Details

Time bar (total: 28.0s)

sample78.0ms

Algorithm
intervals
Results
63.0ms325×body80valid

simplify1.6s

Counts
1 → 1
Iterations
IterNodes
done5001
41448
3357
295
132
015

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (+ (/ (/ PI 2) a) (/ (- (/ PI 2)) b)) (- b a)) (+ a b))
0.2b
(/ (- (/ PI 2)) b)
0.2b
(/ (+ (/ (/ PI 2) a) (/ (- (/ PI 2)) b)) (- b a))
0.3b
(/ (/ PI 2) a)

rewrite373.0ms

Algorithm
rewrite-expression-head
Rules
2587×times-frac
2217×*-un-lft-identity
1031×add-sqr-sqrt
813×add-cube-cbrt
562×distribute-lft-out
455×distribute-rgt-neg-in
157×associate-/l*
109×distribute-lft-out-- difference-of-squares
83×div-inv
52×distribute-lft-neg-in
18×add-cbrt-cube add-exp-log
15×associate-/r*
14×associate-/r/
12×div-sub
8×cbrt-undiv div-exp
6×flip3-- flip-- associate-/l/
5×distribute-frac-neg
4×pow1 clear-num neg-mul-1 frac-2neg insert-posit16 add-log-exp
3×neg-sub0
2×associate-+r- flip3-+ unsub-neg flip-+
1×frac-add distribute-neg-frac
Counts
4 → 849
Calls
4 calls:
155.0ms
(/ (/ (+ (/ (/ PI 2) a) (/ (- (/ PI 2)) b)) (- b a)) (+ a b))
17.0ms
(/ (- (/ PI 2)) b)
132.0ms
(/ (+ (/ (/ PI 2) a) (/ (- (/ PI 2)) b)) (- b a))
9.0ms
(/ (/ PI 2) a)

series361.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(/ (/ (+ (/ (/ PI 2) a) (/ (- (/ PI 2)) b)) (- b a)) (+ a b))
45.0ms
(/ (- (/ PI 2)) b)
109.0ms
(/ (+ (/ (/ PI 2) a) (/ (- (/ PI 2)) b)) (- b a))
87.0ms
(/ (/ PI 2) a)

simplify1.9s

Counts
861 → 861
Iterations
IterNodes
done5001
12343
01062

prune3.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (+ (/ (/ PI 2) a) (* PI (/ -1/2 b))) (- b a)) (+ a b))
0.2b
(/ (+ (/ (/ PI 2) a) (* PI (/ -1/2 b))) (- b a))
0.3b
(/ (/ PI 2) a)
0.4b
(* PI (/ -1/2 b))

rewrite157.0ms

Algorithm
rewrite-expression-head
Rules
259×times-frac
213×*-un-lft-identity
174×add-sqr-sqrt
131×add-cube-cbrt
37×associate-/l*
22×distribute-lft-out
21×add-cbrt-cube add-exp-log
19×distribute-lft-out-- difference-of-squares
14×associate-/r/
13×associate-*r* div-inv
12×associate-/r*
8×cbrt-undiv div-exp
6×pow1 flip3-- flip--
5×associate-/l/
4×insert-posit16 add-log-exp
3×clear-num frac-2neg associate-*l*
2×flip3-+ prod-exp associate-*r/ cbrt-unprod flip-+ unswap-sqr
1×pow-prod-down frac-add *-commutative
Counts
4 → 272
Calls
4 calls:
74.0ms
(/ (/ (+ (/ (/ PI 2) a) (* PI (/ -1/2 b))) (- b a)) (+ a b))
52.0ms
(/ (+ (/ (/ PI 2) a) (* PI (/ -1/2 b))) (- b a))
9.0ms
(/ (/ PI 2) a)
18.0ms
(* PI (/ -1/2 b))

series390.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(/ (/ (+ (/ (/ PI 2) a) (* PI (/ -1/2 b))) (- b a)) (+ a b))
131.0ms
(/ (+ (/ (/ PI 2) a) (* PI (/ -1/2 b))) (- b a))
60.0ms
(/ (/ PI 2) a)
63.0ms
(* PI (/ -1/2 b))

simplify1.9s

Counts
284 → 284
Iterations
IterNodes
done5012
23663
11058
0441

prune1.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize30.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (+ (/ 1/2 a) (/ -1/2 b)) (- b a)) (+ b a))
0.2b
(* PI (/ (/ (+ (/ 1/2 a) (/ -1/2 b)) (- b a)) (+ b a)))
0.2b
(/ (+ (/ 1/2 a) (/ -1/2 b)) (- b a))

