Details

sample93.0ms

Algorithm

intervals

Results

46.0ms	81×	body	1280	valid
13.0ms	43×	body	640	valid
12.0ms	183×	body	80	valid
6.0ms	27×	body	320	valid
2.0ms	15×	body	160	valid

simplify6.0s

Counts

1 → 1

Iterations

Iter	Nodes
8	6498
7	1279
6	374
5	133
4	54
3	27
2	17
1	12
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.4b

localize11.0ms

Local error

Found 1 expressions with local error:

4.4b	(- (exp (* a x)) 1)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt`
4×	`*-un-lft-identity`
3×	`add-log-exp`
2×	`difference-of-squares`
1×	`pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `difference-of-sqr-1` `add-exp-log` `add-cube-cbrt` `insert-posit16` `flip--` `distribute-lft-out--`

Counts

1 → 17

Calls

1 calls:

18.0ms

(- (exp (* a x)) 1)

series38.0ms

Counts

1 → 3

Calls

1 calls:

38.0ms

(- (exp (* a x)) 1)

simplify1.3s

Counts

20 → 20

Iterations

Iter	Nodes
4	2847
3	848
2	269
1	105
0	48

prune187.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* a x) (* (* a x) 1/2))
0.2b	(* (* a x) (* a x))
0.3b	(* (* (* a x) (* (* a x) (* a x))) 1/6)
12.8b	(+ (* (* (* a x) (* (* a x) (* a x))) 1/6) (* (* a x) (* (* a x) 1/2)))

rewrite743.0ms

Algorithm

rewrite-expression-head

Rules

117×	`pow1`
90×	`add-cbrt-cube` `add-exp-log`
74×	`pow-prod-down`
65×	`prod-exp` `cbrt-unprod`
6×	`add-log-exp`
5×	`add-sqr-sqrt` `-un-lft-identity` `associate-r*` `add-cube-cbrt`
4×	`pow-sqr` `pow-prod-up` `insert-posit16`
3×	`associate-l` `*-commutative`
2×	`pow-plus`
1×	`pow2` `+-commutative` `sum-log` `flip3-+` `swap-sqr` `flip-+`

Counts

4 → 122

Calls

4 calls:

93.0ms	(* (* a x) (* (* a x) 1/2))
36.0ms	(* (* a x) (* a x))
297.0ms	(* (* (* a x) (* (* a x) (* a x))) 1/6)
312.0ms	(+ (* (* (* a x) (* (* a x) (* a x))) 1/6) (* (* a x) (* (* a x) 1/2)))

series388.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (* a x) (* (* a x) 1/2))
58.0ms	(* (* a x) (* a x))
120.0ms	(* (* (* a x) (* (* a x) (* a x))) 1/6)
165.0ms	(+ (* (* (* a x) (* (* a x) (* a x))) 1/6) (* (* a x) (* (* a x) 1/2)))

simplify924.0ms

Counts

134 → 134

Iterations

Iter	Nodes
2	2101
1	504
0	165

prune1.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* a x) (* a x))
0.3b	(* (* (* a x) (* (* a x) (* a x))) 1/6)
1.6b	(log (exp (+ (* 1/2 (* (* a x) (* a x))) (* (* (* a x) (* (* a x) (* a x))) 1/6))))
12.8b	(+ (* 1/2 (* (* a x) (* a x))) (* (* (* a x) (* (* a x) (* a x))) 1/6))

rewrite704.0ms

Algorithm

rewrite-expression-head

Rules

97×	`pow1`
69×	`add-cbrt-cube` `add-exp-log`
59×	`pow-prod-down`
50×	`prod-exp` `cbrt-unprod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`add-log-exp`
4×	`log-prod` `associate-r` `pow-sqr` `log-pow` `pow-prod-up` `insert-posit16`
3×	`exp-prod`
2×	`pow-plus` `associate-l` `*-commutative`
1×	`pow2` `+-commutative` `sum-log` `flip3-+` `swap-sqr` `rem-log-exp` `exp-sum` `flip-+`

Counts

4 → 110

Calls

4 calls:

45.0ms	(* (* a x) (* a x))
311.0ms	(* (* (* a x) (* (* a x) (* a x))) 1/6)
240.0ms	(log (exp (+ (* 1/2 (* (* a x) (* a x))) (* (* (* a x) (* (* a x) (* a x))) 1/6))))
104.0ms	(+ (* 1/2 (* (* a x) (* a x))) (* (* (* a x) (* (* a x) (* a x))) 1/6))

series520.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (* a x) (* a x))
94.0ms	(* (* (* a x) (* (* a x) (* a x))) 1/6)
168.0ms	(log (exp (+ (* 1/2 (* (* a x) (* a x))) (* (* (* a x) (* (* a x) (* a x))) 1/6))))
211.0ms	(+ (* 1/2 (* (* a x) (* a x))) (* (* (* a x) (* (* a x) (* a x))) 1/6))

simplify14.3s

Counts

122 → 122

Iterations

Iter	Nodes
3	15462
2	1773
1	442
0	159

prune1.4s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (exp (* a x)) 1)
0.0b	(/ (- (* (exp (* a x)) (exp (* a x))) 1) (+ (exp (* a x)) 1))
4.4b	(- (* (exp (* a x)) (exp (* a x))) 1)

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
24×	`times-frac`
21×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
12×	`difference-of-squares`
8×	`distribute-lft-out`
7×	`add-log-exp`
6×	`difference-of-sqr-1` `associate-/l*`
5×	`add-cbrt-cube` `add-exp-log`
4×	`associate-/r*`
3×	`pow1` `insert-posit16`
2×	`flip3-+` `flip3--` `associate-/r/` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

3 → 81

Calls

3 calls:

9.0ms	(+ (exp (* a x)) 1)
61.0ms	(/ (- (* (exp (* a x)) (exp (* a x))) 1) (+ (exp (* a x)) 1))
15.0ms	(- (* (exp (* a x)) (exp (* a x))) 1)

series585.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(+ (exp (* a x)) 1)
103.0ms	(/ (- (* (exp (* a x)) (exp (* a x))) 1) (+ (exp (* a x)) 1))
449.0ms	(- (* (exp (* a x)) (exp (* a x))) 1)

simplify1.8s

Counts

90 → 90

Iterations

Iter	Nodes
3	3462
2	1057
1	333
0	130

prune742.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes240.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 21.3b

bsearch51.0ms

Steps

Iters	Range		Point
9	-0.12119295063518107	-4.9104404731882355e-11	-0.00015435000108057162

simplify7.0ms

Iterations

Iter	Nodes
2	31
1	31
0	23

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.1s	2709×	body	1280	valid
394.0ms	5469×	body	80	valid
361.0ms	1321×	body	640	valid
153.0ms	741×	body	320	valid
46.0ms	390×	body	160	valid