Details

sample235.0ms

Algorithm

intervals

Results

99.0ms	99×	body	1280	valid
64.0ms	65×	body	640	valid
35.0ms	17×	body	2560	valid
13.0ms	29×	body	320	valid
5.0ms	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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.6b

localize19.0ms

Local error

Found 2 expressions with local error:

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

rewrite77.0ms

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:

30.0ms	(- (tan (+ x eps)) (tan x))
46.0ms	(tan (+ x eps))

series252.0ms

Counts

2 → 6

Calls

2 calls:

163.0ms	(- (tan (+ x eps)) (tan x))
90.0ms	(tan (+ x eps))

simplify2.7s

Counts

31 → 31

Iterations

Useful iterations: 4 (384.0ms)

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

prune120.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.3b

localize14.0ms

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))

rewrite184.0ms

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:

9.0ms	(+ (tan x) (tan eps))
49.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
25.0ms	(* (tan x) (tan eps))
98.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.0s

Counts

4 → 12

Calls

4 calls:

135.0ms	(+ (tan x) (tan eps))
299.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
122.0ms	(* (tan x) (tan eps))
461.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify2.1s

Counts

98 → 98

Iterations

Useful iterations: 3 (698.0ms)

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

prune460.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.2b

localize20.0ms

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)))

rewrite195.0ms

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:

140.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (* (cbrt (* (tan x) (tan eps))) (cbrt (* (tan x) (tan eps)))) (cbrt (* (tan x) (tan eps)))))) (tan x))
14.0ms	(cbrt (* (tan x) (tan eps)))
16.0ms	(cbrt (* (tan x) (tan eps)))
22.0ms	(cbrt (* (tan x) (tan eps)))

series1.2s

Counts

4 → 12

Calls

4 calls:

585.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (* (cbrt (* (tan x) (tan eps))) (cbrt (* (tan x) (tan eps)))) (cbrt (* (tan x) (tan eps)))))) (tan x))
222.0ms	(cbrt (* (tan x) (tan eps)))
195.0ms	(cbrt (* (tan x) (tan eps)))
207.0ms	(cbrt (* (tan x) (tan eps)))

simplify2.3s

Counts

64 → 64

Iterations

Useful iterations: 4 (1.1s)

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

prune494.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 12.2b

localize39.0ms

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))

rewrite429.0ms

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:

12.0ms	(* (cos x) (sin eps))
19.0ms	(* (tan x) (tan eps))
109.0ms	(/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (* (- 1 (* (tan x) (tan eps))) (* (cos x) (cos eps))))
286.0ms	(- (/ (+ (* (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:

62.0ms	(* (cos x) (sin eps))
141.0ms	(* (tan x) (tan eps))
413.0ms	(/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (* (- 1 (* (tan x) (tan eps))) (* (cos x) (cos eps))))
584.0ms	(- (/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (* (- 1 (* (tan x) (tan eps))) (* (cos x) (cos eps)))) (tan x))

simplify1.9s

Counts

96 → 96

Iterations

Useful iterations: done (1.8s)

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

prune542.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 12.2b

regimes340.0ms

Accuracy

88.7% (0.9b remaining)

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

bsearch307.0ms

Steps

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

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample11.0s

Algorithm

intervals

Results

6.2s	3301×	body	1280	valid
1.8s	1873×	body	640	valid
1.8s	598×	body	2560	valid
443.0ms	797×	body	320	valid
216.0ms	1085×	body	80	valid
177.0ms	346×	body	160	valid