Details

Time bar (total: 8.6s)

sample23.0ms

Algorithm
intervals
Results
13.0ms293×body80valid

simplify40.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03110
19010
238410
3182810
4500110

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.6b
(/ 1.0 (- (* b b) (* a a)))
6.1b
(- (* b b) (* a a))
11.1b
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite163.0ms

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:
21.0ms
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
5.0ms
(/ 1.0 (- (* b b) (* a a)))
3.0ms
(- (* b b) (* a a))
94.0ms
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series218.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
45.0ms
(/ 1.0 (- (* b b) (* a a)))
30.0ms
(- (* b b) (* a a))
90.0ms
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify159.0ms

Algorithm
egg-herbie
Counts
513 → 513
Iterations

Useful iterations: 1 (45.0ms)

IterNodesCost
0248115016
1500213008

prune897.0ms

Filtered
513 candidates to 220 candidates (42.9%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 1.0 a) (/ 1.0 b))
0.1b
(/ (/ 1.0 (+ b a)) (- b a))
0.2b
(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
11.1b
(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite288.0ms

Algorithm
rewrite-expression-head
Rules
1061×times-frac
851×*-un-lft-identity
814×add-sqr-sqrt
695×add-cube-cbrt
507×prod-diff
171×distribute-rgt-in distribute-lft-in
108×associate-*r*
97×div-inv
59×add-exp-log add-cbrt-cube
47×distribute-lft-out--
45×difference-of-squares
33×distribute-lft-out
26×associate-/r/
21×cbrt-undiv div-exp
19×prod-exp cbrt-unprod
18×associate-/l*
14×frac-times associate-*l*
13×fma-neg
11×pow1 flip3-+ flip-+
8×associate-*r/ associate-*l/
7×flip3-- flip--
6×add-log-exp unswap-sqr
5×associate-/r* frac-sub
4×expm1-log1p-u pow-prod-down log1p-expm1-u
3×sub-neg
2×*-commutative
1×frac-2neg diff-log clear-num associate-/l/
Counts
4 → 875
Calls
4 calls:
22.0ms
(- (/ 1.0 a) (/ 1.0 b))
16.0ms
(/ (/ 1.0 (+ b a)) (- b a))
59.0ms
(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
122.0ms
(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series240.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(- (/ 1.0 a) (/ 1.0 b))
50.0ms
(/ (/ 1.0 (+ b a)) (- b a))
63.0ms
(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
95.0ms
(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify225.0ms

Algorithm
egg-herbie
Counts
887 → 887
Iterations

Useful iterations: 1 (57.0ms)

IterNodesCost
0315621276
1500319725

prune1.7s

Filtered
887 candidates to 414 candidates (46.7%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 1.0 a) (/ 1.0 b))
0.2b
(/ (* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
0.4b
(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
0.4b
(* (/ PI 2.0) (/ 1.0 (+ b a)))

rewrite302.0ms

Algorithm
rewrite-expression-head
Rules
761×times-frac
619×add-sqr-sqrt
605×*-un-lft-identity
579×add-cube-cbrt
507×prod-diff
171×distribute-rgt-in distribute-lft-in
86×div-inv
59×add-exp-log add-cbrt-cube
30×associate-*r*
27×frac-times
22×prod-exp cbrt-unprod
18×cbrt-undiv div-exp
15×associate-*r/ associate-*l/ associate-/l/
14×associate-*l*
13×fma-neg
12×distribute-lft-out--
11×pow1
10×flip3-- flip-- difference-of-squares
9×frac-sub
6×add-log-exp
5×associate-/r*
4×expm1-log1p-u pow-prod-down associate-/r/ log1p-expm1-u unswap-sqr
3×sub-neg distribute-lft-out
2×*-commutative
1×frac-2neg flip3-+ diff-log clear-num flip-+ associate-/l*
Counts
4 → 707
Calls
4 calls:
22.0ms
(- (/ 1.0 a) (/ 1.0 b))
109.0ms
(/ (* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
91.0ms
(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
20.0ms
(* (/ PI 2.0) (/ 1.0 (+ b a)))

series283.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(- (/ 1.0 a) (/ 1.0 b))
94.0ms
(/ (* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
102.0ms
(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
50.0ms
(* (/ PI 2.0) (/ 1.0 (+ b a)))

simplify333.0ms

Algorithm
egg-herbie
Counts
719 → 719
Iterations

Useful iterations: 1 (47.0ms)

IterNodesCost
0264318215
1500216222

prune1.3s

Filtered
719 candidates to 317 candidates (44.1%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 1.0 a) (/ 1.0 b))
0.2b
(/ (* (/ PI 2.0) (/ 1.0 (+ b a))) (/ (- b a) (- (/ 1.0 a) (/ 1.0 b))))
0.2b
(/ (- b a) (- (/ 1.0 a) (/ 1.0 b)))
0.4b
(* (/ PI 2.0) (/ 1.0 (+ b a)))

rewrite164.0ms

Algorithm
rewrite-expression-head
Rules
685×times-frac
587×add-sqr-sqrt
513×*-un-lft-identity
297×add-cube-cbrt
169×prod-diff
122×distribute-lft-out--
105×difference-of-squares
79×associate-/r*
67×div-inv
59×add-exp-log add-cbrt-cube
28×cbrt-undiv div-exp
18×associate-*r*
13×fma-neg associate-*l*
12×prod-exp associate-/r/ cbrt-unprod
6×pow1 associate-/l* add-log-exp
5×flip3-- flip-- associate-/l/
4×expm1-log1p-u frac-sub log1p-expm1-u unswap-sqr
3×distribute-lft-out
2×frac-times frac-2neg associate-*r/ associate-*l/ clear-num
1×sub-neg flip3-+ diff-log div-sub pow-prod-down *-commutative flip-+
Counts
4 → 531
Calls
4 calls:
22.0ms
(- (/ 1.0 a) (/ 1.0 b))
46.0ms
(/ (* (/ PI 2.0) (/ 1.0 (+ b a))) (/ (- b a) (- (/ 1.0 a) (/ 1.0 b))))
34.0ms
(/ (- b a) (- (/ 1.0 a) (/ 1.0 b)))
20.0ms
(* (/ PI 2.0) (/ 1.0 (+ b a)))

series221.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(- (/ 1.0 a) (/ 1.0 b))
91.0ms
(/ (* (/ PI 2.0) (/ 1.0 (+ b a))) (/ (- b a) (- (/ 1.0 a) (/ 1.0 b))))
50.0ms
(/ (- b a) (- (/ 1.0 a) (/ 1.0 b)))
50.0ms
(* (/ PI 2.0) (/ 1.0 (+ b a)))

simplify108.0ms

Algorithm
egg-herbie
Counts
543 → 543
Iterations

Useful iterations: 1 (37.0ms)

IterNodesCost
021418470
150017240

prune1.2s

Filtered
543 candidates to 336 candidates (61.9%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes69.0ms

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
02212
12212

end0.0ms

sample577.0ms

Algorithm
intervals
Results
424.0ms9578×body80valid