Details

Time bar (total: 8.7s)

sample24.0ms

Algorithm
intervals
Results
13.0ms309×body80valid

simplify41.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03110
19010
238410
3182810
4500110

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.5b
(/ 1.0 (- (* b b) (* a a)))
2.4b
(- (* b b) (* a a))
10.1b
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite248.0ms

Algorithm
rewrite-expression-head
Rules
515×times-frac
419×add-sqr-sqrt
403×*-un-lft-identity
395×add-cube-cbrt
339×prod-diff
171×distribute-rgt-in distribute-lft-in
57×div-inv
36×add-exp-log add-cbrt-cube
30×associate-*r*
14×frac-times associate-*l*
13×prod-exp cbrt-unprod
12×difference-of-squares
11×pow1
9×cbrt-undiv div-exp
8×associate-*r/ associate-*l/
7×flip3-- flip--
6×add-log-exp
5×distribute-lft-out--
4×expm1-log1p-u pow-prod-down associate-/r* associate-/r/ frac-sub log1p-expm1-u unswap-sqr
3×sub-neg associate-/l*
2×*-commutative
1×frac-2neg fma-neg diff-log clear-num
Counts
4 → 501
Calls
4 calls:
43.0ms
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
12.0ms
(/ 1.0 (- (* b b) (* a a)))
8.0ms
(- (* b b) (* a a))
142.0ms
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series231.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
44.0ms
(/ 1.0 (- (* b b) (* a a)))
32.0ms
(- (* b b) (* a a))
94.0ms
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify147.0ms

Algorithm
egg-herbie
Counts
513 → 513
Iterations

Useful iterations: 1 (47.0ms)

IterNodesCost
0248115016
1500213008

prune910.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 9.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 1.0 a) (/ 1.0 b))
0.2b
(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
0.3b
(/ (/ PI 2.0) (+ b a))
10.1b
(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite357.0ms

Algorithm
rewrite-expression-head
Rules
940×times-frac
738×*-un-lft-identity
713×add-sqr-sqrt
662×add-cube-cbrt
507×prod-diff
171×distribute-rgt-in distribute-lft-in
95×div-inv
59×add-exp-log associate-*l* add-cbrt-cube
33×associate-*r*
27×distribute-lft-out
21×cbrt-undiv div-exp
19×prod-exp cbrt-unprod
14×frac-times
13×fma-neg associate-/l* distribute-lft-out--
11×pow1 difference-of-squares
8×associate-*r/ associate-*l/
6×flip3-- associate-/r/ flip-- add-log-exp unswap-sqr
5×frac-sub
4×expm1-log1p-u pow-prod-down associate-/r* log1p-expm1-u
3×sub-neg
2×flip3-+ *-commutative flip-+
1×frac-2neg diff-log clear-num associate-/l/
Counts
4 → 801
Calls
4 calls:
30.0ms
(- (/ 1.0 a) (/ 1.0 b))
72.0ms
(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
18.0ms
(/ (/ PI 2.0) (+ b a))
164.0ms
(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series255.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(- (/ 1.0 a) (/ 1.0 b))
69.0ms
(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
53.0ms
(/ (/ PI 2.0) (+ b a))
100.0ms
(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify194.0ms

Algorithm
egg-herbie
Counts
813 → 813
Iterations

Useful iterations: 1 (50.0ms)

IterNodesCost
0292820392
1500118352

prune1.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 1.0 a) (/ 1.0 b))
0.2b
(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
0.3b
(/ (/ PI 2.0) (+ b a))
0.3b
(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

rewrite406.0ms

Algorithm
rewrite-expression-head
Rules
833×times-frac
661×*-un-lft-identity
641×add-sqr-sqrt
613×add-cube-cbrt
507×prod-diff
171×distribute-rgt-in distribute-lft-in
90×div-inv
43×add-exp-log add-cbrt-cube
14×cbrt-undiv div-exp prod-exp cbrt-unprod distribute-lft-out associate-/l*
13×fma-neg
12×associate-*r* distribute-lft-out--
10×associate-*l/ difference-of-squares
9×pow1 associate-/r*
8×associate-/l/
6×frac-times flip3-- associate-*r/ flip-- add-log-exp
5×frac-sub
4×expm1-log1p-u associate-/r/ log1p-expm1-u
3×sub-neg pow-prod-down
2×frac-2neg clear-num
1×flip3-+ diff-log associate-*l* *-commutative flip-+
Counts
4 → 718
Calls
4 calls:
30.0ms
(- (/ 1.0 a) (/ 1.0 b))
155.0ms
(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
19.0ms
(/ (/ PI 2.0) (+ b a))
138.0ms
(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series295.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(- (/ 1.0 a) (/ 1.0 b))
97.0ms
(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
56.0ms
(/ (/ PI 2.0) (+ b a))
110.0ms
(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify171.0ms

Algorithm
egg-herbie
Counts
730 → 730
Iterations

Useful iterations: 1 (44.0ms)

IterNodesCost
0258618289
1500115335

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 1.0 a) (/ 1.0 b))
0.2b
(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
0.2b
(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)))
0.3b
(/ (/ PI 2.0) (+ b a))

rewrite298.0ms

Algorithm
rewrite-expression-head
Rules
580×times-frac
497×add-sqr-sqrt
477×*-un-lft-identity
303×add-cube-cbrt
169×prod-diff
85×distribute-lft-out--
73×difference-of-squares
66×associate-*r*
59×div-inv
43×add-exp-log add-cbrt-cube
25×associate-/l*
14×cbrt-undiv div-exp prod-exp cbrt-unprod distribute-lft-out
13×fma-neg
9×pow1 associate-/r*
6×associate-/r/ add-log-exp
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u associate-/l/
3×pow-prod-down associate-*l/
2×frac-2neg clear-num frac-sub
1×frac-times sub-neg flip3-+ diff-log div-sub associate-*r/ associate-*l* *-commutative flip-+
Counts
4 → 489
Calls
4 calls:
32.0ms
(- (/ 1.0 a) (/ 1.0 b))
83.0ms
(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
131.0ms
(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)))
16.0ms
(/ (/ PI 2.0) (+ b a))

series245.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(- (/ 1.0 a) (/ 1.0 b))
48.0ms
(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
99.0ms
(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)))
60.0ms
(/ (/ PI 2.0) (+ b a))

simplify91.0ms

Algorithm
egg-herbie
Counts
501 → 501
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
018087484
150016268

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes61.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0167
1167

end0.0ms

sample609.0ms

Algorithm
intervals
Results
407.0ms9594×body80valid