Details

sample241.0ms

Algorithm

intervals

Results

77.0ms	308×	body	80	valid
57.0ms	73×	body	10240	exit
41.0ms	55×	body	1280	valid
28.0ms	46×	body	640	valid
7.0ms	22×	body	320	valid
2.0ms	14×	body	160	valid

simplify1.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	2266
3	377
2	122
1	46
0	19

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.9b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- eps 1.0) x)
0.0b	(exp (* x (+ eps 1.0)))
0.0b	(exp (* (- eps 1.0) x))
2.7b	(+ (/ (- 1.0 (/ 1.0 eps)) (exp (* x (+ eps 1.0)))) (* (exp (* (- eps 1.0) x)) (+ 1.0 (/ 1.0 eps))))

rewrite179.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-log-exp`
10×	`add-sqr-sqrt`
8×	`*-un-lft-identity`
6×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
5×	`associate-l`
3×	`exp-to-pow` `associate-r`
2×	`distribute-rgt-in` `associate-+r+` `exp-prod` `distribute-lft-in` `flip3-+` `exp-sum` `associate-l/` `frac-add` `associate-r/` `flip-+` `rem-exp-log`
1×	`+-commutative` `sum-log` `flip3--` `diff-log` `div-sub` `pow-prod-down` `prod-exp` `*-commutative` `associate-+l-` `cbrt-unprod` `flip--` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 61

Calls

4 calls:

36.0ms	(* (- eps 1.0) x)
8.0ms	(exp (* x (+ eps 1.0)))
13.0ms	(exp (* (- eps 1.0) x))
118.0ms	(+ (/ (- 1.0 (/ 1.0 eps)) (exp (* x (+ eps 1.0)))) (* (exp (* (- eps 1.0) x)) (+ 1.0 (/ 1.0 eps))))

series381.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (- eps 1.0) x)
13.0ms	(exp (* x (+ eps 1.0)))
27.0ms	(exp (* (- eps 1.0) x))
298.0ms	(+ (/ (- 1.0 (/ 1.0 eps)) (exp (* x (+ eps 1.0)))) (* (exp (* (- eps 1.0) x)) (+ 1.0 (/ 1.0 eps))))

simplify1.8s

Counts

73 → 73

Iterations

Iter	Nodes
done	5001
2	1947
1	425
0	159

prune467.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 4.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (* x x))
0.2b	(* (* x (* x x)) 2.7755575615628914e-17)
3.8b	(- (- 2.0 (* x (* x 1.0))) (/ (* (* x (* x x)) 2.7755575615628914e-17) eps))
5.1b	(/ (* (* x (* x x)) 2.7755575615628914e-17) eps)

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-cbrt-cube` `add-exp-log`
27×	`pow1`
15×	`prod-exp` `cbrt-unprod`
11×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
9×	`pow-prod-down` `add-log-exp`
8×	`add-cube-cbrt`
5×	`pow-prod-up`
4×	`cbrt-undiv` `div-exp` `associate-r` `associate-l`
3×	`associate-/r*` `times-frac` `diff-log`
2×	`sub-neg` `flip3--` `associate--l+` `*-commutative` `frac-sub` `flip--`
1×	`associate--l-` `pow2` `clear-num` `frac-2neg` `pow-plus` `cube-unmult` `pow-sqr` `div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

14.0ms	(* x (* x x))
46.0ms	(* (* x (* x x)) 2.7755575615628914e-17)
24.0ms	(- (- 2.0 (* x (* x 1.0))) (/ (* (* x (* x x)) 2.7755575615628914e-17) eps))
58.0ms	(/ (* (* x (* x x)) 2.7755575615628914e-17) eps)

series239.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* x (* x x))
56.0ms	(* (* x (* x x)) 2.7755575615628914e-17)
78.0ms	(- (- 2.0 (* x (* x 1.0))) (/ (* (* x (* x x)) 2.7755575615628914e-17) eps))
43.0ms	(/ (* (* x (* x x)) 2.7755575615628914e-17) eps)

simplify2.3s

Counts

102 → 102

Iterations

Iter	Nodes
done	5002
2	3330
1	447
0	157

prune354.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (* x x))
0.2b	(* (* x (* x x)) 2.7755575615628914e-17)
0.2b	(log (exp (* (* x (* x x)) 2.7755575615628914e-17)))
3.8b	(- (- 2.0 (* x (* x 1.0))) (/ (log (exp (* (* x (* x x)) 2.7755575615628914e-17))) eps))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

28×	`pow1`
18×	`add-cbrt-cube` `add-exp-log`
13×	`add-sqr-sqrt`
10×	`add-log-exp`
9×	`*-un-lft-identity` `pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`add-cube-cbrt`
5×	`pow-prod-up`
4×	`associate-r` `associate-l`
3×	`log-prod` `diff-log` `log-pow`
2×	`sub-neg` `flip3--` `associate--l+` `*-commutative` `frac-sub` `flip--` `difference-of-squares`
1×	`associate--l-` `pow2` `exp-prod` `times-frac` `pow-plus` `exp-to-pow` `cube-unmult` `rem-log-exp` `pow-sqr` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

