Details

sample621.0ms

Algorithm

intervals

Results

234.0ms	58×	body	2560	valid
137.0ms	80×	body	1280	valid
98.0ms	65×	body	640	valid
17.0ms	21×	body	320	valid
10.0ms	20×	body	160	valid
4.0ms	12×	body	80	valid

simplify31.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	41
3	41
2	37
1	25
0	6

prune33.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.7b

localize31.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.9b	(- x (tan x))
1.9b	(- x (sin x))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
15×	`add-cube-cbrt`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
5×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1` `insert-posit16`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `div-inv`

Counts

3 → 83

Calls

3 calls:

16.0ms	(/ (- x (sin x)) (- x (tan x)))
4.0ms	(- x (tan x))
7.0ms	(- x (sin x))

series299.0ms

Counts

3 → 9

Calls

3 calls:

141.0ms	(/ (- x (sin x)) (- x (tan x)))
88.0ms	(- x (tan x))
71.0ms	(- x (sin x))

simplify1.1s

Counts

92 → 92

Iterations

Iter	Nodes
3	2895
2	1388
1	666
0	160

prune903.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (* x x) (* x x)) 27/2800)
0.1b	(* (* x x) (* x x))
0.1b	(* (* x x) 9/40)
14.6b	(- (* (* x x) 9/40) (* (* (* x x) (* x x)) 27/2800))

rewrite216.0ms

Algorithm

rewrite-expression-head

Rules

138×	`pow1`
39×	`add-cbrt-cube` `pow-prod-down` `add-exp-log`
36×	`pow-prod-up`
24×	`prod-exp` `cbrt-unprod`
22×	`pow-sqr`
18×	`pow-plus`
13×	`pow2`
8×	`add-sqr-sqrt`
7×	`associate-r`
6×	`*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
4×	`insert-posit16`
3×	`associate-l` `*-commutative` `unswap-sqr`
1×	`sub-neg` `flip3--` `diff-log` `swap-sqr` `flip--`

Counts

4 → 126

Calls

4 calls:

101.0ms	(* (* (* x x) (* x x)) 27/2800)
44.0ms	(* (* x x) (* x x))
33.0ms	(* (* x x) 9/40)
37.0ms	(- (* (* x x) 9/40) (* (* (* x x) (* x x)) 27/2800))

series337.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* (* (* x x) (* x x)) 27/2800)
40.0ms	(* (* x x) (* x x))
48.0ms	(* (* x x) 9/40)
176.0ms	(- (* (* x x) 9/40) (* (* (* x x) (* x x)) 27/2800))

simplify1.5s

Counts

138 → 138

Iterations

Iter	Nodes
3	3460
2	1285
1	554
0	124

prune1.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (* x x) (- 9/40 (* 27/2800 (* x x))))
0.2b	(* 27/2800 (* x x))
1.9b	(log (exp (* (* x x) (- 9/40 (* 27/2800 (* x x))))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

14×	`pow1`
13×	`add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt`
7×	`log-prod`
6×	`*-un-lft-identity` `pow-prod-down` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
4×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-r` `associate-l` `exp-sum` `add-log-exp`
3×	`log-pow` `insert-posit16`
2×	`associate-r/` `-commutative` `unswap-sqr`
1×	`exp-prod` `flip3--` `exp-to-pow` `rem-log-exp` `flip--`

Counts

3 → 65

Calls

3 calls:

24.0ms	(* (* x x) (- 9/40 (* 27/2800 (* x x))))
13.0ms	(* 27/2800 (* x x))
5.0ms	(log (exp (* (* x x) (- 9/40 (* 27/2800 (* x x))))))

series307.0ms

Counts

3 → 9

Calls

3 calls:

141.0ms	(* (* x x) (- 9/40 (* 27/2800 (* x x))))
38.0ms	(* 27/2800 (* x x))
128.0ms	(log (exp (* (* x x) (- 9/40 (* 27/2800 (* x x))))))

simplify898.0ms

Counts

74 → 74

Iterations

Iter	Nodes
3	2678
2	999
1	437
0	106

prune661.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize63.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 27/2800 (* x x))
0.2b	(* 27/2800 (* x x))
1.7b	(log (* (cbrt (exp (* (* x x) (- 9/40 (* 27/2800 (* x x)))))) (cbrt (exp (* (* x x) (- 9/40 (* 27/2800 (* x x))))))))
1.7b	(log (cbrt (exp (* (* x x) (- 9/40 (* 27/2800 (* x x)))))))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1`
18×	`add-exp-log`
14×	`add-cbrt-cube`
11×	`log-prod` `log-pow`
10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `pow-prod-down` `add-cube-cbrt`
7×	`cbrt-prod` `pow1/3` `prod-exp`
6×	`associate-l` `cbrt-unprod`
4×	`exp-sum` `insert-posit16` `add-log-exp`
3×	`rem-log-exp`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-r` `pow-sqr` `*-commutative` `pow-prod-up` `unswap-sqr`
1×	`pow2` `pow-plus`

Counts

4 → 81

Calls

4 calls:

26.0ms	(* 27/2800 (* x x))
22.0ms	(* 27/2800 (* x x))
36.0ms	(log (* (cbrt (exp (* (* x x) (- 9/40 (* 27/2800 (* x x)))))) (cbrt (exp (* (* x x) (- 9/40 (* 27/2800 (* x x))))))))
11.0ms	(log (cbrt (exp (* (* x x) (- 9/40 (* 27/2800 (* x x)))))))

series3.2s

Counts

4 → 12

Calls

4 calls:

51.0ms	(* 27/2800 (* x x))
36.0ms	(* 27/2800 (* x x))
1.6s	(log (* (cbrt (exp (* (* x x) (- 9/40 (* 27/2800 (* x x)))))) (cbrt (exp (* (* x x) (- 9/40 (* 27/2800 (* x x))))))))
1.4s	(log (cbrt (exp (* (* x x) (- 9/40 (* 27/2800 (* x x)))))))

simplify1.5s

Counts

93 → 93

Iterations

Iter	Nodes
4	3213
3	1497
2	759
1	437
0	114

prune1.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes69.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 30.8b

bsearch138.0ms

Steps

Iters	Range		Point
9	6.676551468262503e-06	0.8715059566266286	0.03271128832128569
6	-0.1548015718904308	-0.015705103038678985	-0.03252464094224265

simplify23.0ms

Iterations

Iter	Nodes
2	27
1	27
0	22

end0.0ms

sample16.6s

Algorithm

intervals

Results

7.5s	1662×	body	2560	valid
5.3s	2681×	body	1280	valid
2.5s	1889×	body	640	valid
665.0ms	958×	body	320	valid
269.0ms	454×	body	160	valid
86.0ms	356×	body	80	valid