Details

sample26.0ms

Algorithm

intervals

Results

11.0ms

270×

body

valid

simplify155.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- t a))
0.0b	(* z (- b y))
1.4b	(+ (* x y) (* z (- t a)))
24.2b	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

rewrite51.0ms

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 (- t a))
12.0ms	(* z (- b y))
6.0ms	(+ (* x y) (* z (- t a)))
13.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

series522.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* z (- t a))
45.0ms	(* z (- b y))
50.0ms	(+ (* x y) (* z (- t a)))
386.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

simplify87.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (72.0ms)

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

prune494.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 24.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- b y))
0.8b	(/ 1 (+ y (* z (- b y))))
1.4b	(+ (* x y) (* z (- t a)))
23.4b	(* (+ (* x y) (* z (- t a))) (/ 1 (+ y (* z (- b y)))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 161

Calls

4 calls:

13.0ms	(* z (- b y))
4.0ms	(/ 1 (+ y (* z (- b y))))
6.0ms	(+ (* x y) (* z (- t a)))
24.0ms	(* (+ (* x y) (* z (- t a))) (/ 1 (+ y (* z (- b y)))))

series576.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* z (- b y))
99.0ms	(/ 1 (+ y (* z (- b y))))
49.0ms	(+ (* x y) (* z (- t a)))
384.0ms	(* (+ (* x y) (* z (- t a))) (/ 1 (+ y (* z (- b y)))))

simplify106.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	658	1375
1	2830	1048
2	5001	1011

prune512.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 24.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- b y))
0.4b	(/ 1 (/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a)))))
1.4b	(+ (* x y) (* z (- t a)))
24.1b	(/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a))))

rewrite52.0ms

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 (- b y))
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:

48.0ms	(* z (- b y))
907.0ms	(/ 1 (/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a)))))
51.0ms	(+ (* x y) (* z (- t a)))
312.0ms	(/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a))))

simplify107.0ms

Algorithm

egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	785	2479
1	3441	2063
2	5001	1964

prune585.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 24.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ 1 (fma z (- b y) y))
1.1b	(/ 1 (+ (* x y) (* z (- t a))))
1.4b	(+ (* x y) (* z (- t a)))
22.7b	(/ (/ 1 (fma z (- b y) y)) (/ 1 (+ (* x y) (* z (- t a)))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

483×	`times-frac`
242×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
52×	`add-exp-log`
36×	`div-exp`
33×	`div-inv`
31×	`associate-/r/`
22×	`associate-+r+`
21×	`associate-/r*`
20×	`add-cbrt-cube`
19×	`associate-/l*`
18×	`prod-diff`
16×	`flip3-+` `flip-+`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`cbrt-undiv` `rec-exp` `1-exp`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`frac-2neg` `clear-num`
2×	`sub-neg` `pow-flip` `inv-pow`
1×	`+-commutative` `fma-def` `sum-log` `associate-/l/`

Counts

4 → 361

Calls

4 calls:

2.0ms	(/ 1 (fma z (- b y) y))
5.0ms	(/ 1 (+ (* x y) (* z (- t a))))
6.0ms	(+ (* x y) (* z (- t a)))
16.0ms	(/ (/ 1 (fma z (- b y) y)) (/ 1 (+ (* x y) (* z (- t a)))))

series708.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(/ 1 (fma z (- b y) y))
65.0ms	(/ 1 (+ (* x y) (* z (- t a))))
51.0ms	(+ (* x y) (* z (- t a)))
522.0ms	(/ (/ 1 (fma z (- b y) y)) (/ 1 (+ (* x y) (* z (- t a)))))

simplify101.0ms

Algorithm

egg-herbie

Counts

373 → 373

Iterations

Useful iterations: 1 (45.0ms)

Iter	Nodes	Cost
0	1514	5862
1	5001	5233

prune981.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.4b

regimes558.0ms

Accuracy

10.7% (11.4b remaining)

Error of 22.1b against oracle of 10.7b and baseline of 23.5b

bsearch250.0ms

Steps

Iters	Range		Point
9	6.524361585217156e+252	1.4763294214405991e+261	7.460210507460028e+253
11	2.2822004650833932e-240	2.5521922643045638e-219	9.730029388593367e-234
8	-4.555131683261645e-301	-3.136441890296061e-305	-9.613594829991698e-302
5	-2.287751869093647e+206	-1.0084824935343875e+206	-1.61354533470295e+206

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	47	28
1	47	28

end0.0ms

sample670.0ms

Algorithm

intervals

Results

372.0ms

8439×

body

valid