Details

sample164.0ms

Algorithm

intervals

Results

88.0ms	125×	body	1280	valid
31.0ms	65×	body	640	valid
9.0ms	256×	pre	80	true
5.0ms	20×	body	320	valid
3.0ms	36×	body	80	valid
2.0ms	10×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.2b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
3.5b	(tan (+ y z))

rewrite46.0ms

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:

20.0ms	(+ x (- (tan (+ y z)) (tan a)))
17.0ms	(- (tan (+ y z)) (tan a))
6.0ms	(tan (+ y z))

series305.0ms

Counts

3 → 9

Calls

3 calls:

128.0ms	(+ x (- (tan (+ y z)) (tan a)))
125.0ms	(- (tan (+ y z)) (tan a))
52.0ms	(tan (+ y z))

simplify87.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (81.0ms)

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

prune215.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

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)) (* (- 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))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

32.0ms	(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
57.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
17.0ms	(* (tan y) (tan z))
15.0ms	(* (tan y) (tan z))

series1.0s

Counts

4 → 12

Calls

4 calls:

312.0ms	(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
503.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
95.0ms	(* (tan y) (tan z))
95.0ms	(* (tan y) (tan z))

simplify88.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	688	1785
1	3265	1583
2	5002	1572

prune562.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

0.0ms	(fma (+ (tan y) (tan z)) (cos a) (- (* (- 1 (* (tan y) (tan z))) (sin a))))
13.0ms	(/ (fma (+ (tan y) (tan z)) (cos a) (- (* (- 1 (* (tan y) (tan z))) (sin a)))) (* (- 1 (* (tan y) (tan z))) (cos a)))
17.0ms	(* (tan y) (tan z))
15.0ms	(* (tan y) (tan z))

series976.0ms

Counts

4 → 12

Calls

4 calls:

296.0ms	(fma (+ (tan y) (tan z)) (cos a) (- (* (- 1 (* (tan y) (tan z))) (sin a))))
488.0ms	(/ (fma (+ (tan y) (tan z)) (cos a) (- (* (- 1 (* (tan y) (tan z))) (sin a)))) (* (- 1 (* (tan y) (tan z))) (cos a)))
96.0ms	(* (tan y) (tan z))
96.0ms	(* (tan y) (tan z))

simplify44.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	323	1193
1	1177	1033
2	5002	1026

prune433.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log` `add-cbrt-cube`
16×	`add-sqr-sqrt`
15×	`associate-*l/`
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`
3×	`associate-*r/`
2×	`frac-2neg` `flip3-+` `pow-prod-down` `frac-add` `clear-num` `associate-/r/` `*-commutative` `flip-+` `div-inv` `unswap-sqr`
1×	`frac-times` `div-sub`

Counts

4 → 102

Calls

4 calls:

14.0ms	(/ (* (sin y) (tan z)) (cos y))
63.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (/ (* (sin y) (tan z)) (cos y))) (cos a)))
14.0ms	(* (tan y) (tan z))
16.0ms	(* (sin y) (tan z))

series785.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ (* (sin y) (tan z)) (cos y))
504.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (/ (* (sin y) (tan z)) (cos y))) (cos a)))
95.0ms	(* (tan y) (tan z))
79.0ms	(* (sin y) (tan z))

simplify77.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	652	1457
1	3149	1262
2	5001	1262

prune560.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.1b

regimes772.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	20
1	31	20
2	31	20

end0.0ms

sample4.9s

Algorithm

intervals

Results

2.8s	3834×	body	1280	valid
1.1s	2063×	body	640	valid
294.0ms	8000×	pre	80	true
193.0ms	677×	body	320	valid
92.0ms	1128×	body	80	valid
56.0ms	298×	body	160	valid