Details

sample212.0ms

Algorithm

intervals

Results

66.0ms	141×	body	80	valid
36.0ms	46×	body	1280	valid
14.0ms	28×	body	640	valid
10.0ms	26×	body	320	valid
4.0ms	15×	body	160	valid

simplify53.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	7	15
1	17	15
2	35	14
3	44	14
done	44	14

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
0.1b	(- 1.0 (* (tan x) (tan x)))
0.1b	(fma (tan x) (tan x) 1.0)
0.2b	(* (tan x) (tan x))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
11×	`pow1`
8×	`add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
5×	`difference-of-squares`
4×	`tan-quot` `expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`fma-neg` `swap-sqr` `associate-r` `associate-l` `prod-diff` `associate-/r*`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-times` `sub-neg` `frac-2neg` `pow-plus` `diff-log` `div-sub` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `fma-udef` `div-inv` `unswap-sqr`

Counts

4 → 97

Calls

4 calls:

28.0ms	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
13.0ms	(- 1.0 (* (tan x) (tan x)))
1.0ms	(fma (tan x) (tan x) 1.0)
34.0ms	(* (tan x) (tan x))

series346.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
46.0ms	(- 1.0 (* (tan x) (tan x)))
68.0ms	(fma (tan x) (tan x) 1.0)
77.0ms	(* (tan x) (tan x))

simplify5.5s

Counts

109 → 109

Iterations

Useful iterations: done (5.5s)

Iter	Nodes	Cost
0	155	1557
1	2975	1453
done	5000	1350

prune434.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1.0 (* (tan x) (tan x)))
0.1b	(fma (tan x) (tan x) 1.0)
0.2b	(* (tan x) (tan x))
0.3b	(log1p (/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
11×	`pow1`
10×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`expm1-log1p-u`
4×	`tan-quot` `log1p-expm1-u`
3×	`fma-neg` `swap-sqr` `associate-r` `associate-l` `prod-diff`
1×	`pow2` `frac-times` `sub-neg` `log1p-udef` `flip3--` `pow-plus` `diff-log` `log1p-expm1` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `fma-udef` `difference-of-squares` `unswap-sqr`

Counts

4 → 72

Calls

4 calls:

12.0ms	(- 1.0 (* (tan x) (tan x)))
1.0ms	(fma (tan x) (tan x) 1.0)
21.0ms	(* (tan x) (tan x))
1.0ms	(log1p (/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0)))

series577.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(- 1.0 (* (tan x) (tan x)))
82.0ms	(fma (tan x) (tan x) 1.0)
52.0ms	(* (tan x) (tan x))
375.0ms	(log1p (/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0)))

simplify4.7s

Counts

84 → 84

Iterations

Useful iterations: done (4.7s)

Iter	Nodes	Cost
0	131	993
1	796	905
done	5000	823

prune340.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1.0 (/ (* (sin x) (tan x)) (cos x)))
0.1b	(* (sin x) (tan x))
0.1b	(/ (* (sin x) (tan x)) (cos x))
0.1b	(fma (tan x) (tan x) 1.0)

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
22×	`add-cube-cbrt`
21×	`prod-diff`
12×	`times-frac`
11×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`fma-neg` `associate-r` `associate-l` `associate-/r*`
2×	`tan-quot` `cbrt-undiv` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod`
1×	`sub-neg` `flip3--` `frac-2neg` `diff-log` `pow-prod-down` `clear-num` `-commutative` `flip--` `fma-udef` `associate-/l/` `associate-/l` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 95

Calls

4 calls:

23.0ms	(- 1.0 (/ (* (sin x) (tan x)) (cos x)))
14.0ms	(* (sin x) (tan x))
15.0ms	(/ (* (sin x) (tan x)) (cos x))
0.0ms	(fma (tan x) (tan x) 1.0)

series299.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- 1.0 (/ (* (sin x) (tan x)) (cos x)))
56.0ms	(* (sin x) (tan x))
97.0ms	(/ (* (sin x) (tan x)) (cos x))
65.0ms	(fma (tan x) (tan x) 1.0)

simplify6.8s

Counts

107 → 107

Iterations

Useful iterations: done (6.8s)

Iter	Nodes	Cost
0	183	2078
1	3038	1587
done	5001	1454

prune582.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (sqrt 1.0) (tan x))
0.2b	(- (sqrt 1.0) (tan x))
0.2b	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
0.3b	(log1p (/ (* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x))) (fma (tan x) (tan x) 1.0)))

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
54×	`*-un-lft-identity` `prod-diff`
46×	`add-cube-cbrt`
35×	`sqrt-prod`
20×	`distribute-rgt-in` `distribute-lft-in`
8×	`add-log-exp`
6×	`pow1` `add-exp-log` `fma-def` `fma-neg` `associate-r` `add-cbrt-cube`
5×	`expm1-log1p-u`
4×	`frac-times` `flip3--` `flip3-+` `associate-l` `flip--` `flip-+` `log1p-expm1-u` `difference-of-squares`
3×	`sub-neg`
2×	`associate-r/` `associate-l/` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `log1p-udef` `diff-log` `log1p-expm1` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 144

Calls

4 calls:

10.0ms	(+ (sqrt 1.0) (tan x))
20.0ms	(- (sqrt 1.0) (tan x))
124.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
1.0ms	(log1p (/ (* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x))) (fma (tan x) (tan x) 1.0)))

series1.0s

Counts

4 → 12

Calls

4 calls:

64.0ms	(+ (sqrt 1.0) (tan x))
48.0ms	(- (sqrt 1.0) (tan x))
178.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
731.0ms	(log1p (/ (* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x))) (fma (tan x) (tan x) 1.0)))

simplify3.5s

Counts

156 → 156

Iterations

Useful iterations: done (3.4s)

Iter	Nodes	Cost
0	230	3664
1	1683	2565
done	5001	2236

prune541.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes113.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	20
1	13	20
done	13	20

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.8s	1546×	body	1280	valid
1.1s	4253×	body	80	valid
887.0ms	1258×	body	640	valid
310.0ms	634×	body	320	valid
79.0ms	309×	body	160	valid