Details

sample249.0ms

Algorithm

intervals

Results

107.0ms	97×	body	1280	valid
73.0ms	21×	body	2560	valid
32.0ms	52×	body	640	valid
11.0ms	26×	body	320	valid
6.0ms	42×	body	80	valid
6.0ms	18×	body	160	valid

simplify2.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.5b

localize10.0ms

Local error

Found 2 expressions with local error:

2.3b	(- (tan (+ x eps)) (tan x))
4.2b	(tan (+ x eps))

rewrite74.0ms

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:

59.0ms	(- (tan (+ x eps)) (tan x))
7.0ms	(tan (+ x eps))

series243.0ms

Counts

2 → 6

Calls

2 calls:

172.0ms	(- (tan (+ x eps)) (tan x))
72.0ms	(tan (+ x eps))

simplify98.0ms

Counts: 31 → 31

prune136.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 14.1b

localize22.0ms

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))
3.6b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite175.0ms

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:

29.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
10.0ms	(+ (tan x) (tan eps))
15.0ms	(* (tan x) (tan eps))
118.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series968.0ms

Counts

4 → 12

Calls

4 calls:

256.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
108.0ms	(+ (tan x) (tan eps))
117.0ms	(* (tan x) (tan eps))
487.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify91.0ms

Counts: 98 → 98

prune317.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 13.9b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
0.3b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
3.6b	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

rewrite474.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 110

Calls

4 calls:

17.0ms	(* (tan x) (tan eps))
18.0ms	(* (tan x) (tan eps))
399.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
33.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

series1.6s

Counts

4 → 12

Calls

4 calls:

123.0ms	(* (tan x) (tan eps))
126.0ms	(* (tan x) (tan eps))
160.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
1.2s	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

simplify67.0ms

Counts: 122 → 122

prune511.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.9b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.3b	(pow (* (tan x) (tan eps)) 3)
3.6b	(- (/ (+ (tan x) (tan eps)) (- 1 (cbrt (pow (* (tan x) (tan eps)) 3)))) (tan x))
28.8b	(cbrt (pow (* (tan x) (tan eps)) 3))

rewrite232.0ms

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:

15.0ms	(* (tan x) (tan eps))
12.0ms	(pow (* (tan x) (tan eps)) 3)
191.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (cbrt (pow (* (tan x) (tan eps)) 3)))) (tan x))
12.0ms	(cbrt (pow (* (tan x) (tan eps)) 3))

series895.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(* (tan x) (tan eps))
195.0ms	(pow (* (tan x) (tan eps)) 3)
445.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (cbrt (pow (* (tan x) (tan eps)) 3)))) (tan x))
102.0ms	(cbrt (pow (* (tan x) (tan eps)) 3))

simplify59.0ms

Counts: 94 → 94

prune391.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 13.9b

regimes200.0ms

Accuracy

87.5% (0.9b remaining)

Error of 15.9b against oracle of 15.0b and baseline of 22.2b

bsearch219.0ms

Steps

Iters	Range		Point
7	1.3230230372033123e-23	3.7781262686978725e-22	2.788637558705096e-22
10	-0.00045950116694092144	-7.210541768011361e-14	-7.301062761093603e-14

simplify96.0ms

end0.0ms

sample9.9s

Algorithm

intervals

Results

5.3s	3300×	body	1280	valid
1.9s	674×	body	2560	valid
1.3s	1842×	body	640	valid
486.0ms	384×	body	160	valid
381.0ms	737×	body	320	valid
144.0ms	1063×	body	80	valid