Details

Time bar (total: 24.2s)

sample53.0ms

Algorithm
intervals
Results
33.0ms303×body80valid

simplify2.2s

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: 0.1b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite47.0ms

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:
0.0ms
(fma (/ PI (* (+ a b) 2)) (/ -1 b) (/ (/ PI (* (+ a b) 2)) a))
16.0ms
(/ (/ PI (* (+ a b) 2)) a)
9.0ms
(/ PI (* (+ a b) 2))
20.0ms
(/ PI (* (+ a b) 2))

series358.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(fma (/ PI (* (+ a b) 2)) (/ -1 b) (/ (/ PI (* (+ a b) 2)) a))
85.0ms
(/ (/ PI (* (+ a b) 2)) a)
89.0ms
(/ PI (* (+ a b) 2))
71.0ms
(/ PI (* (+ a b) 2))

simplify2.9s

Counts
134 → 134
Iterations
IterNodes
36133
21258
1419
0176

prune647.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 4 expressions with local error:

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

rewrite78.0ms

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:
17.0ms
(/ (fma (/ PI (* (+ a b) 2)) (/ -1 b) (/ PI (* a (* (+ a b) 2)))) (- b a))
0.0ms
(fma (/ PI (* (+ a b) 2)) (/ -1 b) (/ PI (* a (* (+ a b) 2))))
18.0ms
(/ PI (* (+ a b) 2))
40.0ms
(/ PI (* a (* (+ a b) 2)))

series485.0ms

Counts
4 → 12
Calls
4 calls:
157.0ms
(/ (fma (/ PI (* (+ a b) 2)) (/ -1 b) (/ PI (* a (* (+ a b) 2)))) (- b a))
133.0ms
(fma (/ PI (* (+ a b) 2)) (/ -1 b) (/ PI (* a (* (+ a b) 2))))
95.0ms
(/ PI (* (+ a b) 2))
100.0ms
(/ PI (* a (* (+ a b) 2)))

simplify3.1s

Counts
117 → 117
Iterations
IterNodes
37034
21387
1415
0185

prune571.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

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

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
31×add-sqr-sqrt
27×add-exp-log
25×*-un-lft-identity
23×times-frac add-cbrt-cube
21×associate-*r*
18×add-cube-cbrt
8×prod-exp
7×div-exp
6×pow1 cbrt-undiv associate-/r/ cbrt-unprod associate-/l*
4×expm1-log1p-u associate-*l/ insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l* associate-*r/ div-inv distribute-lft-out-- difference-of-squares unswap-sqr
2×clear-num associate-/r* frac-2neg flip3-+ flip-+
1×rec-exp flip3-- 1-exp pow-prod-down un-div-inv *-commutative fma-udef flip--
Counts
4 → 112
Calls
4 calls:
0.0ms
(fma (/ PI (* (+ a b) 2)) (/ -1 b) (/ PI (* a (* (+ a b) 2))))
24.0ms
(* (fma (/ PI (* (+ a b) 2)) (/ -1 b) (/ PI (* a (* (+ a b) 2)))) (/ 1 (- b a)))
10.0ms
(/ PI (* (+ a b) 2))
20.0ms
(/ PI (* a (* (+ a b) 2)))

series451.0ms

Counts
4 → 12
Calls
4 calls:
152.0ms
(fma (/ PI (* (+ a b) 2)) (/ -1 b) (/ PI (* a (* (+ a b) 2))))
133.0ms
(* (fma (/ PI (* (+ a b) 2)) (/ -1 b) (/ PI (* a (* (+ a b) 2)))) (/ 1 (- b a)))
88.0ms
(/ PI (* (+ a b) 2))
78.0ms
(/ PI (* a (* (+ a b) 2)))

simplify6.0s

Counts
124 → 124
Iterations
IterNodes
38483
21836
1506
0208

prune658.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (/ PI (* (+ a b) 2))) (cbrt (/ PI (* (+ a b) 2))))
0.7b
(cbrt (/ PI (* (+ a b) 2)))
0.7b
(cbrt (/ PI (* (+ a b) 2)))
0.7b
(cbrt (/ PI (* (+ a b) 2)))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
67×cbrt-prod
30×add-sqr-sqrt
22×*-un-lft-identity add-cube-cbrt
21×times-frac
15×associate-*l/
14×associate-/r/
12×swap-sqr associate-*r* associate-*l*
11×pow1
9×pow1/3
7×cbrt-div flip3-+ flip-+ div-inv
6×add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 frac-times pow-plus prod-exp associate-*r/ *-commutative cbrt-unprod
Counts
4 → 127
Calls
4 calls:
49.0ms
(* (cbrt (/ PI (* (+ a b) 2))) (cbrt (/ PI (* (+ a b) 2))))
12.0ms
(cbrt (/ PI (* (+ a b) 2)))
12.0ms
(cbrt (/ PI (* (+ a b) 2)))
10.0ms
(cbrt (/ PI (* (+ a b) 2)))

series2.1s

Counts
4 → 12
Calls
4 calls:
937.0ms
(* (cbrt (/ PI (* (+ a b) 2))) (cbrt (/ PI (* (+ a b) 2))))
411.0ms
(cbrt (/ PI (* (+ a b) 2)))
378.0ms
(cbrt (/ PI (* (+ a b) 2)))
385.0ms
(cbrt (/ PI (* (+ a b) 2)))

simplify1.3s

Counts
139 → 139
Iterations
IterNodes
32868
21105
1426
0199

prune990.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes230.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 0.6b

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
219
119
016

end0.0ms

sample1.7s

Algorithm
intervals
Results
1.5s9516×body80valid