Details

sample899.0ms

Algorithm

intervals

Results

548.0ms	69×	body	2560	valid
136.0ms	118×	body	1280	valid
109.0ms	66×	body	10240	exit
57.0ms	34×	body	640	valid
13.0ms	322×	pre	80	true
7.0ms	12×	body	320	valid
3.0ms	22×	body	80	valid
0.0ms	1×	body	160	valid

simplify1.4s

Counts

1 → 1

Iterations

Iter	Nodes
5	4110
4	689
3	215
2	98
1	43
0	17

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 56.7b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (* (+ a b) eps))
2.5b	(- (exp (* a eps)) 1)
4.0b	(- (exp (* b eps)) 1)
5.2b	(- (exp (* (+ a b) eps)) 1)

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`add-log-exp`
13×	`*-un-lft-identity`
6×	`difference-of-squares`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16`
3×	`sub-neg` `flip3--` `diff-log` `difference-of-sqr-1` `flip--` `distribute-lft-out--`
2×	`exp-to-pow`
1×	`exp-prod` `sum-log` `rem-exp-log`

Counts

4 → 63

Calls

4 calls:

15.0ms	(exp (* (+ a b) eps))
22.0ms	(- (exp (* a eps)) 1)
23.0ms	(- (exp (* b eps)) 1)
17.0ms	(- (exp (* (+ a b) eps)) 1)

series225.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(exp (* (+ a b) eps))
59.0ms	(- (exp (* a eps)) 1)
54.0ms	(- (exp (* b eps)) 1)
79.0ms	(- (exp (* (+ a b) eps)) 1)

simplify585.0ms

Counts

75 → 75

Iterations

Iter	Nodes
3	2084
2	663
1	258
0	123

prune1.0s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 41.9b

localize61.0ms

Local error

Found 4 expressions with local error:

2.5b	(- (exp (* a eps)) 1)
2.5b	(* (- (exp (* a eps)) 1) (+ (* b (+ (* 1/6 (* eps (* (* eps b) (* eps b)))) eps)) (* (* 1/2 (* eps b)) (* eps b))))
2.8b	(+ (* b (+ (* 1/6 (* eps (* (* eps b) (* eps b)))) eps)) (* (* 1/2 (* eps b)) (* eps b)))
5.2b	(- (exp (* (+ a b) eps)) 1)

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
10×	`add-log-exp`
7×	`associate-l`
6×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `difference-of-squares`
5×	`flip3--` `flip--`
4×	`frac-times` `flip3-+` `flip-+` `insert-posit16`
3×	`difference-of-sqr-1` `associate-r` `distribute-lft-out--`
2×	`distribute-rgt-in` `associate-+l+` `sub-neg` `distribute-lft-in` `diff-log` `associate-l/` `associate-r/`
1×	`+-commutative` `sum-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 81

Calls

4 calls:

23.0ms	(- (exp (* a eps)) 1)
1.1s	(* (- (exp (* a eps)) 1) (+ (* b (+ (* 1/6 (* eps (* (* eps b) (* eps b)))) eps)) (* (* 1/2 (* eps b)) (* eps b))))
295.0ms	(+ (* b (+ (* 1/6 (* eps (* (* eps b) (* eps b)))) eps)) (* (* 1/2 (* eps b)) (* eps b)))
24.0ms	(- (exp (* (+ a b) eps)) 1)

series586.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(- (exp (* a eps)) 1)
286.0ms	(* (- (exp (* a eps)) 1) (+ (* b (+ (* 1/6 (* eps (* (* eps b) (* eps b)))) eps)) (* (* 1/2 (* eps b)) (* eps b))))
160.0ms	(+ (* b (+ (* 1/6 (* eps (* (* eps b) (* eps b)))) eps)) (* (* 1/2 (* eps b)) (* eps b)))
85.0ms	(- (exp (* (+ a b) eps)) 1)

simplify962.0ms

Counts

93 → 93

Iterations

Iter	Nodes
2	2394
1	511
0	167

prune1.6s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 41.8b

localize153.0ms

Local error

Found 4 expressions with local error:

5.2b	(- (exp (* (+ a b) eps)) 1)
22.3b	(cbrt (+ (* b (+ (* 1/6 (* eps (* (* eps b) (* eps b)))) eps)) (* (* 1/2 (* eps b)) (* eps b))))
22.3b	(cbrt (+ (* b (+ (* 1/6 (* eps (* (* eps b) (* eps b)))) eps)) (* (* 1/2 (* eps b)) (* eps b))))
22.3b	(cbrt (+ (* b (+ (* 1/6 (* eps (* (* eps b) (* eps b)))) eps)) (* (* 1/2 (* eps b)) (* eps b))))

rewrite671.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
9×	`cbrt-prod`
7×	`add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16`
3×	`flip3-+` `pow1/3` `flip-+`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `difference-of-sqr-1` `flip--` `distribute-lft-out--`

