Details

Time bar (total: 8.0s)

sample27.0ms

Algorithm
intervals
Results
17.0ms306×body80valid

simplify43.0ms

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

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 14.5b

Counts
2 → 1

localize13.0ms

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)))
3.5b
(- (* b b) (* a a))
9.7b
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite108.0ms

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:
13.0ms
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
5.0ms
(/ 1.0 (- (* b b) (* a a)))
4.0ms
(- (* b b) (* a a))
41.0ms
(* (* (/ 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))))
44.0ms
(/ 1.0 (- (* b b) (* a a)))
30.0ms
(- (* b b) (* a a))
91.0ms
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify166.0ms

Algorithm
egg-herbie
Counts
513 → 513
Iterations

Useful iterations: 1 (48.0ms)

IterNodesCost
0248115016
1500213008

prune809.0ms

Filtered
513 candidates to 220 candidates (42.9%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New5049513
Fresh000
Picked101
Done000
Total5059514

Merged error: 9.5b

Counts
514 → 9

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))
9.7b
(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite178.0ms

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:
21.0ms
(- (/ 1.0 a) (/ 1.0 b))
32.0ms
(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
8.0ms
(/ (/ PI 2.0) (+ b a))
47.0ms
(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series250.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(- (/ 1.0 a) (/ 1.0 b))
66.0ms
(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
49.0ms
(/ (/ PI 2.0) (+ b a))
98.0ms
(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify221.0ms

Algorithm
egg-herbie
Counts
813 → 813
Iterations

Useful iterations: 1 (58.0ms)

IterNodesCost
0292820392
1500118352

prune1.4s

Filtered
813 candidates to 378 candidates (46.5%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New8085813
Fresh448
Picked011
Done000
Total81210822

Merged error: 0.0b

Counts
822 → 10

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) (- (/ 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)))

rewrite186.0ms

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:
17.0ms
(- (/ 1.0 a) (/ 1.0 b))
53.0ms
(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
8.0ms
(/ (/ PI 2.0) (+ b a))
44.0ms
(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series412.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(- (/ 1.0 a) (/ 1.0 b))
97.0ms
(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
181.0ms
(/ (/ PI 2.0) (+ b a))
103.0ms
(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify193.0ms

Algorithm
egg-herbie
Counts
730 → 730
Iterations

Useful iterations: 1 (48.0ms)

IterNodesCost
0258618289
1500115335

prune1.1s

Filtered
730 candidates to 321 candidates (44.0%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New7246730
Fresh628
Picked101
Done011
Total7319740

Merged error: 0b

Counts
740 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite192.0ms

Algorithm
rewrite-expression-head
Rules
809×times-frac
641×*-un-lft-identity
633×add-sqr-sqrt
587×add-cube-cbrt
507×prod-diff
171×distribute-rgt-in distribute-lft-in
91×div-inv
47×add-exp-log add-cbrt-cube
21×distribute-lft-out--
19×difference-of-squares
16×cbrt-undiv div-exp associate-/r/
15×prod-exp cbrt-unprod
13×fma-neg
12×associate-*r*
11×associate-/l*
10×associate-*l/
9×pow1 associate-/r*
8×associate-/l/ distribute-lft-out
7×flip3-+ flip-+
6×frac-times flip3-- associate-*r/ flip-- add-log-exp
5×frac-sub
4×expm1-log1p-u log1p-expm1-u
3×sub-neg pow-prod-down
2×frac-2neg clear-num
1×diff-log associate-*l* *-commutative
Counts
4 → 714
Calls
4 calls:
18.0ms
(- (/ 1.0 a) (/ 1.0 b))
30.0ms
(/ (/ (* (* (/ PI 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a)) (- b a))
43.0ms
(/ (* (* (/ PI 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
37.0ms
(* (* (/ PI 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series300.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(- (/ 1.0 a) (/ 1.0 b))
94.0ms
(/ (/ (* (* (/ PI 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a)) (- b a))
104.0ms
(/ (* (* (/ PI 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
68.0ms
(* (* (/ PI 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify196.0ms

Algorithm
egg-herbie
Counts
726 → 726
Iterations

Useful iterations: 1 (48.0ms)

IterNodesCost
0257817411
1500115285

prune1.2s

Filtered
726 candidates to 320 candidates (44.1%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New7251726
Fresh167
Picked011
Done011
Total7269735

Merged error: 0b

Counts
735 → 9

regimes64.0ms

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
01810
11810

end0.0ms

sample714.0ms

Algorithm
intervals
Results
550.0ms9579×body80valid

Profiling

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