Details

sample295.0ms

Algorithm

intervals

Results

95.0ms	88×	body	2560	valid
90.0ms	60×	body	10240	exit
66.0ms	104×	body	1280	valid
14.0ms	40×	body	640	valid
6.0ms	316×	pre	80	true
2.0ms	10×	body	320	valid
1.0ms	11×	body	80	valid
0.0ms	3×	body	160	valid

simplify2.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	2307
4	629
3	237
2	95
1	40
0	17

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 61.1b

localize38.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.6b	(- (exp (* a eps)) 1.0)
4.4b	(- (exp (* b eps)) 1.0)
5.7b	(- (exp (* (+ a b) eps)) 1.0)

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
49×	`*-un-lft-identity`
45×	`prod-diff`
39×	`add-cube-cbrt`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`add-log-exp`
9×	`flip3--` `fma-neg` `flip--`
6×	`pow1` `add-cbrt-cube` `add-exp-log`
5×	`sub-neg` `associate-r` `associate-l` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u`
3×	`diff-log`
2×	`associate-l/` `associate-r/`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 138

Calls

4 calls:

71.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
11.0ms	(- (exp (* a eps)) 1.0)
15.0ms	(- (exp (* b eps)) 1.0)
12.0ms	(- (exp (* (+ a b) eps)) 1.0)

series222.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
48.0ms	(- (exp (* a eps)) 1.0)
52.0ms	(- (exp (* b eps)) 1.0)
67.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify1.5s

Counts

150 → 150

Iterations

Iter	Nodes
done	5004
2	1681
1	539
0	221

prune1.0s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 50.0b

localize71.0ms

Local error

Found 4 expressions with local error:

4.8b	(* eps (* (* a a) a))
5.7b	(- (exp (* (+ a b) eps)) 1.0)
6.8b	(* (* eps eps) (* eps (* (* a a) a)))
11.9b	(* (* eps eps) (* (* a a) 1/2))

rewrite302.0ms

Algorithm

rewrite-expression-head

Rules

66×	`pow1` `add-cbrt-cube` `add-exp-log`
45×	`pow-prod-down` `prod-exp` `cbrt-unprod`
14×	`add-sqr-sqrt` `*-un-lft-identity`
12×	`add-cube-cbrt`
9×	`prod-diff`
6×	`add-log-exp`
5×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `associate-r` `*-commutative`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 117

Calls

4 calls:

65.0ms	(* eps (* (* a a) a))
20.0ms	(- (exp (* (+ a b) eps)) 1.0)
150.0ms	(* (* eps eps) (* eps (* (* a a) a)))
58.0ms	(* (* eps eps) (* (* a a) 1/2))

series209.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* eps (* (* a a) a))
52.0ms	(- (exp (* (+ a b) eps)) 1.0)
65.0ms	(* (* eps eps) (* eps (* (* a a) a)))
39.0ms	(* (* eps eps) (* (* a a) 1/2))

simplify1.3s

Counts

129 → 129

Iterations

Iter	Nodes
done	5011
2	1732
1	489
0	176

prune612.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 49.5b

localize92.0ms

Local error

Found 4 expressions with local error:

4.4b	(- (exp (* b eps)) 1.0)
5.7b	(- (exp (* (+ a b) eps)) 1.0)
6.8b	(* (* eps eps) (* (* eps a) (* a a)))
11.9b	(* (* eps eps) (* (* a a) 1/2))

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

66×	`pow1` `add-cbrt-cube` `add-exp-log`
46×	`pow-prod-down` `prod-exp` `cbrt-unprod`
22×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`prod-diff` `add-cube-cbrt`
8×	`add-log-exp`
6×	`fma-neg`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`sub-neg` `flip3--` `diff-log` `associate-r` `associate-l` `*-commutative` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 128

Calls

4 calls:

11.0ms	(- (exp (* b eps)) 1.0)
18.0ms	(- (exp (* (+ a b) eps)) 1.0)
73.0ms	(* (* eps eps) (* (* eps a) (* a a)))
54.0ms	(* (* eps eps) (* (* a a) 1/2))

series271.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(- (exp (* b eps)) 1.0)
83.0ms	(- (exp (* (+ a b) eps)) 1.0)
86.0ms	(* (* eps eps) (* (* eps a) (* a a)))
49.0ms	(* (* eps eps) (* (* a a) 1/2))

simplify1.9s

Counts

140 → 140

Iterations

Iter	Nodes
done	5004
2	2343
1	623
0	222

prune961.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 49.4b

localize134.0ms

Local error

Found 4 expressions with local error:

3.2b	(* (- (exp (* a eps)) 1.0) (fma eps b (fma (* (* (* eps eps) eps) 1/6) (* b (* b b)) (* (* b b) (* 1/2 (* eps eps))))))
5.7b	(- (exp (* (+ a b) eps)) 1.0)
13.2b	(* (* b b) (* 1/2 (* eps eps)))
15.0b	(fma (* (* (* eps eps) eps) 1/6) (* b (* b b)) (* (* b b) (* 1/2 (* eps eps))))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

27×	`pow1` `add-cbrt-cube` `add-exp-log`
19×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
16×	`pow-prod-down` `prod-exp` `cbrt-unprod`
13×	`add-cube-cbrt`
9×	`prod-diff`
6×	`associate-l` `add-log-exp`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u`
3×	`fma-neg` `fma-udef`
2×	`flip3--` `associate-l/` `-commutative` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `diff-log` `unswap-sqr`

Counts

4 → 94

Calls

4 calls:

43.0ms	(* (- (exp (* a eps)) 1.0) (fma eps b (fma (* (* (* eps eps) eps) 1/6) (* b (* b b)) (* (* b b) (* 1/2 (* eps eps))))))
12.0ms	(- (exp (* (+ a b) eps)) 1.0)
89.0ms	(* (* b b) (* 1/2 (* eps eps)))
1.0ms	(fma (* (* (* eps eps) eps) 1/6) (* b (* b b)) (* (* b b) (* 1/2 (* eps eps))))

series623.0ms

Counts

4 → 12

Calls

4 calls:

315.0ms	(* (- (exp (* a eps)) 1.0) (fma eps b (fma (* (* (* eps eps) eps) 1/6) (* b (* b b)) (* (* b b) (* 1/2 (* eps eps))))))
76.0ms	(- (exp (* (+ a b) eps)) 1.0)
38.0ms	(* (* b b) (* 1/2 (* eps eps)))
194.0ms	(fma (* (* (* eps eps) eps) 1/6) (* b (* b b)) (* (* b b) (* 1/2 (* eps eps))))

simplify1.9s

Counts

106 → 106

Iterations

Iter	Nodes
done	5001
2	1614
1	521
0	208

prune770.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 48.8b

regimes517.0ms

Accuracy

31.5% (6.6b remaining)

Error of 54.5b against oracle of 47.9b and baseline of 57.5b

bsearch514.0ms

Steps

Iters	Range		Point
4	1.0787056953316223e+113	1.9646879743348034e+113	1.2680456493388715e+113
9	-1.8488733081414263e+176	-8.088804064434993e+170	-8.172706586072208e+170

simplify13.0ms

Iterations

Iter	Nodes
done	69
1	69
0	52

end0.0ms

sample15.7s

Algorithm

intervals

Results

5.3s	2615×	body	2560	valid
4.0s	1952×	body	10240	exit
3.8s	3375×	body	1280	valid
1.2s	1047×	body	640	valid
689.0ms	9954×	pre	80	true
209.0ms	355×	body	320	valid
106.0ms	489×	body	80	valid
27.0ms	121×	body	160	valid