Details

sample171.0ms

Algorithm

intervals

Results

98.0ms	136×	body	1280	valid
34.0ms	71×	body	640	valid
11.0ms	256×	pre	80	true
3.0ms	12×	body	320	valid
3.0ms	31×	body	80	valid
1.0ms	6×	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: 13.0b

localize10.0ms

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))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity` `add-log-exp`
5×	`add-sqr-sqrt`
4×	`tan-quot`
3×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
2×	`sub-neg` `tan-sum` `associate-+r+` `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 → 42

Calls

3 calls:

13.0ms	(- (tan (+ y z)) (tan a))
8.0ms	(+ x (- (tan (+ y z)) (tan a)))
3.0ms	(tan (+ y z))

series288.0ms

Counts

3 → 9

Calls

3 calls:

117.0ms	(- (tan (+ y z)) (tan a))
120.0ms	(+ x (- (tan (+ y z)) (tan a)))
51.0ms	(tan (+ y z))

simplify39.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	196	346
1	467	335
2	1316	334
3	5002	334

prune141.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

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)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

16×	`associate-*l/`
14×	`add-sqr-sqrt`
13×	`add-exp-log` `add-cbrt-cube`
12×	`tan-quot` `*-un-lft-identity`
10×	`add-cube-cbrt`
8×	`pow1` `associate-/l/`
6×	`associate-r` `associate-l` `frac-sub` `add-log-exp`
5×	`flip3--` `flip--`
3×	`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 → 87

Calls

4 calls:

16.0ms	(+ 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))
5.0ms	(* (tan y) (tan z))
21.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

series1.3s

Counts

4 → 12

Calls

4 calls:

687.0ms	(+ x (/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a))))
91.0ms	(* (tan y) (tan z))
94.0ms	(* (tan y) (tan z))
472.0ms	(/ (- (* (+ (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

99 → 99

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	607	1601
1	2699	1448
2	5002	1435

prune444.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

2.0ms	(+ x (* (/ 1 (- 1 (* (tan y) (tan z)))) (/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (cos a))))
19.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (cos a))
5.0ms	(* (tan y) (tan z))
5.0ms	(* (tan y) (tan z))

series1.2s

Counts

4 → 12

Calls

4 calls:

683.0ms	(+ x (* (/ 1 (- 1 (* (tan y) (tan z)))) (/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (cos a))))
356.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (cos a))
91.0ms	(* (tan y) (tan z))
93.0ms	(* (tan y) (tan z))

simplify64.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	548	1562
1	2281	1428
2	5001	1427

prune491.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 4 expressions with local error:

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 (log (exp (* (tan y) (tan z))))) (cos a)))
2.5b	(log (exp (* (tan y) (tan z))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

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 (log (exp (* (tan y) (tan z))))) (cos a)))
1.0ms	(log (exp (* (tan y) (tan z))))

series772.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(* (tan y) (tan z))
92.0ms	(* (tan y) (tan z))
489.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (log (exp (* (tan y) (tan z))))) (cos a)))
96.0ms	(log (exp (* (tan y) (tan z))))

simplify61.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	514	1303
1	2287	1103
2	5001	1081

prune456.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

regimes460.0ms

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	29	22
1	29	22

end0.0ms

sample5.1s

Algorithm

intervals

Results

3.1s	3869×	body	1280	valid
924.0ms	2039×	body	640	valid
339.0ms	8000×	pre	80	true
237.0ms	712×	body	320	valid
104.0ms	1103×	body	80	valid
56.0ms	277×	body	160	valid