Details

sample167.0ms

Algorithm

intervals

Results

91.0ms	123×	body	1280	valid
33.0ms	66×	body	640	valid
10.0ms	256×	pre	80	true
7.0ms	23×	body	320	valid
3.0ms	35×	body	80	valid
2.0ms	9×	body	160	valid

simplify19.0ms

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

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.8b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.1b	(- (tan (+ y z)) (tan a))
3.9b	(tan (+ y z))

rewrite28.0ms

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:

14.0ms	(+ x (- (tan (+ y z)) (tan a)))
8.0ms	(- (tan (+ y z)) (tan a))
3.0ms	(tan (+ y z))

series274.0ms

Counts

3 → 9

Calls

3 calls:

116.0ms	(+ x (- (tan (+ y z)) (tan a)))
110.0ms	(- (tan (+ y z)) (tan a))
48.0ms	(tan (+ y z))

simplify91.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (84.0ms)

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

prune220.0ms

Filtered

81 candidates to 59 candidates (72.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 104

Calls

4 calls:

14.0ms	(* (+ (tan y) (tan z)) (cos a))
21.0ms	(/ (- (* (+ (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))

series780.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(* (+ (tan y) (tan z)) (cos a))
458.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
89.0ms	(* (tan y) (tan z))
89.0ms	(* (tan y) (tan z))

simplify78.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	607	1365
1	2828	1198
2	5002	1191

prune518.0ms

Filtered

116 candidates to 91 candidates (78.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* (tan y) (tan z))) (cbrt (* (tan y) (tan z))))
8.2b	(cbrt (* (tan y) (tan z)))
8.2b	(cbrt (* (tan y) (tan z)))
8.2b	(cbrt (* (tan y) (tan z)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

44×	`tan-quot`
33×	`cbrt-div`
20×	`frac-times`
14×	`associate-r/` `associate-l/`
11×	`pow1`
10×	`add-sqr-sqrt`
9×	`pow1/3`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`cbrt-prod`
6×	`add-exp-log`
4×	`expm1-log1p-u` `swap-sqr` `associate-r` `associate-l` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

17.0ms	(* (cbrt (* (tan y) (tan z))) (cbrt (* (tan y) (tan z))))
3.0ms	(cbrt (* (tan y) (tan z)))
3.0ms	(cbrt (* (tan y) (tan z)))
3.0ms	(cbrt (* (tan y) (tan z)))

series618.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(* (cbrt (* (tan y) (tan z))) (cbrt (* (tan y) (tan z))))
148.0ms	(cbrt (* (tan y) (tan z)))
141.0ms	(cbrt (* (tan y) (tan z)))
146.0ms	(cbrt (* (tan y) (tan z)))

simplify106.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 3 (98.0ms)

Iter	Nodes	Cost
0	252	882
1	873	805
2	3829	729
3	5001	719

prune527.0ms

Filtered

102 candidates to 78 candidates (76.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

17×	`associate-*l/`
16×	`add-sqr-sqrt`
14×	`tan-quot`
12×	`*-un-lft-identity`
10×	`pow1` `add-exp-log` `add-cube-cbrt` `associate-l` `add-cbrt-cube`
9×	`associate-r`
6×	`frac-sub` `add-log-exp`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`flip3-+` `pow-prod-down` `frac-add` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`
2×	`frac-times` `associate-*r/`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff` `distribute-lft-out`

Counts

4 → 92

Calls

4 calls:

11.0ms	(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
12.0ms	(* (+ (tan y) (tan z)) (cos a))
5.0ms	(* (tan y) (tan z))
5.0ms	(* (tan y) (tan z))

series620.0ms

Counts

4 → 12

Calls

4 calls:

290.0ms	(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
148.0ms	(* (+ (tan y) (tan z)) (cos a))
91.0ms	(* (tan y) (tan z))
91.0ms	(* (tan y) (tan z))

simplify75.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	569	1043
1	2562	974
2	5003	965

prune462.0ms

Filtered

104 candidates to 82 candidates (78.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

regimes595.0ms

Accuracy

0% (0.1b 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	31
1	31	31

end0.0ms

sample5.1s

Algorithm

intervals

Results

3.0s	3913×	body	1280	valid
902.0ms	2046×	body	640	valid
350.0ms	690×	body	320	valid
314.0ms	8000×	pre	80	true
98.0ms	1094×	body	80	valid
53.0ms	257×	body	160	valid