Details

sample173.0ms

Algorithm

intervals

Results

94.0ms	123×	body	1280	valid
26.0ms	57×	body	640	valid
15.0ms	256×	pre	80	true
7.0ms	23×	body	320	valid
4.0ms	42×	body	80	valid
3.0ms	11×	body	160	valid

simplify310.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	9
1	15	9
2	22	9
3	31	9
4	37	9
5	47	9
6	54	9
7	64	9
8	82	9
9	99	9
10	107	9
done	107	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.8b

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
2.3b	(tan (+ y z))

rewrite19.0ms

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:

7.0ms	(+ x (- (tan (+ y z)) (tan a)))
8.0ms	(- (tan (+ y z)) (tan a))
3.0ms	(tan (+ y z))

series326.0ms

Counts

3 → 9

Calls

3 calls:

135.0ms	(+ x (- (tan (+ y z)) (tan a)))
129.0ms	(- (tan (+ y z)) (tan a))
63.0ms	(tan (+ y z))

simplify1.7s

Counts

51 → 51

Iterations

Useful iterations: 3 (159.0ms)

Iter	Nodes	Cost
0	91	627
1	197	590
2	430	572
3	1029	570
4	3629	570
done	5000	570

prune177.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 4 expressions with local error:

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

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×	`flip3-+` `frac-add` `flip-+`
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` `diff-log` `div-sub` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 92

Calls

4 calls:

11.0ms	(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
7.0ms	(* (tan y) (tan z))
5.0ms	(* (tan y) (tan z))
22.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

series1.1s

Counts

4 → 12

Calls

4 calls:

325.0ms	(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
101.0ms	(* (tan y) (tan z))
102.0ms	(* (tan y) (tan z))
522.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

simplify1.2s

Counts

104 → 104

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	196	2790
1	653	2612
2	2596	2261
done	5001	2257

prune520.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan y) (tan z))
0.3b	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (cbrt (pow (* (tan y) (tan z)) 3))) (cos a)))
0.3b	(pow (* (tan y) (tan z)) 3)
30.0b	(cbrt (pow (* (tan y) (tan z)) 3))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

17×	`associate-*l/`
16×	`tan-quot`
14×	`add-exp-log` `add-cbrt-cube`
12×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1`
8×	`cbrt-prod` `associate-/l/`
6×	`cube-div` `frac-sub`
5×	`flip3--` `flip--`
4×	`add-log-exp`
3×	`frac-times` `pow-unpow` `cbrt-div` `times-frac` `associate-r/` `associate-r` `associate-l` `prod-exp` `cbrt-unprod` `associate-/l`
2×	`cbrt-undiv` `cube-mult` `unpow-prod-down` `pow-pow` `flip3-+` `unpow3` `cube-prod` `div-exp` `pow-prod-down` `frac-add` `pow-exp` `associate-/r/` `flip-+` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `frac-2neg` `pow1/3` `div-sub` `clear-num` `associate-/r` `-commutative` `rem-cbrt-cube` `div-inv` `unswap-sqr`

Counts

4 → 98

Calls

4 calls:

5.0ms	(* (tan y) (tan z))
27.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (cbrt (pow (* (tan y) (tan z)) 3))) (cos a)))
7.0ms	(pow (* (tan y) (tan z)) 3)
3.0ms	(cbrt (pow (* (tan y) (tan z)) 3))

series821.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(* (tan y) (tan z))
498.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (cbrt (pow (* (tan y) (tan z)) 3))) (cos a)))
129.0ms	(pow (* (tan y) (tan z)) 3)
96.0ms	(cbrt (pow (* (tan y) (tan z)) 3))

simplify1.0s

Counts

110 → 110

Iterations

Useful iterations: 2 (332.0ms)

Iter	Nodes	Cost
0	218	2360
1	644	2043
2	2738	1782
done	5000	1782

prune569.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan z) (tan y))
0.3b	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (cbrt (pow (log (exp (* (tan z) (tan y)))) 3))) (cos a)))
0.3b	(exp (* (tan z) (tan y)))
2.1b	(log (exp (* (tan z) (tan y))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

5.0ms	(* (tan z) (tan y))
39.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (cbrt (pow (log (exp (* (tan z) (tan y)))) 3))) (cos a)))
4.0ms	(exp (* (tan z) (tan y)))
1.0ms	(log (exp (* (tan z) (tan y))))

series813.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(* (tan z) (tan y))
497.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (cbrt (pow (log (exp (* (tan z) (tan y)))) 3))) (cos a)))
123.0ms	(exp (* (tan z) (tan y)))
95.0ms	(log (exp (* (tan z) (tan y))))

simplify910.0ms

Counts

89 → 89

Iterations

Useful iterations: done (907.0ms)

Iter	Nodes	Cost
0	187	2143
1	537	1835
2	2011	1595
done	5001	1594

prune454.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes682.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	32	72
1	41	66
done	41	66

end0.0ms

sample5.2s

Algorithm

intervals

Results

3.1s	3883×	body	1280	valid
920.0ms	1976×	body	640	valid
348.0ms	8000×	pre	80	true
236.0ms	709×	body	320	valid
103.0ms	1126×	body	80	valid
63.0ms	306×	body	160	valid