Details

sample110.0ms

Algorithm

intervals

Results

50.0ms	127×	body	1280	valid
16.0ms	66×	body	640	valid
15.0ms	256×	pre	80	true
3.0ms	22×	body	320	valid
2.0ms	33×	body	80	valid
1.0ms	8×	body	160	valid

simplify24.0ms

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: 15.3b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
2.8b	(tan (+ y z))

rewrite17.0ms

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:

5.0ms	(+ x (- (tan (+ y z)) (tan a)))
7.0ms	(- (tan (+ y z)) (tan a))
4.0ms	(tan (+ y z))

series315.0ms

Counts

3 → 9

Calls

3 calls:

129.0ms	(+ x (- (tan (+ y z)) (tan a)))
126.0ms	(- (tan (+ y z)) (tan a))
60.0ms	(tan (+ y z))

simplify49.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (17.0ms)

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

prune170.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan y) (tan z))
0.1b	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
0.1b	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
0.2b	(* (tan y) (tan z))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
13×	`times-frac`
9×	`tan-quot`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1`
5×	`distribute-lft-out`
4×	`associate-/l*`
3×	`associate-r` `associate-l` `associate-/r*` `associate-/l/`
2×	`flip3--` `flip3-+` `frac-add` `associate-/r/` `flip--` `flip-+` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `frac-times` `sub-neg` `frac-2neg` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

5.0ms	(+ (tan y) (tan z))
8.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
12.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
6.0ms	(* (tan y) (tan z))

series866.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(+ (tan y) (tan z))
238.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
424.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
100.0ms	(* (tan y) (tan z))

simplify126.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	394	1046
1	1350	1000
2	4363	993
3	5001	993

prune389.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan y) (tan z)) (- 1 (/ (* (sin y) (sin z)) (* (cos z) (cos y)))))
0.1b	(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (sin y) (sin z)) (* (cos z) (cos y))))) (tan a))
0.2b	(* (sin y) (sin z))
0.2b	(/ (* (sin y) (sin z)) (* (cos z) (cos y)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

49×	`*-un-lft-identity`
40×	`add-sqr-sqrt`
26×	`times-frac`
20×	`add-exp-log` `add-cbrt-cube`
18×	`add-cube-cbrt`
12×	`difference-of-squares`
7×	`associate-/r*` `distribute-lft-out`
6×	`pow1` `distribute-lft-out--` `add-log-exp`
5×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `associate-/l*`
4×	`associate-/l/`
3×	`tan-quot` `associate-r` `associate-l` `associate-/r/`
2×	`flip3--` `frac-2neg` `clear-num` `flip--` `div-inv` `sin-mult`
1×	`sub-neg` `flip3-+` `diff-log` `pow-prod-down` `frac-add` `cos-mult` `*-commutative` `frac-sub` `flip-+` `unswap-sqr`

Counts

4 → 109

Calls

4 calls:

12.0ms	(/ (+ (tan y) (tan z)) (- 1 (/ (* (sin y) (sin z)) (* (cos z) (cos y)))))
18.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (sin y) (sin z)) (* (cos z) (cos y))))) (tan a))
5.0ms	(* (sin y) (sin z))
9.0ms	(/ (* (sin y) (sin z)) (* (cos z) (cos y)))

series831.0ms

Counts

4 → 12

Calls

4 calls:

241.0ms	(/ (+ (tan y) (tan z)) (- 1 (/ (* (sin y) (sin z)) (* (cos z) (cos y)))))
430.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (sin y) (sin z)) (* (cos z) (cos y))))) (tan a))
53.0ms	(* (sin y) (sin z))
107.0ms	(/ (* (sin y) (sin z)) (* (cos z) (cos y)))

simplify73.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	533	1821
1	2236	1683
2	5001	1683

prune535.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan y) (tan z))
0.3b	(* (tan z) (tan z))
0.3b	(* (tan y) (tan y))
4.4b	(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (- (tan y) (tan z)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
38×	`tan-quot`
35×	`*-un-lft-identity`
25×	`add-cube-cbrt`
20×	`pow1` `times-frac`
12×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/l/` `difference-of-squares`
10×	`frac-sub`
9×	`frac-times` `associate-r/` `associate-r` `associate-l` `associate-l/`
6×	`swap-sqr`
5×	`associate-/r*` `distribute-lft-out--`
4×	`associate-/l*` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`pow2` `flip3--` `pow-plus` `pow-sqr` `pow-prod-up` `flip--`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 133

Calls

4 calls:

5.0ms	(* (tan y) (tan z))
6.0ms	(* (tan z) (tan z))
6.0ms	(* (tan y) (tan y))
16.0ms	(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (- (tan y) (tan z)))

series428.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(* (tan y) (tan z))
39.0ms	(* (tan z) (tan z))
36.0ms	(* (tan y) (tan y))
250.0ms	(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (- (tan y) (tan z)))

simplify85.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	521	1251
1	2392	1138
2	5001	1094

prune528.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes640.0ms

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	28	17
1	28	17

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.7s	3850×	body	1280	valid
477.0ms	2047×	body	640	valid
325.0ms	8000×	pre	80	true
116.0ms	708×	body	320	valid
52.0ms	1100×	body	80	valid
35.0ms	295×	body	160	valid