-out`
4×	`pow1` `distribute-lft-neg-out` `expm1-log1p-u` `fma-def` `flip3-+` `associate-/r*` `flip-+` `log1p-expm1-u`
3×	`unsub-neg` `associate-/l*`
2×	`+-commutative` `div-sub` `sum-log` `associate-/r/` `distribute-rgt-neg-out` `fma-udef` `associate-/l/`
1×	`cbrt-undiv` `associate-+l+` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 85

Calls

4 calls:

0.0ms	(fma x y (* t z))
2.0ms	(+ (fma x y (* t z)) (* (- a) z))
3.0ms	(+ (* z b) (* z (- y)))
18.0ms	(/ (+ (fma x y (* t z)) (* (- a) z)) (+ y (+ (* z b) (* z (- y)))))

series483.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(fma x y (* t z))
54.0ms	(+ (fma x y (* t z)) (* (- a) z))
48.0ms	(+ (* z b) (* z (- y)))
337.0ms	(/ (+ (fma x y (* t z)) (* (- a) z)) (+ y (+ (* z b) (* z (- y)))))

simplify65.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	346	923
1	1552	794
2	5002	761

prune369.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 22.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- t a))
0.2b	(/ 1 (/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a)))))
1.3b	(+ (* x y) (* z (- t a)))
24.0b	(/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 201

Calls

4 calls:

12.0ms	(* z (- t a))
11.0ms	(/ 1 (/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a)))))
6.0ms	(+ (* x y) (* z (- t a)))
12.0ms	(/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a))))

series1.3s

Counts

4 → 12

Calls

4 calls:

47.0ms	(* z (- t a))
920.0ms	(/ 1 (/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a)))))
55.0ms	(+ (* x y) (* z (- t a)))
304.0ms	(/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a))))

simplify100.0ms

Algorithm

egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	716	2474
1	3125	2063
2	5002	1958

prune559.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 22.8b

regimes455.0ms

Accuracy

0% (2.8b remaining)

Error of 23.9b against oracle of 21.1b and baseline of 23.9b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	11
1	35	11
2	37	11
3	37	11

end0.0ms

sample657.0ms

Algorithm

intervals

Results

358.0ms

8413×

body

valid