Counts

4 → 59

Calls

4 calls:

18.0ms	(- (exp (* (+ a b) eps)) 1)
203.0ms	(cbrt (+ (* b (+ (* 1/6 (* eps (* (* eps b) (* eps b)))) eps)) (* (* 1/2 (* eps b)) (* eps b))))
224.0ms	(cbrt (+ (* b (+ (* 1/6 (* eps (* (* eps b) (* eps b)))) eps)) (* (* 1/2 (* eps b)) (* eps b))))
225.0ms	(cbrt (+ (* b (+ (* 1/6 (* eps (* (* eps b) (* eps b)))) eps)) (* (* 1/2 (* eps b)) (* eps b))))

series1.1s

Counts

4 → 12

Calls

4 calls:

58.0ms	(- (exp (* (+ a b) eps)) 1)
352.0ms	(cbrt (+ (* b (+ (* 1/6 (* eps (* (* eps b) (* eps b)))) eps)) (* (* 1/2 (* eps b)) (* eps b))))
337.0ms	(cbrt (+ (* b (+ (* 1/6 (* eps (* (* eps b) (* eps b)))) eps)) (* (* 1/2 (* eps b)) (* eps b))))
359.0ms	(cbrt (+ (* b (+ (* 1/6 (* eps (* (* eps b) (* eps b)))) eps)) (* (* 1/2 (* eps b)) (* eps b))))

simplify2.7s

Counts

71 → 71

Iterations

Iter	Nodes
3	5252
2	1003
1	322
0	128

prune1.7s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 41.8b

localize62.0ms

Local error

Found 4 expressions with local error:

2.6b	(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (+ (* (* 1/6 a) (* eps (* (* a eps) (* a eps)))) (+ (* (* 1/2 (* eps a)) (* eps a)) (* eps a))) (- (exp (* b eps)) 1)))
2.8b	(* (* 1/6 a) (* eps (* (* a eps) (* a eps))))
4.0b	(- (exp (* b eps)) 1)
5.2b	(- (exp (* (+ a b) eps)) 1)

rewrite654.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-cbrt-cube` `add-exp-log`
60×	`pow1`
48×	`prod-exp` `cbrt-unprod`
44×	`pow-prod-down`
12×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`associate-/r/` `add-log-exp`
6×	`flip3--` `flip--`
4×	`frac-times` `cbrt-undiv` `div-exp` `associate-*r/` `add-cube-cbrt` `insert-posit16` `difference-of-squares`
3×	`flip3-+` `flip-+`
2×	`sub-neg` `diff-log` `difference-of-sqr-1` `associate-*l/` `distribute-lft-out--` `associate-/l/`
1×	`clear-num` `associate-/r` `frac-2neg` `times-frac` `associate-r` `associate-l` `-commutative` `div-inv` `associate-/l*`

Counts

4 → 113

Calls

4 calls:

450.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (+ (* (* 1/6 a) (* eps (* (* a eps) (* a eps)))) (+ (* (* 1/2 (* eps a)) (* eps a)) (* eps a))) (- (exp (* b eps)) 1)))
175.0ms	(* (* 1/6 a) (* eps (* (* a eps) (* a eps))))
11.0ms	(- (exp (* b eps)) 1)
12.0ms	(- (exp (* (+ a b) eps)) 1)

series1.3s

Counts

4 → 12

Calls

4 calls:

1.1s	(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (+ (* (* 1/6 a) (* eps (* (* a eps) (* a eps)))) (+ (* (* 1/2 (* eps a)) (* eps a)) (* eps a))) (- (exp (* b eps)) 1)))
83.0ms	(* (* 1/6 a) (* eps (* (* a eps) (* a eps))))
41.0ms	(- (exp (* b eps)) 1)
73.0ms	(- (exp (* (+ a b) eps)) 1)

simplify2.4s

Counts

125 → 125

Iterations

Iter	Nodes
2	3880
1	825
0	268

prune2.4s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes192.0ms

Accuracy

-30.1% (4.3b remaining)

Error of 4.4b against oracle of 0.1b and baseline of 3.4b

bsearch280.0ms

Steps

Iters	Range		Point
0	2.532568332403625e+271	2.5403003595008445e+271	2.5364343459522345e+271
7	7.953854072811988e+238	1.2845334277761248e+241	9.568816560533687e+240

simplify9.0ms

Iterations

Iter	Nodes
2	61
1	61
0	43

end0.0ms

sample20.2s

Algorithm

intervals

Results

7.0s	2572×	body	2560	valid
5.3s	3482×	body	1280	valid
4.3s	1970×	body	10240	exit
1.0s	9972×	pre	80	true
972.0ms	1008×	body	640	valid
686.0ms	359×	body	320	valid
575.0ms	459×	body	80	valid
46.0ms	122×	body	160	valid