13.0ms	(* x (* x x))
42.0ms	(* (* x (* x x)) 2.7755575615628914e-17)
7.0ms	(log (exp (* (* x (* x x)) 2.7755575615628914e-17)))
29.0ms	(- (- 2.0 (* x (* x 1.0))) (/ (log (exp (* (* x (* x x)) 2.7755575615628914e-17))) eps))

series264.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* x (* x x))
54.0ms	(* (* x (* x x)) 2.7755575615628914e-17)
70.0ms	(log (exp (* (* x (* x x)) 2.7755575615628914e-17)))
83.0ms	(- (- 2.0 (* x (* x 1.0))) (/ (log (exp (* (* x (* x x)) 2.7755575615628914e-17))) eps))

simplify1.8s

Counts

92 → 92

Iterations

Iter	Nodes
done	5000
2	2229
1	373
0	145

prune494.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b	(log (exp (* (* x (* x x)) 2.7755575615628914e-17)))
0.7b	(* (sqrt (- (- 2.0 (* x (* x 1.0))) (/ (log (exp (* (* x (* x x)) 2.7755575615628914e-17))) eps))) (sqrt (- (- 2.0 (* x (* x 1.0))) (/ (log (exp (* (* x (* x x)) 2.7755575615628914e-17))) eps))))
3.8b	(- (- 2.0 (* x (* x 1.0))) (/ (log (exp (* (* x (* x x)) 2.7755575615628914e-17))) eps))
3.8b	(- (- 2.0 (* x (* x 1.0))) (/ (log (exp (* (* x (* x x)) 2.7755575615628914e-17))) eps))

rewrite305.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
40×	`sqrt-div`
34×	`sqrt-prod`
31×	`*-un-lft-identity`
24×	`flip3--` `frac-sub` `flip--`
20×	`pow1`
16×	`frac-times`
15×	`add-log-exp`
13×	`swap-sqr` `add-cube-cbrt`
12×	`difference-of-squares`
9×	`associate-r` `associate-l`
8×	`sqrt-pow1` `pow1/2` `distribute-lft-out--`
6×	`times-frac` `add-cbrt-cube` `diff-log` `add-exp-log`
5×	`pow-prod-up`
4×	`sub-neg` `associate-l/` `associate--l+` `associate-r/` `unswap-sqr`
3×	`log-prod` `pow-prod-down` `pow-sqr` `log-pow`
2×	`associate--l-`
1×	`pow2` `exp-prod` `rem-square-sqrt` `pow-plus` `exp-to-pow` `sqrt-unprod` `rem-log-exp` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 140

Calls

4 calls:

6.0ms	(log (exp (* (* x (* x x)) 2.7755575615628914e-17)))
191.0ms	(* (sqrt (- (- 2.0 (* x (* x 1.0))) (/ (log (exp (* (* x (* x x)) 2.7755575615628914e-17))) eps))) (sqrt (- (- 2.0 (* x (* x 1.0))) (/ (log (exp (* (* x (* x x)) 2.7755575615628914e-17))) eps))))
54.0ms	(- (- 2.0 (* x (* x 1.0))) (/ (log (exp (* (* x (* x x)) 2.7755575615628914e-17))) eps))
42.0ms	(- (- 2.0 (* x (* x 1.0))) (/ (log (exp (* (* x (* x x)) 2.7755575615628914e-17))) eps))

series304.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(log (exp (* (* x (* x x)) 2.7755575615628914e-17)))
91.0ms	(* (sqrt (- (- 2.0 (* x (* x 1.0))) (/ (log (exp (* (* x (* x x)) 2.7755575615628914e-17))) eps))) (sqrt (- (- 2.0 (* x (* x 1.0))) (/ (log (exp (* (* x (* x x)) 2.7755575615628914e-17))) eps))))
79.0ms	(- (- 2.0 (* x (* x 1.0))) (/ (log (exp (* (* x (* x x)) 2.7755575615628914e-17))) eps))
93.0ms	(- (- 2.0 (* x (* x 1.0))) (/ (log (exp (* (* x (* x x)) 2.7755575615628914e-17))) eps))

simplify1.8s

Counts

152 → 152

Iterations

Iter	Nodes
done	5000
2	1619
1	389
0	198

prune954.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

regimes139.0ms

Accuracy

93.9% (1.0b remaining)

Error of 1.4b against oracle of 0.4b and baseline of 17.0b

bsearch244.0ms

Steps

Iters	Range		Point
8	7.492487599876036e-13	1.167960668237619e-09	1.1486676066584133e-09

simplify7.0ms

Iterations

Iter	Nodes
done	42
1	42
0	33

end0.0ms

sample8.7s

Algorithm

intervals

Results

2.9s	1902×	body	10240	exit
1.9s	1789×	body	1280	valid
1.9s	10094×	body	80	valid
1.2s	1236×	body	640	valid
265.0ms	664×	body	320	valid
66.0ms	307×	body	160	valid