rewrite258.0ms

Algorithm
rewrite-expression-head
Rules
713×*-un-lft-identity
603×times-frac
290×add-sqr-sqrt
179×add-cube-cbrt
165×distribute-lft-out
130×associate-*r*
51×distribute-lft-out-- difference-of-squares
36×associate-/l*
24×associate-/r/
19×add-cbrt-cube add-exp-log
12×div-inv
10×flip3-- flip--
9×associate-/r*
7×cbrt-undiv div-exp
5×pow1
4×associate-/l/
3×flip3-+ associate-*l* prod-exp cbrt-unprod flip-+ insert-posit16 add-log-exp unswap-sqr
2×clear-num frac-2neg
1×pow-prod-down frac-add associate-*r/ *-commutative
Counts
3 → 383
Calls
3 calls:
69.0ms
(/ (/ (+ (/ 1/2 a) (/ -1/2 b)) (- b a)) (+ b a))
115.0ms
(* PI (/ (/ (+ (/ 1/2 a) (/ -1/2 b)) (- b a)) (+ b a)))
52.0ms
(/ (+ (/ 1/2 a) (/ -1/2 b)) (- b a))

series329.0ms

Counts
3 → 9
Calls
3 calls:
131.0ms
(/ (/ (+ (/ 1/2 a) (/ -1/2 b)) (- b a)) (+ b a))
127.0ms
(* PI (/ (/ (+ (/ 1/2 a) (/ -1/2 b)) (- b a)) (+ b a)))
70.0ms
(/ (+ (/ 1/2 a) (/ -1/2 b)) (- b a))

simplify2.2s

Counts
392 → 392
Iterations
IterNodes
done5001
23165
1923
0349

prune1.4s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize63.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ PI (sqrt 2)) a)
0.2b
(/ (+ (/ (/ PI (sqrt 2)) a) (/ (- (/ PI (sqrt 2))) b)) (- b a))
0.3b
(* (/ 1 (sqrt 2)) (/ (/ (+ (/ (/ PI (sqrt 2)) a) (/ (- (/ PI (sqrt 2))) b)) (- b a)) (+ a b)))
1.0b
(/ 1 (sqrt 2))

rewrite570.0ms

Algorithm
rewrite-expression-head
Rules
4466×times-frac
3547×*-un-lft-identity
1950×add-sqr-sqrt
1255×add-cube-cbrt
951×distribute-lft-out
728×distribute-rgt-neg-in
690×associate-*r*
687×sqrt-prod
166×distribute-lft-out-- difference-of-squares
65×div-inv
58×associate-/l*
54×add-exp-log
34×add-cbrt-cube
24×div-exp
22×associate-*l*
15×unswap-sqr
14×cbrt-undiv associate-/r*
12×prod-exp associate-/r/
8×pow1
6×cbrt-unprod
5×flip3-- flip--
4×rec-exp 1-exp div-sub insert-posit16 add-log-exp associate-/l/
3×clear-num frac-2neg pow-flip
2×flip3-+ distribute-frac-neg flip-+
1×neg-sub0 frac-times associate-+r- sqrt-pow1 pow1/2 unsub-neg pow-prod-down associate-*l/ frac-add associate-*r/ *-commutative inv-pow
Counts
4 → 1135
Calls
4 calls:
16.0ms
(/ (/ PI (sqrt 2)) a)
198.0ms
(/ (+ (/ (/ PI (sqrt 2)) a) (/ (- (/ PI (sqrt 2))) b)) (- b a))
224.0ms
(* (/ 1 (sqrt 2)) (/ (/ (+ (/ (/ PI (sqrt 2)) a) (/ (- (/ PI (sqrt 2))) b)) (- b a)) (+ a b)))
5.0ms
(/ 1 (sqrt 2))

series673.0ms

Counts
4 → 10
Calls
4 calls:
88.0ms
(/ (/ PI (sqrt 2)) a)
199.0ms
(/ (+ (/ (/ PI (sqrt 2)) a) (/ (- (/ PI (sqrt 2))) b)) (- b a))
386.0ms
(* (/ 1 (sqrt 2)) (/ (/ (+ (/ (/ PI (sqrt 2)) a) (/ (- (/ PI (sqrt 2))) b)) (- b a)) (+ a b)))
0.0ms
(/ 1 (sqrt 2))

simplify3.8s

Counts
1145 → 1145
Iterations
IterNodes
done5001
13689
01155

prune4.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes101.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done16
116
013

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.9s9595×body80valid