Details

sample41.0ms

Algorithm

intervals

Results

30.0ms

297×

body

valid

simplify41.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	10
1	90	10
2	384	10
3	1828	10
4	5001	10

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.7b	(/ 1.0 (- (* b b) (* a a)))
4.8b	(- (* b b) (* a a))
8.0b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite182.0ms

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:

23.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
5.0ms	(/ 1.0 (- (* b b) (* a a)))
3.0ms	(- (* b b) (* a a))
102.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series230.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
42.0ms	(/ 1.0 (- (* b b) (* a a)))
35.0ms	(- (* b b) (* a a))
94.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify209.0ms

Algorithm

egg-herbie

Counts

513 → 513

Iterations

Useful iterations: 1 (73.0ms)

Iter	Nodes	Cost
0	2481	15016
1	5002	13008

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.1b	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
0.2b	(/ (/ PI 2.0) (+ b a))
8.0b	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite292.0ms

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:

26.0ms	(- (/ 1.0 a) (/ 1.0 b))
55.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
12.0ms	(/ (/ PI 2.0) (+ b a))
123.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series394.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (/ 1.0 a) (/ 1.0 b))
63.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
56.0ms	(/ (/ PI 2.0) (+ b a))
240.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify212.0ms

Algorithm

egg-herbie

Counts

813 → 813

Iterations

Useful iterations: 1 (55.0ms)

Iter	Nodes	Cost
0	2928	20392
1	5001	18352

prune1.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

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

rewrite508.0ms

Algorithm

rewrite-expression-head

Rules

1868×	`times-frac`
1466×	`*-un-lft-identity`
1425×	`add-sqr-sqrt`
1390×	`add-cube-cbrt`
1183×	`prod-diff`
855×	`distribute-rgt-in` `distribute-lft-in`
199×	`div-inv`
79×	`associate-l`
50×	`add-exp-log` `add-cbrt-cube`
27×	`distribute-lft-out`
17×	`prod-exp` `cbrt-unprod`
16×	`cbrt-undiv` `frac-times` `associate-*r/` `div-exp`
13×	`fma-neg` `associate-r` `associate-/l*` `distribute-lft-out--`
11×	`pow1` `difference-of-squares`
8×	`flip3--` `flip--`
7×	`sub-neg` `frac-sub`
6×	`associate-/r/` `add-log-exp`
4×	`expm1-log1p-u` `pow-prod-down` `associate-l/` `associate-/r` `log1p-expm1-u`
2×	`flip3-+` `*-commutative` `flip-+` `unswap-sqr`
1×	`frac-2neg` `diff-log` `clear-num` `associate-/l/`

Counts

4 → 1481

Calls

4 calls:

25.0ms	(- (/ 1.0 a) (/ 1.0 b))
193.0ms	(* (/ (/ PI 2.0) (+ b a)) (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
10.0ms	(/ (/ PI 2.0) (+ b a))
109.0ms	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))

series251.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (/ 1.0 a) (/ 1.0 b))
99.0ms	(* (/ (/ PI 2.0) (+ b a)) (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
57.0ms	(/ (/ PI 2.0) (+ b a))
62.0ms	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))

simplify397.0ms

Algorithm

egg-herbie

Counts

1493 → 1493

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5002	44700

prune5.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

129×	`times-frac`
120×	`add-exp-log` `add-cbrt-cube`
115×	`*-un-lft-identity`
92×	`add-sqr-sqrt`
73×	`add-cube-cbrt`
49×	`cbrt-undiv` `div-exp`
42×	`prod-exp` `cbrt-unprod`
21×	`associate-l`
17×	`associate-/l*`
14×	`distribute-lft-out`
12×	`associate-/l/`
11×	`frac-times` `associate-*r/`
10×	`associate-/r*`
9×	`div-inv`
8×	`flip3--` `flip--`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1` `associate-/r/`
4×	`expm1-log1p-u` `associate-*l/` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `associate-r` `clear-num`
2×	`sub-neg` `prod-diff` `unswap-sqr`
1×	`flip3-+` `pow-prod-down` `*-commutative` `flip-+`

Counts

4 → 245

Calls

4 calls:

5.0ms	(/ 1.0 (- b a))
27.0ms	(* (/ 1.0 (- b a)) (- (* 1.0 b) (* a 1.0)))
43.0ms	(/ (* (/ (/ PI 2.0) (+ b a)) (* (/ 1.0 (- b a)) (- (* 1.0 b) (* a 1.0)))) (* a b))
9.0ms	(/ (/ PI 2.0) (+ b a))

series289.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(/ 1.0 (- b a))
54.0ms	(* (/ 1.0 (- b a)) (- (* 1.0 b) (* a 1.0)))
135.0ms	(/ (* (/ (/ PI 2.0) (+ b a)) (* (/ 1.0 (- b a)) (- (* 1.0 b) (* a 1.0)))) (* a b))
58.0ms	(/ (/ PI 2.0) (+ b a))

simplify57.0ms

Algorithm

egg-herbie

Counts

257 → 257

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1218	2622
1	5002	2012

prune591.0ms

Pruning

7 alts after pruning (7 fresh and 0 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	18	10
1	18	10

end0.0ms

sample1.2s

Algorithm

intervals

Results

987.0ms

9633×

body

valid