Details

sample162.0ms

Algorithm

intervals

Results

71.0ms	93×	body	1280	valid
41.0ms	24×	body	2560	valid
26.0ms	62×	body	640	valid
6.0ms	23×	body	320	valid
3.0ms	39×	body	80	valid
3.0ms	15×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.1b

localize8.0ms

Local error

Found 2 expressions with local error:

1.9b	(tan (+ x eps))
2.4b	(- (tan (+ x eps)) (tan x))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

4×	`tan-quot` `add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `tan-sum` `frac-sub` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 25

Calls

2 calls:

3.0ms	(tan (+ x eps))
8.0ms	(- (tan (+ x eps)) (tan x))

series147.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(tan (+ x eps))
94.0ms	(- (tan (+ x eps)) (tan x))

simplify1.2s

Counts

31 → 31

Iterations

Useful iterations: 4 (314.0ms)

Iter	Nodes	Cost
0	68	367
1	135	355
2	295	341
3	633	337
4	2041	335
done	5000	335

prune92.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
3.7b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite64.0ms

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:

12.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
3.0ms	(+ (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
42.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series797.0ms

Counts

4 → 12

Calls

4 calls:

217.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
90.0ms	(+ (tan x) (tan eps))
94.0ms	(* (tan x) (tan eps))
396.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify565.0ms

Counts

98 → 98

Iterations

Useful iterations: done (562.0ms)

Iter	Nodes	Cost
0	172	1724
1	412	1649
2	1289	1579
done	5001	1564

prune293.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 14.6b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.2b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.3b	(pow (* (tan x) (tan eps)) 3)
3.7b	(- (* (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan x) (tan eps)) 3))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (tan x))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

48×	`pow1`
45×	`tan-quot`
21×	`add-exp-log` `frac-times` `add-cbrt-cube`
19×	`pow-prod-down`
15×	`associate-*r/`
14×	`associate-*l/`
10×	`prod-exp` `cbrt-unprod`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-log-exp`
5×	`frac-sub`
4×	`associate-r` `associate-l` `pow-sqr` `pow-prod-up`
3×	`cube-div` `pow-unpow`
2×	`pow-pow` `flip3-+` `pow-plus` `pow-exp` `associate--l+` `*-commutative` `flip-+` `rem-cube-cbrt`
1×	`pow2` `distribute-rgt-in` `cube-mult` `pow-to-exp` `sub-neg` `unpow-prod-down` `flip3--` `distribute-lft-in` `diff-log` `unpow3` `cube-prod` `swap-sqr` `flip--` `unswap-sqr` `sqr-pow`

Counts

4 → 114

Calls

4 calls:

5.0ms	(* (tan x) (tan eps))
22.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
5.0ms	(pow (* (tan x) (tan eps)) 3)
43.0ms	(- (* (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan x) (tan eps)) 3))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (tan x))

series2.0s

Counts

4 → 12

Calls

4 calls:

90.0ms	(* (tan x) (tan eps))
116.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
125.0ms	(pow (* (tan x) (tan eps)) 3)
1.7s	(- (* (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan x) (tan eps)) 3))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (tan x))

simplify1.9s

Counts

126 → 126

Iterations

Useful iterations: 2 (370.0ms)

Iter	Nodes	Cost
0	274	3217
1	855	2480
2	4324	2288
done	5000	2288

prune469.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 13.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.3b	(pow (* (tan x) (tan eps)) 3)
3.7b	(- (/ (+ (tan x) (tan eps)) (- 1 (cbrt (pow (* (tan x) (tan eps)) 3)))) (tan x))
26.6b	(cbrt (pow (* (tan x) (tan eps)) 3))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`tan-quot`
10×	`*-un-lft-identity`
9×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`cbrt-prod` `add-cube-cbrt`
6×	`cube-div` `add-log-exp`
3×	`frac-times` `pow-unpow` `cbrt-div` `associate-r/` `associate-r` `associate-l` `associate-l/`
2×	`cube-mult` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt` `difference-of-squares` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `flip3--` `times-frac` `pow1/3` `diff-log` `*-commutative` `frac-sub` `flip--` `rem-cbrt-cube` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 82

Calls

4 calls:

5.0ms	(* (tan x) (tan eps))
4.0ms	(pow (* (tan x) (tan eps)) 3)
112.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (cbrt (pow (* (tan x) (tan eps)) 3)))) (tan x))
3.0ms	(cbrt (pow (* (tan x) (tan eps)) 3))

series941.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(* (tan x) (tan eps))
124.0ms	(pow (* (tan x) (tan eps)) 3)
351.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (cbrt (pow (* (tan x) (tan eps)) 3)))) (tan x))
361.0ms	(cbrt (pow (* (tan x) (tan eps)) 3))

simplify533.0ms

Counts

94 → 94

Iterations

Useful iterations: 2 (137.0ms)

Iter	Nodes	Cost
0	163	1405
1	411	1180
2	1663	1110
done	5000	1110

prune270.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 13.3b

regimes229.0ms

Accuracy

94.4% (0.5b remaining)

Error of 13.7b against oracle of 13.2b and baseline of 21.7b

bsearch172.0ms

Steps

Iters	Range		Point
8	3.2660908088195926e-19	2.2877419438552398e-15	5.292479129902051e-18
9	-3.927952458448369e-14	-3.2217872713112076e-19	-6.9054160181468085e-18

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	146
1	61	146
done	61	146

end0.0ms

sample5.1s

Algorithm

intervals

Results

2.5s	3267×	body	1280	valid
1.1s	649×	body	2560	valid
807.0ms	1830×	body	640	valid
231.0ms	786×	body	320	valid
98.0ms	1065×	body	80	valid
82.0ms	403×	body	160	valid