Details

sample24.0ms

Algorithm

intervals

Results

15.0ms

299×

body

valid

simplify40.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 13.4b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.9b	(/ 1.0 (- (* b b) (* a a)))
3.5b	(- (* b b) (* a a))
8.7b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite7.6s

Algorithm

rewrite-expression-head

Rules

66791×	`add-sqr-sqrt`
63118×	`frac-times`
59991×	`associate-/r*`
34546×	`associate-/l*`
34050×	`*-un-lft-identity`
32562×	`frac-sub`
23625×	`add-cube-cbrt`
21529×	`difference-of-squares`
11572×	`clear-num`
11487×	`frac-2neg`
10425×	`swap-sqr`
8658×	`unswap-sqr`
8644×	`*-commutative`
4310×	`distribute-lft-out--`
3690×	`associate-l`
3398×	`associate-*r/`
1166×	`associate-*l/`
805×	`times-frac`
563×	`prod-diff`
406×	`flip3--` `flip--`
315×	`associate-r`
171×	`distribute-rgt-in` `distribute-lft-in`
170×	`un-div-inv`
59×	`div-inv`
36×	`add-exp-log` `add-cbrt-cube`
15×	`fma-neg`
13×	`prod-exp` `cbrt-unprod`
11×	`pow1`
9×	`cbrt-undiv` `div-exp`
6×	`associate-/r/` `add-log-exp`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u`
3×	`sub-neg`
1×	`diff-log`

Counts

4 → 35252

Calls

4 calls:

70.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
21.0ms	(/ 1.0 (- (* b b) (* a a)))
22.0ms	(- (* b b) (* a a))
880.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series226.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
44.0ms	(/ 1.0 (- (* b b) (* a a)))
30.0ms	(- (* b b) (* a a))
95.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify8.5s

Algorithm

egg-herbie

Counts

35264 → 35264

Iterations

Useful iterations: 0 (249.0ms)

Iter	Nodes	Cost
0	20152	855490

prune53.5s

Filtered

35264 candidates to 12467 candidates (35.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	35256	8	35264
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	35256	9	35265

Merged error: 0b

Counts

35265 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite779.0ms

Algorithm

rewrite-expression-head

Rules

3482×	`*-un-lft-identity`
3366×	`add-sqr-sqrt`
2527×	`add-cube-cbrt`
2441×	`times-frac`
2189×	`associate-/l*`
2187×	`frac-sub`
2155×	`associate-/r*`
1992×	`frac-times`
1858×	`associate-*r/`
1605×	`associate-l`
1091×	`associate-/l/`
988×	`associate-r`
825×	`clear-num`
656×	`frac-2neg`
507×	`prod-diff`
338×	`un-div-inv`
241×	`distribute-lft-out`
240×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
219×	`unswap-sqr`
176×	`distribute-lft-out--`
171×	`distribute-rgt-in` `distribute-lft-in`
152×	`div-inv` `difference-of-squares`
103×	`*-commutative`
80×	`neg-mul-1`
50×	`add-exp-log` `associate-/r/` `add-cbrt-cube`
28×	`flip3--` `flip--`
24×	`flip3-+` `associate-*l/` `flip-+`
21×	`prod-exp` `cbrt-unprod`
13×	`fma-neg`
12×	`cbrt-undiv` `div-exp`
11×	`pow1`
6×	`add-log-exp`
5×	`distribute-lft-neg-out`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u`
3×	`sub-neg`
1×	`diff-log` `distribute-frac-neg`

Counts

4 → 4199

Calls

4 calls:

22.0ms	(- (/ 1.0 a) (/ 1.0 b))
188.0ms	(/ (* (* (- PI) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* (- 2.0) (- b a)))
91.0ms	(* (* (- PI) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
13.0ms	(* (- PI) (/ 1.0 (+ b a)))

series289.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (/ 1.0 a) (/ 1.0 b))
105.0ms	(/ (* (* (- PI) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* (- 2.0) (- b a)))
104.0ms	(* (* (- PI) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
49.0ms	(* (- PI) (/ 1.0 (+ b a)))

simplify691.0ms

Algorithm

egg-herbie

Counts

4211 → 4211

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5001	73634

prune12.6s

Filtered

4211 candidates to 3005 candidates (71.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	4209	2	4211
Fresh	3	4	7
Picked	0	1	1
Done	0	1	1
Total	4212	8	4220

Merged error: 0b

Counts

4220 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (* (- PI) (/ (* (cbrt 1.0) (cbrt 1.0)) 1)) (- (sqrt 2.0))) (/ (* (/ (cbrt 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b))) (* (sqrt 2.0) (- b a))))
0.2b	(/ (* (/ (cbrt 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b))) (* (sqrt 2.0) (- b a)))
0.4b	(* (/ (cbrt 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b)))
0.4b	(* (sqrt 2.0) (- b a))

rewrite1.2m

Algorithm

rewrite-expression-head

Rules

416378×	`associate-/l*`
407787×	`frac-times`
350848×	`add-sqr-sqrt`
281694×	`*-un-lft-identity`
251692×	`associate-/l/`
233164×	`add-cube-cbrt`
220145×	`associate-/r*`
200718×	`frac-sub`
143324×	`cbrt-prod`
142418×	`associate-r`
137749×	`times-frac`
63390×	`clear-num`
62142×	`frac-2neg`
57094×	`associate-*r/`
56419×	`unswap-sqr`
54054×	`associate-l`
35320×	`swap-sqr`
16146×	`distribute-lft-out`
11985×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
9388×	`sqrt-prod`
9342×	`*-commutative`
3744×	`un-div-inv`
2629×	`neg-mul-1`
2481×	`flip3--` `flip--`
2475×	`associate-*l/`
1957×	`div-inv`
1342×	`distribute-lft-out--`
1129×	`difference-of-squares`
507×	`add-cbrt-cube`
430×	`associate-/r/`
356×	`prod-diff`
340×	`add-exp-log`
256×	`cbrt-unprod`
218×	`cbrt-undiv`
213×	`flip3-+` `flip-+`
182×	`distribute-rgt-in` `distribute-lft-in`
157×	`prod-exp`
135×	`div-exp`
14×	`1-exp`
10×	`pow1`
4×	`expm1-log1p-u` `sub-neg` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down`
2×	`distribute-lft-neg-out`
1×	`distribute-frac-neg`

Counts

4 → 225246

Calls

4 calls:

22.9s	(* (/ (* (- PI) (/ (* (cbrt 1.0) (cbrt 1.0)) 1)) (- (sqrt 2.0))) (/ (* (/ (cbrt 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b))) (* (sqrt 2.0) (- b a))))
182.0ms	(/ (* (/ (cbrt 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b))) (* (sqrt 2.0) (- b a)))
77.0ms	(* (/ (cbrt 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b)))
8.0ms	(* (sqrt 2.0) (- b a))

series743.0ms

Counts

4 → 12

Calls

4 calls:

302.0ms	(* (/ (* (- PI) (/ (* (cbrt 1.0) (cbrt 1.0)) 1)) (- (sqrt 2.0))) (/ (* (/ (cbrt 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b))) (* (sqrt 2.0) (- b a))))
212.0ms	(/ (* (/ (cbrt 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b))) (* (sqrt 2.0) (- b a)))
144.0ms	(* (/ (cbrt 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b)))
71.0ms	(* (sqrt 2.0) (- b a))

simplify1.5m

Algorithm

egg-herbie

Counts

225258 → 225258

Iterations

Useful iterations: 0 (6.3s)

Iter	Nodes	Cost
0	176077	8431606

prune5.8m

Filtered: 225258 candidates to 124299 candidates (55.2%)