Details

sample352.0ms

Algorithm

intervals

Results

109.0ms	88×	body	2560	valid
78.0ms	104×	body	1280	valid
75.0ms	60×	body	10240	exit
43.0ms	316×	pre	80	true
17.0ms	40×	body	640	valid
3.0ms	10×	body	320	valid
1.0ms	11×	body	80	valid
1.0ms	3×	body	160	valid

simplify2.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	2045
4	572
3	224
2	95
1	40
0	17

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 61.1b

localize40.0ms

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)

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

79.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
12.0ms	(- (exp (* a eps)) 1.0)
12.0ms	(- (exp (* b eps)) 1.0)
12.0ms	(- (exp (* (+ a b) eps)) 1.0)

series226.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
43.0ms	(- (exp (* a eps)) 1.0)
44.0ms	(- (exp (* b eps)) 1.0)
67.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify1.2s

Counts

88 → 88

Iterations

Iter	Nodes
done	5009
2	1335
1	359
0	143

prune591.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 49.8b

localize61.0ms

Local error

Found 4 expressions with local error:

4.8b	(* (* 1/6 (* a (* a a))) eps)
5.7b	(- (exp (* (+ a b) eps)) 1.0)
7.3b	(+ (* (* a a) 1/2) (* (* 1/6 (* a (* a a))) eps))
10.6b	(* (* eps eps) (+ (* (* a a) 1/2) (* (* 1/6 (* a (* a a))) eps)))

rewrite202.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1` `add-cbrt-cube` `add-exp-log`
13×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-log-exp`
6×	`associate-r` `add-cube-cbrt`
2×	`flip3-+` `associate-l` `associate-r/` `-commutative` `flip-+`
1×	`distribute-rgt-in` `+-commutative` `sum-log` `sub-neg` `distribute-lft-in` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 72

Calls

4 calls:

120.0ms	(* (* 1/6 (* a (* a a))) eps)
10.0ms	(- (exp (* (+ a b) eps)) 1.0)
14.0ms	(+ (* (* a a) 1/2) (* (* 1/6 (* a (* a a))) eps))
55.0ms	(* (* eps eps) (+ (* (* a a) 1/2) (* (* 1/6 (* a (* a a))) eps)))

series363.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (* 1/6 (* a (* a a))) eps)
54.0ms	(- (exp (* (+ a b) eps)) 1.0)
79.0ms	(+ (* (* a a) 1/2) (* (* 1/6 (* a (* a a))) eps))
187.0ms	(* (* eps eps) (+ (* (* a a) 1/2) (* (* 1/6 (* a (* a a))) eps)))

simplify2.3s

Counts

84 → 84

Iterations

Iter	Nodes
done	5001
2	1976
1	486
0	158

prune594.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 49.7b

localize75.0ms

Local error

Found 4 expressions with local error:

4.8b	(* (* 1/6 (* a (* a a))) eps)
4.8b	(* eps (+ (* (* a a) 1/2) (* (* 1/6 (* a (* a a))) eps)))
5.7b	(- (exp (* (+ a b) eps)) 1.0)
7.3b	(+ (* (* a a) 1/2) (* (* 1/6 (* a (* a a))) eps))

rewrite282.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

191.0ms	(* (* 1/6 (* a (* a a))) eps)
60.0ms	(* eps (+ (* (* a a) 1/2) (* (* 1/6 (* a (* a a))) eps)))
10.0ms	(- (exp (* (+ a b) eps)) 1.0)
20.0ms	(+ (* (* a a) 1/2) (* (* 1/6 (* a (* a a))) eps))

series393.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (* 1/6 (* a (* a a))) eps)
185.0ms	(* eps (+ (* (* a a) 1/2) (* (* 1/6 (* a (* a a))) eps)))
85.0ms	(- (exp (* (+ a b) eps)) 1.0)
84.0ms	(+ (* (* a a) 1/2) (* (* 1/6 (* a (* a a))) eps))

simplify1.6s

Counts

83 → 83

Iterations

Iter	Nodes
done	5001
2	1617
1	440
0	153

prune652.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 49.3b

localize81.0ms

Local error

Found 4 expressions with local error:

4.4b	(- (exp (* b eps)) 1.0)
4.8b	(* eps (+ (* (* a a) 1/2) (* (* (* a eps) (* a a)) 1/6)))
5.7b	(- (exp (* (+ a b) eps)) 1.0)
7.3b	(+ (* (* a a) 1/2) (* (* (* a eps) (* a a)) 1/6))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

18.0ms	(- (exp (* b eps)) 1.0)
75.0ms	(* eps (+ (* (* a a) 1/2) (* (* (* a eps) (* a a)) 1/6)))
12.0ms	(- (exp (* (+ a b) eps)) 1.0)
15.0ms	(+ (* (* a a) 1/2) (* (* (* a eps) (* a a)) 1/6))

series347.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(- (exp (* b eps)) 1.0)
143.0ms	(* eps (+ (* (* a a) 1/2) (* (* (* a eps) (* a a)) 1/6)))
66.0ms	(- (exp (* (+ a b) eps)) 1.0)
97.0ms	(+ (* (* a a) 1/2) (* (* (* a eps) (* a a)) 1/6))

simplify1.8s

Counts

73 → 73

Iterations

Iter	Nodes
done	5004
2	1456
1	400
0	142

prune620.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 49.1b

regimes364.0ms

Accuracy

50.4% (4.4b remaining)

Error of 52.9b against oracle of 48.5b and baseline of 57.4b

bsearch786.0ms

Steps

Iters	Range		Point
10	1.9512761569531488e+87	2.1498767242488486e+105	4.1933485224945856e+103
9	-82841354042492.34	-55576812.421804816	-2140545190609.44

simplify13.0ms

Iterations

Iter	Nodes
done	68
1	68
0	46

end0.0ms

sample14.4s

Algorithm

intervals

Results

4.7s	2615×	body	2560	valid
4.1s	3375×	body	1280	valid
3.5s	1952×	body	10240	exit
661.0ms	9954×	pre	80	true
652.0ms	1047×	body	640	valid
169.0ms	355×	body	320	valid
47.0ms	489×	body	80	valid
26.0ms	121×	body	160	valid