Details

Time bar (total: 46.7s)

sample65.0ms

Algorithm
intervals
Results
50.0ms306×body80valid

simplify2.5s

Counts
1 → 1
Iterations
IterNodes
54980
41403
3361
293
131
015

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
45×times-frac
26×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
23×add-cbrt-cube add-exp-log
15×associate-/l*
12×associate-*l/ associate-/r/
9×cbrt-undiv div-exp
7×div-inv
6×flip3-+ flip-+
5×associate-/r*
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg prod-exp cbrt-unprod
1×fma-udef associate-/l/
Counts
4 → 122
Calls
4 calls:
30.0ms
(/ (/ PI (* (+ a b) 2)) a)
17.0ms
(/ PI (* (+ a b) 2))
24.0ms
(/ PI (* (+ a b) 2))
1.0ms
(fma (/ PI (* (+ a b) 2)) (/ -1 b) (/ (/ PI (* (+ a b) 2)) a))

series406.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(/ (/ PI (* (+ a b) 2)) a)
79.0ms
(/ PI (* (+ a b) 2))
77.0ms
(/ PI (* (+ a b) 2))
165.0ms
(fma (/ PI (* (+ a b) 2)) (/ -1 b) (/ (/ PI (* (+ a b) 2)) a))

simplify3.0s

Counts
134 → 134
Iterations
IterNodes
36028
21262
1415
0176

prune1.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (fma (/ PI (* (+ a b) 2)) (/ -1 b) (/ PI (* a (* (+ a b) 2)))) (- b a))
0.3b
(/ PI (* (+ a b) 2))
0.4b
(fma (/ PI (* (+ a b) 2)) (/ -1 b) (/ PI (* a (* (+ a b) 2))))
1.7b
(/ PI (* a (* (+ a b) 2)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt *-un-lft-identity
21×times-frac
20×add-cbrt-cube add-exp-log
18×add-cube-cbrt
9×associate-/l*
7×associate-/r*
6×cbrt-undiv div-exp associate-/r/
4×expm1-log1p-u pow1 associate-*l/ prod-exp cbrt-unprod insert-posit16 log1p-expm1-u distribute-lft-out-- add-log-exp difference-of-squares
3×clear-num frac-2neg div-inv
2×flip3-+ associate-*r/ flip-+
1×flip3-- fma-udef flip--
Counts
4 → 105
Calls
4 calls:
13.0ms
(/ (fma (/ PI (* (+ a b) 2)) (/ -1 b) (/ PI (* a (* (+ a b) 2)))) (- b a))
9.0ms
(/ PI (* (+ a b) 2))
0.0ms
(fma (/ PI (* (+ a b) 2)) (/ -1 b) (/ PI (* a (* (+ a b) 2))))
19.0ms
(/ PI (* a (* (+ a b) 2)))

series444.0ms

Counts
4 → 12
Calls
4 calls:
138.0ms
(/ (fma (/ PI (* (+ a b) 2)) (/ -1 b) (/ PI (* a (* (+ a b) 2)))) (- b a))
69.0ms
(/ PI (* (+ a b) 2))
149.0ms
(fma (/ PI (* (+ a b) 2)) (/ -1 b) (/ PI (* a (* (+ a b) 2))))
87.0ms
(/ PI (* a (* (+ a b) 2)))

simplify3.2s

Counts
117 → 117
Iterations
IterNodes
37021
21389
1417
0185

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (/ (* (/ PI (+ a b)) -1/2) b) (/ PI (* (* a 2) (+ a b)))) (- b a))
0.2b
(/ (* (/ PI (+ a b)) -1/2) b)
0.3b
(/ PI (+ a b))
1.7b
(/ PI (* (* a 2) (+ a b)))

rewrite173.0ms

Algorithm
rewrite-expression-head
Rules
58×*-un-lft-identity
38×add-sqr-sqrt times-frac
28×add-cube-cbrt
26×add-cbrt-cube add-exp-log
13×associate-/r*
11×associate-/l*
10×distribute-lft-out
9×cbrt-undiv div-exp
6×associate-/r/
5×prod-exp cbrt-unprod distribute-lft-out-- difference-of-squares
4×expm1-log1p-u pow1 clear-num frac-2neg insert-posit16 log1p-expm1-u div-inv add-log-exp associate-/l/
3×flip3-+ flip-+
2×associate-*r/
1×flip3-- associate-*l/ frac-add flip--
Counts
4 → 140
Calls
4 calls:
119.0ms
(/ (+ (/ (* (/ PI (+ a b)) -1/2) b) (/ PI (* (* a 2) (+ a b)))) (- b a))
28.0ms
(/ (* (/ PI (+ a b)) -1/2) b)
8.0ms
(/ PI (+ a b))
16.0ms
(/ PI (* (* a 2) (+ a b)))

series402.0ms

Counts
4 → 12
Calls
4 calls:
150.0ms
(/ (+ (/ (* (/ PI (+ a b)) -1/2) b) (/ PI (* (* a 2) (+ a b)))) (- b a))
105.0ms
(/ (* (/ PI (+ a b)) -1/2) b)
44.0ms
(/ PI (+ a b))
102.0ms
(/ PI (* (* a 2) (+ a b)))

simplify693.0ms

Counts
152 → 152
Iterations
IterNodes
22272
1606
0235

prune1.7s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

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

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
2664×times-frac
1343×*-un-lft-identity
1073×add-sqr-sqrt add-cube-cbrt
135×distribute-lft-out
128×div-inv
113×associate-/r/
58×associate-/r*
53×add-exp-log
46×flip3-+ flip-+
35×add-cbrt-cube div-exp
24×associate-/l*
20×cbrt-undiv
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
3×rec-exp clear-num frac-2neg 1-exp
2×associate-*l/
1×prod-exp cbrt-unprod fma-udef associate-/l/
Counts
4 → 997
Calls
4 calls:
17.0ms
(/ (/ 1 (+ a b)) (/ a (/ PI 2)))
6.0ms
(/ a (/ PI 2))
18.0ms
(/ PI (* (+ a b) 2))
1.0ms
(fma (/ PI (* (+ a b) 2)) (/ -1 b) (/ (/ 1 (+ a b)) (/ a (/ PI 2))))

series419.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(/ (/ 1 (+ a b)) (/ a (/ PI 2)))
79.0ms
(/ a (/ PI 2))
70.0ms
(/ PI (* (+ a b) 2))
169.0ms
(fma (/ PI (* (+ a b) 2)) (/ -1 b) (/ (/ 1 (+ a b)) (/ a (/ PI 2))))

simplify13.8s

Counts
1009 → 1009
Iterations
IterNodes
15053
01468

prune13.8s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

regimes232.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
220
120
015

end0.0ms

sample2.4s

Algorithm
intervals
Results
2.2s9656×body80valid