Details

sample325.0ms

Algorithm

intervals

Results

131.0ms	99×	body	1280	valid
63.0ms	29×	body	320	valid
54.0ms	65×	body	640	valid
48.0ms	17×	body	2560	valid
6.0ms	33×	body	80	valid
5.0ms	13×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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: 37.6b

localize9.0ms

Local error

Found 2 expressions with local error:

2.0b	(- (tan (+ x eps)) (tan x))
4.0b	(tan (+ x eps))

rewrite32.0ms

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:

24.0ms	(- (tan (+ x eps)) (tan x))
7.0ms	(tan (+ x eps))

series275.0ms

Counts

2 → 6

Calls

2 calls:

148.0ms	(- (tan (+ x eps)) (tan x))
126.0ms	(tan (+ x eps))

simplify2.4s

Counts

31 → 31

Iterations

Useful iterations: 4 (322.0ms)

Iter	Nodes	Cost
0	68	367
1	135	355
2	278	341
3	528	337
4	1109	335
5	2471	335
done	5000	335

prune98.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.2b	(* (tan x) (tan eps))
3.0b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite213.0ms

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:

18.0ms	(+ (tan x) (tan eps))
45.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
25.0ms	(* (tan x) (tan eps))
120.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts

4 → 12

Calls

4 calls:

121.0ms	(+ (tan x) (tan eps))
297.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
150.0ms	(* (tan x) (tan eps))
495.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify2.1s

Counts

98 → 98

Iterations

Useful iterations: 3 (779.0ms)

Iter	Nodes	Cost
0	172	1724
1	397	1649
2	1091	1579
3	2924	1563
done	5001	1563

prune380.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.2b

localize21.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (* (cbrt (* (tan x) (tan eps))) (cbrt (* (tan x) (tan eps)))) (cbrt (* (tan x) (tan eps)))))) (tan x))
7.6b	(cbrt (* (tan x) (tan eps)))
7.6b	(cbrt (* (tan x) (tan eps)))
7.6b	(cbrt (* (tan x) (tan eps)))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

13×	`tan-quot`
9×	`add-sqr-sqrt` `cbrt-div`
6×	`*-un-lft-identity` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
3×	`cbrt-prod` `frac-times` `pow1/3` `associate-r/` `associate-l/`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `times-frac` `diff-log` `frac-sub` `flip--` `distribute-lft-out--`

Counts

4 → 52

Calls

4 calls:

110.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (* (cbrt (* (tan x) (tan eps))) (cbrt (* (tan x) (tan eps)))) (cbrt (* (tan x) (tan eps)))))) (tan x))
10.0ms	(cbrt (* (tan x) (tan eps)))
21.0ms	(cbrt (* (tan x) (tan eps)))
10.0ms	(cbrt (* (tan x) (tan eps)))

series1.1s

Counts

4 → 12

Calls

4 calls:

513.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (* (cbrt (* (tan x) (tan eps))) (cbrt (* (tan x) (tan eps)))) (cbrt (* (tan x) (tan eps)))))) (tan x))
187.0ms	(cbrt (* (tan x) (tan eps)))
201.0ms	(cbrt (* (tan x) (tan eps)))
238.0ms	(cbrt (* (tan x) (tan eps)))

simplify2.6s

Counts

64 → 64

Iterations

Useful iterations: 4 (1.2s)

Iter	Nodes	Cost
0	101	1420
1	223	1404
2	490	1003
3	1159	906
4	3477	883
done	5000	883

prune348.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 12.2b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos x) (sin eps))
0.2b	(* (tan x) (tan eps))
0.3b	(/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (* (- 1 (* (tan x) (tan eps))) (* (cos x) (cos eps))))
6.6b	(- (/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (* (- 1 (* (tan x) (tan eps))) (* (cos x) (cos eps)))) (tan x))

rewrite325.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-exp-log` `add-cbrt-cube`
16×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`add-cube-cbrt`
8×	`pow1`
6×	`associate-r` `associate-l` `add-log-exp`
5×	`tan-quot` `prod-exp` `associate-/r/` `cbrt-unprod`
3×	`cbrt-undiv` `frac-times` `flip3--` `times-frac` `div-exp` `associate-l/` `cos-mult` `flip--` `associate-/l`
2×	`associate-r/` `pow-prod-down` `-commutative` `associate-/l/` `unswap-sqr`
1×	`sub-neg` `frac-2neg` `flip3-+` `diff-log` `clear-num` `associate-/r*` `frac-sub` `flip-+` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 84

Calls

4 calls:

17.0ms	(* (cos x) (sin eps))
17.0ms	(* (tan x) (tan eps))
73.0ms	(/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (* (- 1 (* (tan x) (tan eps))) (* (cos x) (cos eps))))
214.0ms	(- (/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (* (- 1 (* (tan x) (tan eps))) (* (cos x) (cos eps)))) (tan x))

series1.2s

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (cos x) (sin eps))
141.0ms	(* (tan x) (tan eps))
483.0ms	(/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (* (- 1 (* (tan x) (tan eps))) (* (cos x) (cos eps))))
500.0ms	(- (/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (* (- 1 (* (tan x) (tan eps))) (* (cos x) (cos eps)))) (tan x))

simplify1.5s

Counts

96 → 96

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	218	2291
1	580	2197
2	2080	1963
done	5001	1939

prune582.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 12.2b

regimes249.0ms

Accuracy

88.7% (0.9b remaining)

Error of 15.0b against oracle of 14.1b and baseline of 22.1b

bsearch258.0ms

Steps

Iters	Range		Point
7	9.893396450191569e-20	8.666561730544872e-18	1.084923224249313e-19
9	-1.6407970181994926e-76	-4.024269261797611e-82	-6.929244313528967e-77

simplify12.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	37	78
1	54	78
done	54	78

end0.0ms

sample10.2s

Algorithm

intervals

Results

4.6s	3301×	body	1280	valid
2.4s	1873×	body	640	valid
2.0s	598×	body	2560	valid
532.0ms	797×	body	320	valid
239.0ms	1085×	body	80	valid
145.0ms	346×	body	160	valid