Details

sample151.0ms

Algorithm

intervals

Results

69.0ms	95×	body	1280	valid
37.0ms	22×	body	2560	valid
23.0ms	58×	body	640	valid
6.0ms	25×	body	320	valid
3.0ms	38×	body	80	valid
3.0ms	18×	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: 34.0b

localize9.0ms

Local error

Found 2 expressions with local error:

2.6b	(- (tan (+ x eps)) (tan x))
3.9b	(tan (+ x eps))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
4×	`tan-quot` `add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `tan-sum` `frac-sub` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 41

Calls

2 calls:

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

series142.0ms

Counts

2 → 6

Calls

2 calls:

87.0ms	(- (tan (+ x eps)) (tan x))
55.0ms	(tan (+ x eps))

simplify1.3s

Counts

47 → 47

Iterations

Useful iterations: 3 (271.0ms)

Iter	Nodes	Cost
0	94	720
1	199	597
2	544	510
3	2330	450
done	5000	450

prune118.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.3b

localize11.0ms

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))
4.0b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

102×	`*-un-lft-identity`
73×	`add-sqr-sqrt`
66×	`add-cube-cbrt`
61×	`times-frac`
54×	`prod-diff`
18×	`fma-neg`
17×	`distribute-lft-out`
10×	`associate-/r/`
9×	`tan-quot`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1` `flip3--` `flip--`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`fma-def` `associate-r` `associate-l` `associate-/r*` `associate-/l/`
2×	`flip3-+` `frac-add` `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` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 169

Calls

4 calls:

11.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
3.0ms	(+ (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
50.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series730.0ms

Counts

4 → 12

Calls

4 calls:

207.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
89.0ms	(+ (tan x) (tan eps))
89.0ms	(* (tan x) (tan eps))
346.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.1s

Counts

181 → 181

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	240	4762
1	576	3970
2	1936	3549
done	5000	3525

prune452.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 13.2b

localize19.0ms

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)))
4.0b	(fma (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (fma (tan eps) (tan x) 1) (- (tan x)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
40×	`tan-quot`
20×	`add-exp-log` `add-cbrt-cube`
19×	`frac-times` `pow-prod-down`
13×	`associate-r/` `associate-l/`
12×	`add-sqr-sqrt`
10×	`prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `pow-sqr` `pow-prod-up` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`pow-plus` `unswap-sqr`
1×	`pow2` `swap-sqr` `fma-udef`

Counts

4 → 107

Calls

4 calls:

6.0ms	(* (tan x) (tan eps))
6.0ms	(* (tan x) (tan eps))
24.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
1.0ms	(fma (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (fma (tan eps) (tan x) 1) (- (tan x)))

series966.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(* (tan x) (tan eps))
91.0ms	(* (tan x) (tan eps))
125.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
655.0ms	(fma (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (fma (tan eps) (tan x) 1) (- (tan x)))

simplify637.0ms

Counts

119 → 119

Iterations

Useful iterations: 2 (160.0ms)

Iter	Nodes	Cost
0	157	1832
1	424	1746
2	1775	1476
done	5000	1476

prune420.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 13.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (tan eps))
0.2b	(* (tan x) (tan eps))
0.2b	(* (* (sin x) (tan eps)) (* (tan x) (tan eps)))
4.0b	(fma (/ (+ (tan x) (tan eps)) (- 1 (/ (* (* (sin x) (tan eps)) (* (tan x) (tan eps))) (cos x)))) (fma (tan eps) (tan x) 1) (- (tan x)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1` `add-exp-log` `add-cbrt-cube`
17×	`tan-quot`
12×	`add-sqr-sqrt`
11×	`associate-*r/`
10×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r` `associate-l`
6×	`frac-times`
4×	`expm1-log1p-u` `associate-*l/` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`unswap-sqr`
1×	`fma-udef`

Counts

4 → 85

Calls

4 calls:

4.0ms	(* (sin x) (tan eps))
5.0ms	(* (tan x) (tan eps))
23.0ms	(* (* (sin x) (tan eps)) (* (tan x) (tan eps)))
0.0ms	(fma (/ (+ (tan x) (tan eps)) (- 1 (/ (* (* (sin x) (tan eps)) (* (tan x) (tan eps))) (cos x)))) (fma (tan eps) (tan x) 1) (- (tan x)))

series965.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(* (sin x) (tan eps))
94.0ms	(* (tan x) (tan eps))
135.0ms	(* (* (sin x) (tan eps)) (* (tan x) (tan eps)))
655.0ms	(fma (/ (+ (tan x) (tan eps)) (- 1 (/ (* (* (sin x) (tan eps)) (* (tan x) (tan eps))) (cos x)))) (fma (tan eps) (tan x) 1) (- (tan x)))

simplify736.0ms

Counts

97 → 97

Iterations

Useful iterations: 2 (193.0ms)

Iter	Nodes	Cost
0	170	1673
1	458	1642
2	2023	1373
done	5001	1373

prune387.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

regimes99.0ms

Accuracy

0% (0.3b remaining)

Error of 0.6b against oracle of 0.3b and baseline of 0.6b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	115
1	43	115
done	43	115

end0.0ms

sample5.0s

Algorithm

intervals

Results

2.5s	3289×	body	1280	valid
1.2s	686×	body	2560	valid
787.0ms	1815×	body	640	valid
220.0ms	736×	body	320	valid
109.0ms	1115×	body	80	valid
66.0ms	359×	body	160	valid