Details

sample49.0ms

Algorithm

intervals

Results

19.0ms	93×	body	1280	valid
5.0ms	177×	body	80	valid
4.0ms	34×	body	640	valid
2.0ms	24×	body	320	valid
0.0ms	5×	body	160	valid

simplify3.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5028
8	3392
7	883
6	221
5	93
4	44
3	23
2	16
1	11
0	6

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.8b

localize14.0ms

Local error

Found 1 expressions with local error:

2.2b	(- (exp (* a x)) 1.0)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 14

Calls

1 calls:

19.0ms

(- (exp (* a x)) 1.0)

series60.0ms

Counts

1 → 3

Calls

1 calls:

60.0ms

(- (exp (* a x)) 1.0)

simplify2.5s

Counts

17 → 17

Iterations

Iter	Nodes
done	5009
4	3224
3	982
2	293
1	105
0	45

prune79.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (* a x) (* (* a x) (* a x))) 1/6)
0.2b	(* (* a x) (* a x))
0.2b	(* (* a x) (* a x))
14.3b	(+ (* (* (* a x) (* (* a x) (* a x))) 1/6) (/ (* (* a x) (* a x)) 2))

rewrite706.0ms

Algorithm

rewrite-expression-head

Rules

135×	`pow1`
81×	`add-cbrt-cube` `add-exp-log`
76×	`pow-prod-down`
58×	`prod-exp` `cbrt-unprod`
8×	`pow-sqr` `pow-prod-up`
6×	`add-log-exp`
5×	`add-sqr-sqrt` `-un-lft-identity` `associate-r*` `add-cube-cbrt`
4×	`pow-plus`
3×	`associate-l` `*-commutative`
2×	`pow2` `swap-sqr`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+`

Counts

4 → 124

Calls

4 calls:

354.0ms	(* (* (* a x) (* (* a x) (* a x))) 1/6)
33.0ms	(* (* a x) (* a x))
21.0ms	(* (* a x) (* a x))
291.0ms	(+ (* (* (* a x) (* (* a x) (* a x))) 1/6) (/ (* (* a x) (* a x)) 2))

series407.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(* (* (* a x) (* (* a x) (* a x))) 1/6)
42.0ms	(* (* a x) (* a x))
61.0ms	(* (* a x) (* a x))
210.0ms	(+ (* (* (* a x) (* (* a x) (* a x))) 1/6) (/ (* (* a x) (* a x)) 2))

simplify2.0s

Counts

136 → 136

Iterations

Iter	Nodes
done	5004
2	1875
1	417
0	132

prune387.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt (exp (* a x))) (sqrt 1.0))
0.0b	(sqrt (exp (* a x)))
0.0b	(sqrt (exp (* a x)))
2.2b	(- (sqrt (exp (* a x))) (sqrt 1.0))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`*-un-lft-identity` `sqrt-prod`
10×	`add-log-exp`
6×	`pow1` `sqrt-pow1` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `difference-of-squares`
2×	`rem-sqrt-square` `exp-prod` `exp-to-pow` `pow1/2` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `sum-log` `sub-neg` `flip3-+` `flip3--` `diff-log` `flip-+` `flip--`

Counts

4 → 61

Calls

4 calls:

20.0ms	(+ (sqrt (exp (* a x))) (sqrt 1.0))
2.0ms	(sqrt (exp (* a x)))
2.0ms	(sqrt (exp (* a x)))
14.0ms	(- (sqrt (exp (* a x))) (sqrt 1.0))

series196.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(+ (sqrt (exp (* a x))) (sqrt 1.0))
33.0ms	(sqrt (exp (* a x)))
27.0ms	(sqrt (exp (* a x)))
74.0ms	(- (sqrt (exp (* a x))) (sqrt 1.0))

simplify2.3s

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
4	2235
3	845
2	361
1	147
0	70

prune450.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize65.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (* (sqrt 1.0) (sqrt (exp (* a x)))))
0.0b	(/ (- (* (exp (* a x)) (sqrt (exp (* a x)))) (* (sqrt 1.0) 1.0)) (+ (exp (* a x)) (+ 1.0 (* (sqrt 1.0) (sqrt (exp (* a x)))))))
0.0b	(* (exp (* a x)) (sqrt (exp (* a x))))
2.2b	(- (* (exp (* a x)) (sqrt (exp (* a x)))) (* (sqrt 1.0) 1.0))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
17×	`add-cube-cbrt`
16×	`times-frac`
12×	`add-log-exp`
9×	`pow1`
8×	`add-cbrt-cube`
7×	`pow3` `add-exp-log`
6×	`difference-cubes` `cube-unmult` `associate-r` `pow-prod-up` `distribute-lft-out`
5×	`sqrt-pow1`
4×	`exp-prod` `associate-/r` `exp-to-pow` `sqrt-prod` `associate-/l`
3×	`associate-l`
2×	`flip3-+` `flip3--` `associate-/r/` `flip-+` `flip--` `unswap-sqr` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `pow1/2` `diff-log` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 95

Calls

4 calls:

4.0ms	(+ 1.0 (* (sqrt 1.0) (sqrt (exp (* a x)))))
66.0ms	(/ (- (* (exp (* a x)) (sqrt (exp (* a x)))) (* (sqrt 1.0) 1.0)) (+ (exp (* a x)) (+ 1.0 (* (sqrt 1.0) (sqrt (exp (* a x)))))))
38.0ms	(* (exp (* a x)) (sqrt (exp (* a x))))
34.0ms	(- (* (exp (* a x)) (sqrt (exp (* a x)))) (* (sqrt 1.0) 1.0))

series1.6s

Counts

4 → 12

Calls

4 calls:

90.0ms	(+ 1.0 (* (sqrt 1.0) (sqrt (exp (* a x)))))
1.3s	(/ (- (* (exp (* a x)) (sqrt (exp (* a x)))) (* (sqrt 1.0) 1.0)) (+ (exp (* a x)) (+ 1.0 (* (sqrt 1.0) (sqrt (exp (* a x)))))))
73.0ms	(* (exp (* a x)) (sqrt (exp (* a x))))
136.0ms	(- (* (exp (* a x)) (sqrt (exp (* a x)))) (* (sqrt 1.0) 1.0))

simplify2.2s

Counts

107 → 107

Iterations

Iter	Nodes
done	5004
2	2698
1	639
0	231

prune713.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes322.0ms

Accuracy

98.8% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 22.0b

bsearch53.0ms

Steps

Iters	Range		Point
9	-0.0026744779238242673	-1.8483037069943186e-10	-0.0001933321263417943

simplify7.0ms

Iterations

Iter	Nodes
done	41
1	41
0	29

end0.0ms

sample2.1s

Algorithm

intervals

Results

758.0ms	2619×	body	1280	valid
671.0ms	5536×	body	80	valid
232.0ms	1346×	body	640	valid
119.0ms	749×	body	320	valid
74.0ms	381×	body	160	valid