Details

sample38.0ms

Algorithm

intervals

Results

23.0ms

269×

body

valid

simplify136.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.1b

localize13.0ms

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)))
20.4b	(/ (+ (* 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))
15.0ms	(* z (- b y))
6.0ms	(+ (* x y) (* z (- t a)))
11.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

series462.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* z (- t a))
35.0ms	(* z (- b y))
47.0ms	(+ (* x y) (* z (- t a)))
340.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

simplify83.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (68.0ms)

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

prune455.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 20.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- b y))
0.3b	(/ 1 (/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a)))))
1.4b	(+ (* x y) (* z (- t a)))
20.4b	(/ (+ 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))
10.0ms	(/ 1 (/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a)))))
6.0ms	(+ (* x y) (* z (- t a)))
11.0ms	(/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a))))

series1.3s

Counts

4 → 12

Calls

4 calls:

40.0ms	(* z (- b y))
894.0ms	(/ 1 (/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a)))))
44.0ms	(+ (* x y) (* z (- t a)))
287.0ms	(/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a))))

simplify118.0ms

Algorithm

egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 2 (94.0ms)

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

prune605.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 20.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma z (- b y) y)
0.4b	(/ 1 (fma z (- b y) y))
0.8b	(fma x y (* z (- t a)))
20.1b	(* (/ 1 (fma z (- b y) y)) (fma x y (* z (- t a))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
20×	`add-cube-cbrt` `times-frac`
17×	`add-exp-log`
13×	`associate-l`
11×	`add-cbrt-cube`
7×	`pow1`
4×	`expm1-log1p-u` `div-exp` `prod-exp` `fma-udef` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-/r` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `1-exp` `cbrt-unprod` `div-inv`
1×	`distribute-rgt-in` `pow-flip` `frac-2neg` `distribute-lft-in` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `inv-pow`

Counts

4 → 92

Calls

4 calls:

0.0ms	(fma z (- b y) y)
2.0ms	(/ 1 (fma z (- b y) y))
0.0ms	(fma x y (* z (- t a)))
14.0ms	(* (/ 1 (fma z (- b y) y)) (fma x y (* z (- t a))))

series660.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(fma z (- b y) y)
66.0ms	(/ 1 (fma z (- b y) y))
51.0ms	(fma x y (* z (- t a)))
516.0ms	(* (/ 1 (fma z (- b y) y)) (fma x y (* z (- t a))))

simplify115.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	256	684
1	955	586
2	4393	560
3	5001	560

prune317.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 9.2b

localize22.0ms

Local error

Found 4 expressions with local error:

3.1b	(- (* t t) (* a a))
8.2b	(* z (- (* t t) (* a a)))
15.5b	(/ (* z (- (* t t) (* a a))) (+ t a))
20.4b	(/ (+ (* x y) (/ (* z (- (* t t) (* a a))) (+ t a))) (+ y (* z (- b y))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

3.0ms	(- (* t t) (* a a))
10.0ms	(* z (- (* t t) (* a a)))
11.0ms	(/ (* z (- (* t t) (* a a))) (+ t a))
34.0ms	(/ (+ (* x y) (/ (* z (- (* t t) (* a a))) (+ t a))) (+ y (* z (- b y))))

series993.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (* t t) (* a a))
72.0ms	(* z (- (* t t) (* a a)))
87.0ms	(/ (* z (- (* t t) (* a a))) (+ t a))
791.0ms	(/ (+ (* x y) (/ (* z (- (* t t) (* a a))) (+ t a))) (+ y (* z (- b y))))

simplify87.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	518	1154
1	2468	1030
2	5003	1021

prune384.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 9.1b

regimes471.0ms

Accuracy

41.9% (7.4b remaining)

Error of 18.6b against oracle of 11.2b and baseline of 23.9b

bsearch3.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	44	51
1	44	51

end0.0ms

sample1.0s

Algorithm

intervals

Results

740.0ms

8418×

body

valid