Details

sample37.0ms

Algorithm

intervals

Results

23.0ms

269×

body

valid

simplify145.0ms

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: 25.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ y (* z (- b y)))
0.0b	(* z (- b y))
0.3b	(+ (* x y) (* z (- t a)))
24.4b	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 153

Calls

4 calls:

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

series483.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(+ y (* z (- b y)))
43.0ms	(* z (- b y))
46.0ms	(+ (* x y) (* z (- t a)))
362.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

simplify86.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	602	1288
1	2282	956
2	5001	937

prune552.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 24.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- t a))
0.3b	(fma x y (* z (- t a)))
0.3b	(/ 1 (/ (fma z (- b y) y) (fma x y (* z (- t a)))))
24.4b	(/ (fma z (- b y) y) (fma x y (* z (- t a))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 163

Calls

4 calls:

12.0ms	(* z (- t a))
0.0ms	(fma x y (* z (- t a)))
5.0ms	(/ 1 (/ (fma z (- b y) y) (fma x y (* z (- t a)))))
3.0ms	(/ (fma z (- b y) y) (fma x y (* z (- t a))))

series721.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* z (- t a))
52.0ms	(fma x y (* z (- t a)))
512.0ms	(/ 1 (/ (fma z (- b y) y) (fma x y (* z (- t a)))))
114.0ms	(/ (fma z (- b y) y) (fma x y (* z (- t a))))

simplify79.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	520	1776
1	2152	1503
2	5001	1426

prune468.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.9b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(* z (- t a))
0.3b	(fma x y (* z (- t a)))
24.4b	(/ (fma x y (* z (- t a))) (fma z (- b y) y))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 85

Calls

3 calls:

12.0ms	(* z (- t a))
0.0ms	(fma x y (* z (- t a)))
2.0ms	(/ (fma x y (* z (- t a))) (fma z (- b y) y))

series466.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(* z (- t a))
57.0ms	(fma x y (* z (- t a)))
369.0ms	(/ (fma x y (* z (- t a))) (fma z (- b y) y))

simplify165.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	291	724
1	1055	551
2	4974	521
3	5001	521

prune287.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- t a))
0.3b	(fma x y (* z (- t a)))
0.7b	(/ 1 (fma z (- b y) y))
24.0b	(* (/ 1 (fma z (- b y) y)) (fma x y (* z (- t a))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
34×	`add-cube-cbrt`
20×	`times-frac`
19×	`add-exp-log`
18×	`prod-diff`
16×	`associate-l`
13×	`add-cbrt-cube`
12×	`distribute-rgt-in` `distribute-lft-in`
9×	`pow1`
8×	`associate-r`
5×	`prod-exp`
4×	`expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-/r` `cbrt-unprod` `fma-udef` `associate-/l`
2×	`cbrt-undiv` `sub-neg` `rec-exp` `1-exp` `associate-r/` `pow-prod-down` `-commutative` `div-inv`
1×	`flip3--` `pow-flip` `frac-2neg` `associate-*l/` `clear-num` `flip--` `distribute-lft-out--` `inv-pow` `difference-of-squares`

Counts

4 → 128

Calls

4 calls:

12.0ms	(* z (- t a))
0.0ms	(fma x y (* z (- t a)))
3.0ms	(/ 1 (fma z (- b y) y))
10.0ms	(* (/ 1 (fma z (- b y) y)) (fma x y (* z (- t a))))

series674.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* z (- t a))
52.0ms	(fma x y (* z (- t a)))
64.0ms	(/ 1 (fma z (- b y) y))
515.0ms	(* (/ 1 (fma z (- b y) y)) (fma x y (* z (- t a))))

simplify66.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	413	990
1	1650	767
2	5001	741

prune363.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.9b

regimes497.0ms

Accuracy

9.1% (11.3b remaining)

Error of 22.5b against oracle of 11.2b and baseline of 23.6b

bsearch129.0ms

Steps

Iters	Range		Point
9	4.9619032486579096e+169	5.604005689223389e+176	5.255820672532275e+176
8	-3.6036155535193067e+207	-5.1406143375706616e+203	-2.643206603729434e+207

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	7
1	27	7

end0.0ms

sample1.1s

Algorithm

intervals

Results

760.0ms

8401×

body

valid