Details

Time bar (total: 7.0s)

sample24.0ms

Algorithm
intervals
Results
13.0ms306×body80valid

simplify42.0ms

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: 12.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.8b
(/ 1.0 (- (* b b) (* a a)))
2.9b
(- (* b b) (* a a))
8.8b
(* (* (/ 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)))
10.0ms
(- (* b b) (* a a))
145.0ms
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series204.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
37.0ms
(/ 1.0 (- (* b b) (* a a)))
31.0ms
(- (* b b) (* a a))
82.0ms
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify160.0ms

Algorithm
egg-herbie
Counts
513 → 513
Iterations

Useful iterations: 1 (49.0ms)

IterNodesCost
0248115016
1500213008

prune848.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (+ b a))
0.1b
(/ (/ 1.0 (+ b a)) (- b a))
0.2b
(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
8.8b
(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite360.0ms

Algorithm
rewrite-expression-head
Rules
820×times-frac
669×*-un-lft-identity
620×add-sqr-sqrt
513×add-cube-cbrt
338×prod-diff
171×distribute-rgt-in distribute-lft-in
108×associate-*r*
69×div-inv
61×add-exp-log add-cbrt-cube
42×distribute-lft-out--
41×difference-of-squares
37×distribute-lft-out
28×associate-/r/
22×cbrt-undiv div-exp
21×associate-/l*
19×prod-exp cbrt-unprod
14×frac-times associate-*l*
12×flip3-+ flip-+
11×pow1
9×associate-/r*
8×associate-*r/ associate-*l/
6×flip3-- flip-- unswap-sqr
4×expm1-log1p-u pow-prod-down frac-sub log1p-expm1-u add-log-exp
2×sub-neg frac-2neg clear-num *-commutative
1×associate-/l/
Counts
4 → 704
Calls
4 calls:
11.0ms
(/ 1.0 (+ b a))
28.0ms
(/ (/ 1.0 (+ b a)) (- b a))
85.0ms
(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
181.0ms
(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series236.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(/ 1.0 (+ b a))
43.0ms
(/ (/ 1.0 (+ b a)) (- b a))
61.0ms
(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
91.0ms
(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify193.0ms

Algorithm
egg-herbie
Counts
716 → 716
Iterations

Useful iterations: 1 (59.0ms)

IterNodesCost
0314016922
1500315938

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite356.0ms

Algorithm
rewrite-expression-head
Rules
504×times-frac
411×*-un-lft-identity
406×add-sqr-sqrt
389×add-cube-cbrt
338×prod-diff
171×distribute-rgt-in distribute-lft-in
57×div-inv
52×add-exp-log add-cbrt-cube
30×associate-*r*
21×prod-exp cbrt-unprod
17×associate-*r/
13×cbrt-undiv div-exp
11×pow1
7×associate-/l/ distribute-lft-out
6×frac-times associate-/r/
5×flip3-- associate-/r* flip-- distribute-lft-out--
4×expm1-log1p-u associate-*l* pow-prod-down frac-sub log1p-expm1-u associate-/l* add-log-exp difference-of-squares
2×sub-neg frac-2neg flip3-+ associate-*l/ clear-num *-commutative flip-+ unswap-sqr
Counts
4 → 494
Calls
4 calls:
11.0ms
(/ 1.0 (+ b a))
146.0ms
(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
127.0ms
(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
27.0ms
(* PI (/ 1.0 (+ b a)))

series273.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(/ 1.0 (+ b a))
88.0ms
(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
97.0ms
(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
47.0ms
(* PI (/ 1.0 (+ b a)))

simplify146.0ms

Algorithm
egg-herbie
Counts
506 → 506
Iterations

Useful iterations: 1 (47.0ms)

IterNodesCost
0240912732
1500111631

prune822.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (+ b a))
0.2b
(/ (* PI (/ 1.0 (+ b a))) (/ (* 2.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
0.3b
(/ (* 2.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))
0.4b
(* PI (/ 1.0 (+ b a)))

rewrite163.0ms

Algorithm
rewrite-expression-head
Rules
120×times-frac
89×add-sqr-sqrt
82×*-un-lft-identity
52×add-exp-log add-cbrt-cube
36×add-cube-cbrt
35×associate-/r*
22×cbrt-undiv div-exp
20×distribute-lft-out--
18×associate-*r*
16×difference-of-squares
14×associate-/r/ div-inv
12×prod-exp cbrt-unprod
7×distribute-lft-out
6×pow1
5×associate-/l*
4×expm1-log1p-u flip3-- associate-*r/ flip-- log1p-expm1-u add-log-exp
3×frac-2neg associate-*l* clear-num frac-sub associate-/l/
2×flip3-+ flip-+ unswap-sqr
1×pow-prod-down *-commutative
Counts
4 → 191
Calls
4 calls:
10.0ms
(/ 1.0 (+ b a))
59.0ms
(/ (* PI (/ 1.0 (+ b a))) (/ (* 2.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
56.0ms
(/ (* 2.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))
27.0ms
(* PI (/ 1.0 (+ b a)))

series361.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(/ 1.0 (+ b a))
84.0ms
(/ (* PI (/ 1.0 (+ b a))) (/ (* 2.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
197.0ms
(/ (* 2.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))
45.0ms
(* PI (/ 1.0 (+ b a)))

simplify114.0ms

Algorithm
egg-herbie
Counts
203 → 203
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
08871784
148851499
250011499

prune432.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

regimes63.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01810
11810

end0.0ms

sample608.0ms

Algorithm
intervals
Results
399.0ms9500×body80valid