Details

sample40.0ms

Algorithm

intervals

Results

23.0ms

310×

body

valid

simplify57.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	30	10
1	89	10
2	377	10
3	1779	10
4	5001	10

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.2b	(/ 1.0 (- (* b b) (* a a)))
6.3b	(- (* b b) (* a a))
7.4b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
47×	`times-frac`
39×	`*-un-lft-identity`
36×	`add-exp-log` `add-cbrt-cube`
31×	`add-cube-cbrt`
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×	`div-inv` `distribute-lft-out--`
4×	`pow-prod-down` `associate-/r*` `associate-/r/` `frac-sub` `unswap-sqr`
3×	`sub-neg` `associate-/l*`
2×	`distribute-rgt-in` `distribute-lft-in` `*-commutative`
1×	`frac-2neg` `diff-log` `clear-num`

Counts

4 → 153

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))
83.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series209.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
39.0ms	(/ 1.0 (- (* b b) (* a a)))
29.0ms	(- (* b b) (* a a))
85.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify103.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	804	1567
1	4503	1342
2	5002	1342

prune382.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- b a))
0.2b	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
0.3b	(/ (/ PI 2.0) (+ b a))
7.4b	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

234×	`times-frac`
193×	`*-un-lft-identity`
164×	`add-sqr-sqrt`
117×	`add-cube-cbrt`
61×	`add-exp-log` `add-cbrt-cube`
59×	`associate-l`
33×	`associate-r`
27×	`distribute-lft-out`
22×	`cbrt-undiv` `div-exp`
19×	`prod-exp` `cbrt-unprod`
16×	`associate-/l*`
15×	`div-inv`
14×	`frac-times`
12×	`distribute-lft-out--`
11×	`pow1` `difference-of-squares`
9×	`associate-/r*`
8×	`associate-r/` `associate-l/` `associate-/r/`
6×	`flip3--` `flip--` `unswap-sqr`
4×	`pow-prod-down` `frac-sub` `add-log-exp`
2×	`distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `flip3-+` `clear-num` `*-commutative` `flip-+`
1×	`associate-/l/`

Counts

4 → 288

Calls

4 calls:

5.0ms	(/ 1.0 (- b a))
55.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
9.0ms	(/ (/ PI 2.0) (+ b a))
91.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series255.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ 1.0 (- b a))
65.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
49.0ms	(/ (/ PI 2.0) (+ b a))
95.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify52.0ms

Algorithm

egg-herbie

Counts

300 → 300

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1260	2632
1	5001	2332

prune691.0ms

Pruning

7 alts after pruning (7 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))
0.5b	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

rewrite170.0ms

Algorithm

rewrite-expression-head

Rules

122×	`times-frac`
108×	`*-un-lft-identity`
88×	`add-sqr-sqrt`
60×	`add-cube-cbrt`
43×	`add-exp-log` `add-cbrt-cube`
14×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `distribute-lft-out` `associate-/l*`
12×	`associate-r` `distribute-lft-out--`
11×	`div-inv`
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×	`associate-/r/`
3×	`sub-neg` `pow-prod-down`
2×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num`
1×	`flip3-+` `diff-log` `associate-l` `*-commutative` `flip-+`

Counts

4 → 190

Calls

4 calls:

17.0ms	(- (/ 1.0 a) (/ 1.0 b))
58.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
9.0ms	(/ (/ PI 2.0) (+ b a))
77.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series285.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (/ 1.0 a) (/ 1.0 b))
94.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
54.0ms	(/ (/ PI 2.0) (+ b a))
101.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify112.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	931	1844
1	4583	1596
2	5001	1596

prune470.0ms

Pruning

7 alts after pruning (7 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))
0.5b	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))

rewrite192.0ms

Algorithm

rewrite-expression-head

Rules

337×	`times-frac`
308×	`add-sqr-sqrt`
288×	`*-un-lft-identity`
114×	`add-cube-cbrt`
85×	`distribute-lft-out--`
73×	`difference-of-squares`
66×	`associate-r`
43×	`add-exp-log` `add-cbrt-cube`
32×	`div-inv`
25×	`associate-/l*`
14×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `distribute-lft-out`
9×	`pow1` `associate-/r*`
6×	`associate-/r/` `add-log-exp`
4×	`flip3--` `flip--` `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 → 299

Calls

4 calls:

17.0ms	(- (/ 1.0 a) (/ 1.0 b))
93.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)))
9.0ms	(/ (/ PI 2.0) (+ b a))
53.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))

series232.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (/ 1.0 a) (/ 1.0 b))
96.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)))
55.0ms	(/ (/ PI 2.0) (+ b a))
51.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))

simplify56.0ms

Algorithm

egg-herbie

Counts

311 → 311

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1249	3083
1	5001	2836

prune713.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes60.0ms

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)

Iter	Nodes	Cost
0	16	7
1	16	7

end0.0ms

sample573.0ms

Algorithm

intervals

Results

418.0ms

9556×

body

valid