Details

sample101.0ms

Algorithm

intervals

Results

45.0ms	118×	body	1280	valid
15.0ms	71×	body	640	valid
11.0ms	256×	pre	80	true
4.0ms	23×	body	320	valid
2.0ms	36×	body	80	valid
1.0ms	8×	body	160	valid

simplify22.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	5
1	22	5
2	33	5
3	39	5
4	50	5
5	70	5
6	99	5
7	124	5
8	166	5
9	259	5
10	260	5
11	260	5

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.9b

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.1b	(- (tan (+ y z)) (tan a))
3.2b	(tan (+ y z))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
18×	`prod-diff`
17×	`add-cube-cbrt`
11×	`associate-+r+`
10×	`add-log-exp`
4×	`tan-quot`
3×	`pow1` `add-exp-log` `expm1-log1p-u` `fma-def` `fma-neg` `add-cbrt-cube` `log1p-expm1-u`
2×	`sub-neg` `tan-sum` `diff-log` `sum-log` `frac-sub` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `associate-+r-` `flip3--` `flip3-+` `flip--` `flip-+` `difference-of-squares`

Counts

3 → 72

Calls

3 calls:

7.0ms	(+ x (- (tan (+ y z)) (tan a)))
8.0ms	(- (tan (+ y z)) (tan a))
4.0ms	(tan (+ y z))

series333.0ms

Counts

3 → 9

Calls

3 calls:

139.0ms	(+ x (- (tan (+ y z)) (tan a)))
137.0ms	(- (tan (+ y z)) (tan a))
57.0ms	(tan (+ y z))

simplify94.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (87.0ms)

Iter	Nodes	Cost
0	276	685
1	732	540
2	3128	507
3	5001	488

prune244.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan y) (tan z))
0.2b	(* (tan y) (tan z))
0.2b	(* (tan y) (tan z))
0.2b	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

16×	`associate-*l/`
15×	`add-sqr-sqrt`
14×	`tan-quot`
13×	`add-exp-log` `*-un-lft-identity` `add-cbrt-cube`
11×	`add-cube-cbrt`
8×	`pow1` `associate-/l/`
6×	`associate-r` `associate-l` `frac-sub` `add-log-exp`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def` `flip3-+` `times-frac` `frac-add` `prod-exp` `cbrt-unprod` `flip-+` `associate-/l*`
2×	`cbrt-undiv` `frac-times` `associate-r/` `div-exp` `pow-prod-down` `associate-/r/` `-commutative` `unswap-sqr`
1×	`+-commutative` `frac-2neg` `div-sub` `clear-num` `associate-/r*` `sum-log` `div-inv` `distribute-lft-out`

Counts

4 → 98

Calls

4 calls:

6.0ms	(+ (tan y) (tan z))
6.0ms	(* (tan y) (tan z))
8.0ms	(* (tan y) (tan z))
16.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

series843.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(+ (tan y) (tan z))
103.0ms	(* (tan y) (tan z))
103.0ms	(* (tan y) (tan z))
530.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

simplify73.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	562	1271
1	2568	1119
2	5002	1111

prune534.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan y) (tan z))
0.2b	(* (tan y) (sin z))
0.2b	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (/ (* (tan y) (sin z)) (cos z))) (cos a)))
0.2b	(/ (* (tan y) (sin z)) (cos z))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log` `add-cbrt-cube`
17×	`associate-*l/`
16×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
10×	`tan-quot`
9×	`associate-/l/`
8×	`pow1`
6×	`times-frac` `associate-r` `associate-l` `frac-sub`
5×	`flip3--` `flip--`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `prod-exp` `associate-/r` `cbrt-unprod` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`frac-2neg` `flip3-+` `pow-prod-down` `frac-add` `clear-num` `associate-/r/` `*-commutative` `flip-+` `div-inv` `unswap-sqr`
1×	`frac-times` `div-sub` `associate-*r/`

Counts

4 → 102

Calls

4 calls:

6.0ms	(* (tan y) (tan z))
6.0ms	(* (tan y) (sin z))
19.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (/ (* (tan y) (sin z)) (cos z))) (cos a)))
7.0ms	(/ (* (tan y) (sin z)) (cos z))

series828.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(* (tan y) (tan z))
73.0ms	(* (tan y) (sin z))
538.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (/ (* (tan y) (sin z)) (cos z))) (cos a)))
111.0ms	(/ (* (tan y) (sin z)) (cos z))

simplify83.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	650	1457
1	3082	1262
2	5002	1262

prune604.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (tan y) (sin z)) (cos z))
0.2b	(/ (* (tan y) (sin z)) (cos z))
0.2b	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (/ (* (tan y) (sin z)) (cos z)) (/ (* (tan y) (sin z)) (cos z)))) (cos a)))
0.3b	(* (/ (* (tan y) (sin z)) (cos z)) (/ (* (tan y) (sin z)) (cos z)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-exp-log` `add-cbrt-cube`
21×	`times-frac`
20×	`add-sqr-sqrt`
18×	`cbrt-undiv` `add-cube-cbrt` `*-un-lft-identity` `div-exp` `prod-exp` `cbrt-unprod`
17×	`associate-*l/`
11×	`pow1`
10×	`associate-/l/`
7×	`swap-sqr` `associate-r` `associate-l` `associate-/r*` `div-inv`
6×	`tan-quot` `frac-sub`
5×	`flip3--` `flip--` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`flip3-+` `frac-add` `associate-/r/` `flip-+`
1×	`pow2` `frac-times` `pow-plus` `div-sub` `associate-r/` `pow-prod-down` `pow-sqr` `-commutative` `pow-prod-up` `unswap-sqr`

Counts

4 → 140

Calls

4 calls:

7.0ms	(/ (* (tan y) (sin z)) (cos z))
6.0ms	(/ (* (tan y) (sin z)) (cos z))
17.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (/ (* (tan y) (sin z)) (cos z)) (/ (* (tan y) (sin z)) (cos z)))) (cos a)))
13.0ms	(* (/ (* (tan y) (sin z)) (cos z)) (/ (* (tan y) (sin z)) (cos z)))

series948.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ (* (tan y) (sin z)) (cos z))
111.0ms	(/ (* (tan y) (sin z)) (cos z))
587.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (/ (* (tan y) (sin z)) (cos z)) (/ (* (tan y) (sin z)) (cos z)))) (cos a)))
140.0ms	(* (/ (* (tan y) (sin z)) (cos z)) (/ (* (tan y) (sin z)) (cos z)))

simplify117.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	833	2458
1	4608	1959
2	5001	1959

prune772.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes559.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	37
1	39	37

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.6s	3943×	body	1280	valid
434.0ms	1912×	body	640	valid
327.0ms	8000×	pre	80	true
112.0ms	717×	body	320	valid
53.0ms	1146×	body	80	valid
30.0ms	282×	body	160	valid