Details

Time bar (total: 2.7m)

sample47.0ms

Algorithm
intervals
Results
34.0ms311×body80valid

simplify1.9s

Counts
1 → 1
Iterations
IterNodes
done5001
41503
3361
295
133
015

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.3b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (/ PI 2) (/ -1 b) (/ (/ PI 2) a))
0.3b
(/ (/ PI 2) a)
4.0b
(- (* b b) (* a a))
8.9b
(/ (fma (/ PI 2) (/ -1 b) (/ (/ PI 2) a)) (- (* b b) (* a a)))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
87×times-frac
55×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
16×associate-/l*
11×add-cbrt-cube add-exp-log
7×associate-/r*
6×div-inv add-log-exp
5×difference-of-squares
4×expm1-log1p-u pow1 cbrt-undiv div-exp insert-posit16 log1p-expm1-u
2×clear-num frac-2neg flip3-- associate-/r/ flip--
1×sub-neg fma-neg diff-log prod-diff fma-udef associate-/l/
Counts
4 → 138
Calls
4 calls:
0.0ms
(fma (/ PI 2) (/ -1 b) (/ (/ PI 2) a))
11.0ms
(/ (/ PI 2) a)
10.0ms
(- (* b b) (* a a))
23.0ms
(/ (fma (/ PI 2) (/ -1 b) (/ (/ PI 2) a)) (- (* b b) (* a a)))

series341.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(fma (/ PI 2) (/ -1 b) (/ (/ PI 2) a))
46.0ms
(/ (/ PI 2) a)
60.0ms
(- (* b b) (* a a))
147.0ms
(/ (fma (/ PI 2) (/ -1 b) (/ (/ PI 2) a)) (- (* b b) (* a a)))

simplify1.4s

Counts
150 → 150
Iterations
IterNodes
done5001
21516
1560
0253

prune856.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize52.0ms

Local error

Found 4 expressions with local error:

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

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
249×times-frac
204×*-un-lft-identity
160×add-sqr-sqrt
122×add-cube-cbrt
34×associate-/l*
22×distribute-lft-out
19×distribute-lft-out-- difference-of-squares
16×add-cbrt-cube add-exp-log associate-/r/
13×div-inv
12×associate-/r*
7×cbrt-undiv flip3-+ div-exp flip-+
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg
2×associate-/l/
1×flip3-- fma-udef flip--
Counts
4 → 253
Calls
4 calls:
28.0ms
(/ (/ (fma (/ PI 2) (/ -1 b) (/ (/ PI 2) a)) (+ b a)) (- b a))
0.0ms
(fma (/ PI 2) (/ -1 b) (/ (/ PI 2) a))
16.0ms
(/ (fma (/ PI 2) (/ -1 b) (/ (/ PI 2) a)) (+ b a))
22.0ms
(/ (/ PI 2) a)

series522.0ms

Counts
4 → 12
Calls
4 calls:
175.0ms
(/ (/ (fma (/ PI 2) (/ -1 b) (/ (/ PI 2) a)) (+ b a)) (- b a))
100.0ms
(fma (/ PI 2) (/ -1 b) (/ (/ PI 2) a))
181.0ms
(/ (fma (/ PI 2) (/ -1 b) (/ (/ PI 2) a)) (+ b a))
65.0ms
(/ (/ PI 2) a)

simplify2.4s

Counts
265 → 265
Iterations
IterNodes
done5002
22753
1922
0391

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite559.0ms

Algorithm
rewrite-expression-head
Rules
3882×times-frac
2704×*-un-lft-identity
2490×add-sqr-sqrt
1112×add-cube-cbrt
602×distribute-lft-out--
515×difference-of-squares
281×distribute-lft-out
213×div-inv
212×associate-/l*
22×add-cbrt-cube add-exp-log
16×associate-/r/
15×associate-/r*
11×cbrt-undiv div-exp
7×flip3-+ flip-+
5×div-sub
4×expm1-log1p-u pow1 clear-num frac-2neg insert-posit16 log1p-expm1-u add-log-exp
2×associate-/l/
1×flip3-- flip--
Counts
4 → 1309
Calls
4 calls:
200.0ms
(/ (/ (/ (- (/ PI a) (/ PI b)) 2) (+ b a)) (- b a))
8.0ms
(/ PI b)
140.0ms
(/ (/ (- (/ PI a) (/ PI b)) 2) (+ b a))
7.0ms
(/ PI a)

series330.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(/ (/ (/ (- (/ PI a) (/ PI b)) 2) (+ b a)) (- b a))
39.0ms
(/ PI b)
128.0ms
(/ (/ (- (/ PI a) (/ PI b)) 2) (+ b a))
44.0ms
(/ PI a)

simplify2.8s

Counts
1321 → 1321
Iterations
IterNodes
done5000
13464
01489

prune4.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 1 a) (/ 1 b))
0.1b
(/ (/ (/ PI 1) (/ (+ b a) (/ (- (/ 1 a) (/ 1 b)) 2))) (- b a))
0.3b
(/ (+ b a) (/ (- (/ 1 a) (/ 1 b)) 2))
0.4b
(/ (/ PI 1) (/ (+ b a) (/ (- (/ 1 a) (/ 1 b)) 2)))

rewrite8.3s

Algorithm
rewrite-expression-head
Rules
118921×times-frac
67989×*-un-lft-identity
65601×add-sqr-sqrt
32235×add-cube-cbrt
13323×difference-of-squares
11083×distribute-lft-out--
6725×div-inv
5674×distribute-lft-out
3259×associate-/l*
315×associate-/r*
169×prod-diff
102×associate-/r/
80×add-exp-log
61×div-exp
59×add-cbrt-cube
40×cbrt-undiv
13×fma-neg
6×1-exp add-log-exp
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u associate-/l/
3×clear-num frac-2neg
2×flip3-- flip--
1×sub-neg flip3-+ diff-log frac-sub flip-+
Counts
4 → 23562
Calls
4 calls:
62.0ms
(- (/ 1 a) (/ 1 b))
2.0s
(/ (/ (/ PI 1) (/ (+ b a) (/ (- (/ 1 a) (/ 1 b)) 2))) (- b a))
138.0ms
(/ (+ b a) (/ (- (/ 1 a) (/ 1 b)) 2))
241.0ms
(/ (/ PI 1) (/ (+ b a) (/ (- (/ 1 a) (/ 1 b)) 2)))

series327.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(- (/ 1 a) (/ 1 b))
114.0ms
(/ (/ (/ PI 1) (/ (+ b a) (/ (- (/ 1 a) (/ 1 b)) 2))) (- b a))
87.0ms
(/ (+ b a) (/ (- (/ 1 a) (/ 1 b)) 2))
103.0ms
(/ (/ PI 1) (/ (+ b a) (/ (- (/ 1 a) (/ 1 b)) 2)))

simplify28.2s

Counts
23574 → 23574
Iterations
IterNodes
done20922
020922

prune1.7m

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes98.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done19
119
016

end0.0ms

sample951.0ms

Algorithm
intervals
Results
805.0ms9615×body80valid