Details

sample205.0ms

Algorithm

intervals

Results

35.0ms	50×	body	1280	valid
19.0ms	40×	body	640	valid
14.0ms	135×	body	80	valid
6.0ms	21×	body	320	valid
2.0ms	10×	body	160	valid

simplify60.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	45
6	45
5	43
4	37
3	29
2	22
1	13
0	7

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize29.0ms

Local error

Found 3 expressions with local error:

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

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
5×	`add-cbrt-cube` `add-exp-log`
3×	`expm1-log1p-u` `pow1` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`fma-udef`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

3 → 49

Calls

3 calls:

0.0ms	(fma (tan x) (tan x) 1.0)
8.0ms	(/ (fma (- (tan x)) (tan x) 1.0) (fma (tan x) (tan x) 1.0))
3.0ms	(fma (- (tan x)) (tan x) 1.0)

series393.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(fma (tan x) (tan x) 1.0)
223.0ms	(/ (fma (- (tan x)) (tan x) 1.0) (fma (tan x) (tan x) 1.0))
113.0ms	(fma (- (tan x)) (tan x) 1.0)

simplify1.0s

Counts

58 → 58

Iterations

Iter	Nodes
done	5000
3	1873
2	456
1	161
0	87

prune357.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (log (exp (fma (- (tan x)) (tan x) 1.0))) (fma (tan x) (tan x) 1.0))
0.2b	(log (exp (fma (- (tan x)) (tan x) 1.0)))
0.3b	(fma (- (tan x)) (tan x) 1.0)
0.3b	(exp (fma (- (tan x)) (tan x) 1.0))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
21×	`times-frac`
20×	`log-pow`
18×	`exp-prod`
9×	`pow1`
7×	`associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`add-log-exp`
4×	`expm1-log1p-u` `log-prod` `log1p-expm1-u`
3×	`associate-/r*` `fma-udef`
2×	`exp-sum`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `rem-log-exp` `div-inv` `rem-exp-log`

Counts

4 → 87

Calls

4 calls:

16.0ms	(/ (log (exp (fma (- (tan x)) (tan x) 1.0))) (fma (tan x) (tan x) 1.0))
2.0ms	(log (exp (fma (- (tan x)) (tan x) 1.0)))
0.0ms	(fma (- (tan x)) (tan x) 1.0)
2.0ms	(exp (fma (- (tan x)) (tan x) 1.0))

series469.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(/ (log (exp (fma (- (tan x)) (tan x) 1.0))) (fma (tan x) (tan x) 1.0))
71.0ms	(log (exp (fma (- (tan x)) (tan x) 1.0)))
97.0ms	(fma (- (tan x)) (tan x) 1.0)
122.0ms	(exp (fma (- (tan x)) (tan x) 1.0))

simplify1.9s

Counts

99 → 99

Iterations

Iter	Nodes
done	5000
3	4350
2	791
1	253
0	141

prune671.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (fma (tan x) (tan x) 1.0))
0.1b	(fma (tan x) (tan x) 1.0)
0.1b	(* (fma (tan x) (- (tan x)) 1.0) (/ 1 (fma (tan x) (tan x) 1.0)))
0.3b	(fma (tan x) (- (tan x)) 1.0)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
20×	`times-frac` `add-cube-cbrt`
17×	`add-exp-log`
13×	`associate-r`
11×	`add-cbrt-cube`
7×	`pow1`
4×	`expm1-log1p-u` `div-exp` `prod-exp` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-l` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `1-exp` `cbrt-unprod` `fma-udef` `div-inv`
1×	`clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `pow-flip` `inv-pow`

Counts

4 → 91

Calls

4 calls:

8.0ms	(/ 1 (fma (tan x) (tan x) 1.0))
0.0ms	(fma (tan x) (tan x) 1.0)
22.0ms	(* (fma (tan x) (- (tan x)) 1.0) (/ 1 (fma (tan x) (tan x) 1.0)))
1.0ms	(fma (tan x) (- (tan x)) 1.0)

series423.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(/ 1 (fma (tan x) (tan x) 1.0))
62.0ms	(fma (tan x) (tan x) 1.0)
196.0ms	(* (fma (tan x) (- (tan x)) 1.0) (/ 1 (fma (tan x) (tan x) 1.0)))
86.0ms	(fma (tan x) (- (tan x)) 1.0)

simplify1.0s

Counts

103 → 103

Iterations

Iter	Nodes
done	5001
2	1467
1	281
0	131

prune491.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (log (* (exp (* (- (tan x)) (tan x))) (exp 1.0))) (fma (tan x) (tan x) 1.0))
0.2b	(log (* (exp (* (- (tan x)) (tan x))) (exp 1.0)))
0.3b	(* (- (tan x)) (tan x))
0.3b	(exp (* (- (tan x)) (tan x)))

rewrite177.0ms

Algorithm

rewrite-expression-head

Rules

21×	`pow1`
20×	`add-sqr-sqrt`
18×	`*-un-lft-identity` `add-cube-cbrt`
15×	`times-frac`
10×	`associate-l` `log-pow`
9×	`add-exp-log`
8×	`add-cbrt-cube`
7×	`add-log-exp`
6×	`pow-prod-down`
5×	`associate-/l*`
4×	`distribute-lft-neg-out` `expm1-log1p-u` `tan-quot` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `exp-neg` `associate-/r` `distribute-rgt-neg-in` `associate-r` `associate-l/`
2×	`log-div` `exp-to-pow` `rem-log-exp` `prod-exp` `distribute-neg-frac`
1×	`frac-times` `cbrt-undiv` `log-prod` `exp-prod` `clear-num` `neg-mul-1` `frac-2neg` `div-sub` `div-exp` `neg-log` `associate-r/` `-commutative` `cbrt-unprod` `div-inv` `unswap-sqr` `rem-exp-log`

Counts

4 → 98

Calls

4 calls:

91.0ms	(/ (log (* (exp (* (- (tan x)) (tan x))) (exp 1.0))) (fma (tan x) (tan x) 1.0))
25.0ms	(log (* (exp (* (- (tan x)) (tan x))) (exp 1.0)))
28.0ms	(* (- (tan x)) (tan x))
31.0ms	(exp (* (- (tan x)) (tan x)))

series953.0ms

Counts

4 → 12

Calls

4 calls:

431.0ms	(/ (log (* (exp (* (- (tan x)) (tan x))) (exp 1.0))) (fma (tan x) (tan x) 1.0))
345.0ms	(log (* (exp (* (- (tan x)) (tan x))) (exp 1.0)))
68.0ms	(* (- (tan x)) (tan x))
108.0ms	(exp (* (- (tan x)) (tan x)))

simplify869.0ms

Counts

110 → 110

Iterations

Iter	Nodes
done	5000
2	1329
1	317
0	154

prune505.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes215.0ms

Accuracy

0% (1.0b remaining)

Error of 1.1b against oracle of 0.1b and baseline of 1.1b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	15
1	15
0	11

end0.0ms

sample4.6s

Algorithm

intervals

Results

2.5s	1466×	body	1280	valid
874.0ms	1241×	body	640	valid
569.0ms	4372×	body	80	valid
276.0ms	592×	body	320	valid
133.0ms	329×	body	160	valid