Details

sample22.0ms

Algorithm

intervals

Results

13.0ms

300×

body

valid

simplify42.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.7b

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)))
4.0b	(- (* b b) (* a a))
7.5b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite179.0ms

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:

24.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
6.0ms	(/ 1.0 (- (* b b) (* a a)))
3.0ms	(- (* b b) (* a a))
104.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series211.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
43.0ms	(/ 1.0 (- (* b b) (* a a)))
29.0ms	(- (* b b) (* a a))
87.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify157.0ms

Algorithm

egg-herbie

Counts

513 → 513

Iterations

Useful iterations: 1 (44.0ms)

Iter	Nodes	Cost
0	2481	15016
1	5002	13008

prune844.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.4b

localize15.0ms

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))
7.5b	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite283.0ms

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))
58.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
10.0ms	(/ (/ PI 2.0) (+ b a))
122.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series245.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (/ 1.0 a) (/ 1.0 b))
59.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
54.0ms	(/ (/ PI 2.0) (+ b a))
95.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify208.0ms

Algorithm

egg-herbie

Counts

813 → 813

Iterations

Useful iterations: 1 (49.0ms)

Iter	Nodes	Cost
0	2928	20392
1	5001	18352

prune1.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

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

rewrite331.0ms

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:

24.0ms	(- (/ 1.0 a) (/ 1.0 b))
125.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
10.0ms	(/ (/ PI 2.0) (+ b a))
111.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series292.0ms

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))
55.0ms	(/ (/ PI 2.0) (+ b a))
106.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify188.0ms

Algorithm

egg-herbie

Counts

730 → 730

Iterations

Useful iterations: 1 (50.0ms)

Iter	Nodes	Cost
0	2586	18289
1	5001	15335

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

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

rewrite238.0ms

Algorithm

rewrite-expression-head

Rules

580×	`times-frac`
497×	`add-sqr-sqrt`
477×	`*-un-lft-identity`
303×	`add-cube-cbrt`
169×	`prod-diff`
85×	`distribute-lft-out--`
73×	`difference-of-squares`
66×	`associate-r`
59×	`div-inv`
43×	`add-exp-log` `add-cbrt-cube`
25×	`associate-/l*`
14×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `distribute-lft-out`
13×	`fma-neg`
9×	`pow1` `associate-/r*`
6×	`associate-/r/` `add-log-exp`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `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 → 489

Calls

4 calls:

25.0ms	(- (/ 1.0 a) (/ 1.0 b))
96.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)))
12.0ms	(/ (/ PI 2.0) (+ b a))
69.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))

series233.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (/ 1.0 a) (/ 1.0 b))
94.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)))
49.0ms	(/ (/ PI 2.0) (+ b a))
53.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))

simplify101.0ms

Algorithm

egg-herbie

Counts

501 → 501

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1808	7484
1	5001	6268

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes65.0ms

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

sample573.0ms

Algorithm

intervals

Results

413.0ms

9568×

body

valid