Details

sample162.0ms

Algorithm

intervals

Results

87.0ms	122×	body	1280	valid
27.0ms	66×	body	640	valid
13.0ms	256×	pre	80	true
5.0ms	18×	body	320	valid
3.0ms	38×	body	80	valid
2.0ms	12×	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: 13.6b

localize17.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
3.4b	(tan (+ y z))

rewrite42.0ms

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:

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

series453.0ms

Counts

3 → 9

Calls

3 calls:

105.0ms	(+ x (- (tan (+ y z)) (tan a)))
101.0ms	(- (tan (+ y z)) (tan a))
247.0ms	(tan (+ y z))

simplify89.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (83.0ms)

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

prune204.0ms

Pruning

6 alts after pruning (6 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))

rewrite121.0ms

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:

29.0ms	(* (+ (tan y) (tan z)) (cos a))
57.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
14.0ms	(* (tan y) (tan z))
17.0ms	(* (tan y) (tan z))

series713.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(* (+ (tan y) (tan z)) (cos a))
420.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
82.0ms	(* (tan y) (tan z))
82.0ms	(* (tan y) (tan z))

simplify76.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (65.0ms)

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

prune472.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log` `add-cbrt-cube`
15×	`associate-*l/`
14×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-/l/`
8×	`tan-quot` `pow1`
7×	`prod-exp` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp` `associate-r` `associate-l` `frac-sub`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `times-frac` `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` `sin-mult` `unswap-sqr`
1×	`frac-times` `div-sub` `associate-*r/` `cos-mult`

Counts

4 → 103

Calls

4 calls:

11.0ms	(* (sin y) (sin z))
74.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (/ (* (sin y) (sin z)) (* (cos y) (cos z)))) (cos a)))
14.0ms	(* (tan y) (tan z))
17.0ms	(/ (* (sin y) (sin z)) (* (cos y) (cos z)))

series627.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (sin y) (sin z))
416.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (/ (* (sin y) (sin z)) (* (cos y) (cos z)))) (cos a)))
81.0ms	(* (tan y) (tan z))
88.0ms	(/ (* (sin y) (sin z)) (* (cos y) (cos z)))

simplify87.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	708	1619
1	3722	1375
2	5002	1375

prune603.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize54.0ms

Local error

Found 4 expressions with local error:

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

rewrite725.0ms

Algorithm

rewrite-expression-head

Rules

97×	`associate-*l/`
55×	`add-exp-log` `add-cbrt-cube`
43×	`associate-/l/`
41×	`frac-times`
40×	`frac-sub`
31×	`cos-mult`
30×	`flip3-+` `associate-*r/` `flip-+`
26×	`prod-exp` `cbrt-unprod`
21×	`flip3--` `flip--`
18×	`pow1`
10×	`cbrt-undiv` `add-sqr-sqrt` `div-exp`
9×	`pow-prod-down`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-/r/`
4×	`tan-quot` `expm1-log1p-u` `times-frac` `associate-r` `associate-l` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`frac-2neg` `clear-num` `associate-/r` `-commutative` `div-inv`
1×	`div-sub` `sin-mult` `unswap-sqr`

Counts

4 → 156

Calls

4 calls:

15.0ms	(* (tan y) (tan z))
17.0ms	(/ (* (sin y) (sin z)) (* (cos z) (cos y)))
564.0ms	(/ (- (* (* (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (cos a)) (+ 1 (* (tan y) (tan z)))) (* (* (cos y) (cos z)) (* (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z)))) (sin a)))) (* (* (* (- 1 (/ (* (sin y) (sin z)) (* (cos z) (cos y)))) (cos a)) (* (cos y) (cos z))) (fma (tan y) (tan z) 1)))
118.0ms	(* (* (cos y) (cos z)) (* (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z)))) (sin a)))

series1.4s

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (tan y) (tan z))
93.0ms	(/ (* (sin y) (sin z)) (* (cos z) (cos y)))
1.0s	(/ (- (* (* (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (cos a)) (+ 1 (* (tan y) (tan z)))) (* (* (cos y) (cos z)) (* (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z)))) (sin a)))) (* (* (* (- 1 (/ (* (sin y) (sin z)) (* (cos z) (cos y)))) (cos a)) (* (cos y) (cos z))) (fma (tan y) (tan z) 1)))
192.0ms	(* (* (cos y) (cos z)) (* (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z)))) (sin a)))

simplify77.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	1595	5722
1	5001	5343

prune1.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

regimes727.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	49
1	41	49

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.9s	3914×	body	1280	valid
844.0ms	1995×	body	640	valid
303.0ms	8000×	pre	80	true
195.0ms	656×	body	320	valid
110.0ms	1123×	body	80	valid
62.0ms	312×	body	160	valid