Details

sample161.0ms

Algorithm

intervals

Results

74.0ms	98×	body	1280	valid
39.0ms	24×	body	2560	valid
24.0ms	62×	body	640	valid
7.0ms	25×	body	320	valid
3.0ms	33×	body	80	valid
2.0ms	14×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4
done	10	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.2b

localize9.0ms

Local error

Found 2 expressions with local error:

2.1b	(- (tan (+ x eps)) (tan x))
5.2b	(tan (+ x eps))

rewrite26.0ms

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:

18.0ms	(- (tan (+ x eps)) (tan x))
7.0ms	(tan (+ x eps))

series155.0ms

Counts

2 → 6

Calls

2 calls:

96.0ms	(- (tan (+ x eps)) (tan x))
59.0ms	(tan (+ x eps))

simplify77.0ms

Counts

31 → 31

Iterations

Useful iterations: 3 (23.0ms)

Iter	Nodes	Cost
0	134	211
1	295	202
2	757	200
3	2482	199
4	5001	199
done	5001	199

prune94.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 16.8b

localize12.0ms

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))
4.7b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite146.0ms

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:

31.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
9.0ms	(+ (tan x) (tan eps))
18.0ms	(* (tan x) (tan eps))
86.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series794.0ms

Counts

4 → 12

Calls

4 calls:

220.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
97.0ms	(+ (tan x) (tan eps))
97.0ms	(* (tan x) (tan eps))
381.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify43.0ms

Counts

98 → 98

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	397	1052
1	1432	1007
2	5001	996
done	5001	996

prune303.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 16.6b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (sin eps))
0.3b	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
0.3b	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
4.7b	(- (+ (/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x))) (/ (sin eps) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos eps)))) (/ (sin x) (cos x)))

rewrite724.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

14.0ms	(* (sin x) (sin eps))
19.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
19.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
669.0ms	(- (+ (/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x))) (/ (sin eps) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos eps)))) (/ (sin x) (cos x)))

series651.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (sin x) (sin eps))
104.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
104.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
396.0ms	(- (+ (/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x))) (/ (sin eps) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos eps)))) (/ (sin x) (cos x)))

simplify61.0ms

Counts

98 → 98

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	464	1846
1	2215	1611
2	5001	1611
done	5001	1611

prune396.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 16.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
0.2b	(* (tan x) (tan eps))
0.2b	(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
9.3b	(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))

rewrite225.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 178

Calls

4 calls:

25.0ms	(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
16.0ms	(* (tan x) (tan eps))
28.0ms	(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
148.0ms	(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))

series1.0s

Counts

4 → 12

Calls

4 calls:

286.0ms	(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
100.0ms	(* (tan x) (tan eps))
234.0ms	(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
389.0ms	(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))

simplify79.0ms

Counts

190 → 190

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	703	2793
1	3290	2509
2	5001	2506
done	5001	2506

prune403.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 16.6b

regimes241.0ms

Accuracy

84.5% (1.2b remaining)

Error of 16.0b against oracle of 14.8b and baseline of 22.4b

bsearch179.0ms

Steps

Iters	Range		Point
9	1.1913964172771682e-31	1.0234318601461633e-26	6.4364749232124024e-27
9	-1.5455237205817756e-98	-2.323654281091449e-103	-1.5226418109876482e-98

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	52
1	58	52
2	58	52
done	58	52

end0.0ms

sample5.0s

Algorithm

intervals

Results

2.4s	3282×	body	1280	valid
1.1s	646×	body	2560	valid
803.0ms	1854×	body	640	valid
207.0ms	761×	body	320	valid
104.0ms	1086×	body	80	valid
66.0ms	371×	body	160	valid