Details

sample305.0ms

Algorithm

intervals

Results

156.0ms	105×	body	1280	valid
58.0ms	82×	body	640	valid
18.0ms	256×	pre	80	true
14.0ms	21×	body	320	valid
7.0ms	38×	body	80	valid
3.0ms	10×	body	160	valid

simplify6.9s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	314
1	15	314
2	22	314
3	33	314
4	39	314
5	89	314
6	193	314
7	446	314
8	1354	314
9	4724	314
done	5000	314

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.2b

localize20.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
2.5b	(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×	`expm1-log1p-u` `pow1` `fma-def` `add-cbrt-cube` `fma-neg` `add-exp-log` `log1p-expm1-u`
2×	`tan-sum` `sum-log` `sub-neg` `diff-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:

16.0ms	(+ x (- (tan (+ y z)) (tan a)))
17.0ms	(- (tan (+ y z)) (tan a))
7.0ms	(tan (+ y z))

series515.0ms

Counts

3 → 9

Calls

3 calls:

231.0ms	(+ x (- (tan (+ y z)) (tan a)))
180.0ms	(- (tan (+ y z)) (tan a))
104.0ms	(tan (+ y z))

simplify1.5s

Counts

81 → 81

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	128	32704
1	284	30442
2	1003	27582
done	5000	26331

prune600.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize51.0ms

Local error

Found 4 expressions with local error:

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

rewrite367.0ms

Algorithm

rewrite-expression-head

Rules

151×	`*-un-lft-identity`
108×	`prod-diff`
107×	`add-sqr-sqrt`
100×	`add-cube-cbrt`
85×	`times-frac`
56×	`associate-+r+`
24×	`distribute-lft-out`
18×	`fma-neg`
14×	`associate-/r/`
13×	`add-log-exp`
8×	`flip3--` `flip--`
7×	`tan-quot` `div-inv`
6×	`pow1` `fma-def` `add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sum-log` `associate-r` `associate-l`
2×	`+-commutative` `sub-neg` `flip3-+` `diff-log` `flip-+` `distribute-lft-out--` `difference-of-squares`
1×	`frac-times` `associate-+r-` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `associate-r/` `*-commutative` `frac-sub` `cbrt-unprod` `unswap-sqr`

Counts

4 → 207

Calls

4 calls:

10.0ms	(+ (tan y) (tan z))
207.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
114.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
25.0ms	(* (tan y) (tan z))

series1.3s

Counts

4 → 12

Calls

4 calls:

113.0ms	(+ (tan y) (tan z))
465.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
546.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
219.0ms	(* (tan y) (tan z))

simplify2.2s

Counts

219 → 219

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	297	145925
1	700	132538
2	2697	118394
done	5001	117537

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize70.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* (tan y) (tan z))) (cbrt (* (tan y) (tan z))))
8.1b	(cbrt (* (tan y) (tan z)))
8.1b	(cbrt (* (tan y) (tan z)))
8.1b	(cbrt (* (tan y) (tan z)))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

44×	`tan-quot`
33×	`cbrt-div`
20×	`frac-times`
14×	`associate-l/` `associate-r/`
11×	`pow1`
10×	`add-sqr-sqrt`
9×	`pow1/3`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`cbrt-prod`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `swap-sqr` `associate-r` `associate-l` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

95.0ms	(* (cbrt (* (tan y) (tan z))) (cbrt (* (tan y) (tan z))))
8.0ms	(cbrt (* (tan y) (tan z)))
8.0ms	(cbrt (* (tan y) (tan z)))
8.0ms	(cbrt (* (tan y) (tan z)))

series1.2s

Counts

4 → 12

Calls

4 calls:

349.0ms	(* (cbrt (* (tan y) (tan z))) (cbrt (* (tan y) (tan z))))
253.0ms	(cbrt (* (tan y) (tan z)))
287.0ms	(cbrt (* (tan y) (tan z)))
281.0ms	(cbrt (* (tan y) (tan z)))

simplify1.3s

Counts

102 → 102

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	122	47629
1	291	42973
2	1135	42512
done	5000	41652

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize74.0ms

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))

rewrite191.0ms

Algorithm

rewrite-expression-head

Rules

28×	`associate-*l/`
16×	`tan-quot`
14×	`add-sqr-sqrt`
13×	`add-cbrt-cube` `add-exp-log`
12×	`frac-sub`
10×	`*-un-lft-identity` `add-cube-cbrt`
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×	`frac-times` `cbrt-undiv` `div-exp` `pow-prod-down` `associate-r/` `associate-/r/` `-commutative` `unswap-sqr`
1×	`clear-num` `associate-/r*` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `prod-diff` `div-inv`

Counts

4 → 102

Calls

4 calls:

61.0ms	(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
64.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
26.0ms	(* (tan y) (tan z))
36.0ms	(* (tan y) (tan z))

series1.5s

Counts

4 → 12

Calls

4 calls:

503.0ms	(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
696.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
157.0ms	(* (tan y) (tan z))
184.0ms	(* (tan y) (tan z))

simplify3.3s

Counts

114 → 114

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	206	68941
1	712	63946
2	4049	63101
done	5000	62834

prune843.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes516.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	17	690
1	23	690
done	23	690

end0.0ms

sample9.2s

Algorithm

intervals

Results

5.4s	3831×	body	1280	valid
1.7s	2070×	body	640	valid
650.0ms	1139×	body	80	valid
590.0ms	8000×	pre	80	true
417.0ms	688×	body	320	valid
74.0ms	272×	body	160	valid