Details

sample188.0ms

Algorithm

intervals

Results

110.0ms	136×	body	1280	valid
32.0ms	71×	body	640	valid
12.0ms	256×	pre	80	true
4.0ms	12×	body	320	valid
3.0ms	31×	body	80	valid
1.0ms	6×	body	160	valid

simplify26.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 13.0b

localize22.0ms

Local error

Found 3 expressions with local error:

0.1b	(- (tan (+ y z)) (tan a))
0.2b	(+ x (- (tan (+ y z)) (tan a)))
3.7b	(tan (+ y z))

rewrite24.0ms

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:

9.0ms	(- (tan (+ y z)) (tan a))
9.0ms	(+ x (- (tan (+ y z)) (tan a)))
4.0ms	(tan (+ y z))

series322.0ms

Counts

3 → 9

Calls

3 calls:

126.0ms	(- (tan (+ y z)) (tan a))
139.0ms	(+ x (- (tan (+ y z)) (tan a)))
57.0ms	(tan (+ y z))

simplify106.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (98.0ms)

Iter	Nodes	Cost
0	276	685
1	732	540
2	3057	507
3	5001	488

prune257.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

16×	`associate-*l/`
15×	`add-sqr-sqrt`
13×	`add-exp-log` `*-un-lft-identity` `add-cbrt-cube`
12×	`tan-quot`
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` `prod-exp` `cbrt-unprod` `flip-+` `associate-/l*`
2×	`cbrt-undiv` `frac-times` `div-sub` `associate-r/` `div-exp` `pow-prod-down` `frac-add` `associate-/r/` `-commutative` `unswap-sqr`
1×	`+-commutative` `associate-+r-` `frac-2neg` `clear-num` `associate-/r*` `sum-log` `div-inv` `distribute-lft-out`

Counts

4 → 98

Calls

4 calls:

17.0ms	(+ x (/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a))))
5.0ms	(* (tan y) (tan z))
6.0ms	(* (tan y) (tan z))
26.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

series1.5s

Counts

4 → 12

Calls

4 calls:

765.0ms	(+ x (/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a))))
101.0ms	(* (tan y) (tan z))
102.0ms	(* (tan y) (tan z))
531.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

simplify91.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	627	1694
1	2825	1530
2	5001	1511

prune570.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 103

Calls

4 calls:

5.0ms	(* (tan y) (tan z))
5.0ms	(* (tan y) (tan z))
5.0ms	(* (tan y) (tan z))
24.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (* (tan y) (tan z)) (* (tan y) (tan z)))) (cos a)))

series885.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(* (tan y) (tan z))
101.0ms	(* (tan y) (tan z))
102.0ms	(* (tan y) (tan z))
578.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (* (tan y) (tan z)) (* (tan y) (tan z)))) (cos a)))

simplify92.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	547	1508
1	2706	1310
2	5002	1309

prune647.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan y) (tan z))
0.2b	(* (tan y) (tan z))
0.2b	(* (tan y) (tan z))
0.2b	(* (tan y) (tan z))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
16×	`tan-quot`
12×	`pow1` `add-exp-log` `add-cube-cbrt` `-un-lft-identity` `associate-r` `associate-l*` `add-cbrt-cube`
4×	`expm1-log1p-u` `frac-times` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`

Counts

4 → 92

Calls

4 calls:

5.0ms	(* (tan y) (tan z))
5.0ms	(* (tan y) (tan z))
5.0ms	(* (tan y) (tan z))
6.0ms	(* (tan y) (tan z))

series423.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(* (tan y) (tan z))
105.0ms	(* (tan y) (tan z))
106.0ms	(* (tan y) (tan z))
105.0ms	(* (tan y) (tan z))

simplify76.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 3 (32.0ms)

Iter	Nodes	Cost
0	121	528
1	381	472
2	951	472
3	2028	468
4	5001	468

prune521.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes703.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	29
1	31	29

end0.0ms

sample5.1s

Algorithm

intervals

Results

3.0s	3869×	body	1280	valid
927.0ms	2039×	body	640	valid
365.0ms	8000×	pre	80	true
218.0ms	712×	body	320	valid
118.0ms	1103×	body	80	valid
57.0ms	277×	body	160	valid