Details

sample23.0ms

Algorithm

intervals

Results

14.0ms

310×

body

valid

simplify37.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.9b

localize12.0ms

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)))
4.0b	(- (* b b) (* a a))
9.9b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite102.0ms

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:

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))
66.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series213.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
45.0ms	(/ 1.0 (- (* b b) (* a a)))
30.0ms	(- (* b b) (* a a))
86.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify109.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 1 (20.0ms)

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

prune379.0ms

Filtered

165 candidates to 119 candidates (72.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 9.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.2b	(/ (/ 1.0 (+ b a)) (- b a))
0.2b	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
9.9b	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite202.0ms

Algorithm

rewrite-expression-head

Rules

350×	`times-frac`
298×	`*-un-lft-identity`
261×	`add-sqr-sqrt`
142×	`add-cube-cbrt`
108×	`associate-r`
59×	`add-exp-log` `add-cbrt-cube`
47×	`distribute-lft-out--`
45×	`difference-of-squares`
33×	`distribute-lft-out`
26×	`associate-/r/`
21×	`cbrt-undiv` `div-exp`
19×	`prod-exp` `cbrt-unprod`
18×	`div-inv` `associate-/l*`
14×	`frac-times` `associate-l`
11×	`pow1` `flip3-+` `flip-+`
8×	`associate-r/` `associate-l/`
7×	`flip3--` `flip--`
6×	`add-log-exp` `unswap-sqr`
5×	`associate-/r*` `frac-sub`
4×	`pow-prod-down`
3×	`sub-neg`
2×	`distribute-rgt-in` `distribute-lft-in` `*-commutative`
1×	`frac-2neg` `diff-log` `clear-num` `associate-/l/`

Counts

4 → 347

Calls

4 calls:

15.0ms	(- (/ 1.0 a) (/ 1.0 b))
15.0ms	(/ (/ 1.0 (+ b a)) (- b a))
57.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
93.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series239.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (/ 1.0 a) (/ 1.0 b))
46.0ms	(/ (/ 1.0 (+ b a)) (- b a))
63.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
93.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify61.0ms

Algorithm

egg-herbie

Counts

359 → 359

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1498	3481
1	5002	3169

prune816.0ms

Filtered

359 candidates to 230 candidates (64.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.1b	(/ (* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
0.3b	(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
0.3b	(* (/ PI 2.0) (/ 1.0 (+ b a)))

rewrite156.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt`
59×	`add-exp-log` `add-cbrt-cube`
52×	`*-un-lft-identity`
50×	`times-frac`
30×	`associate-r`
27×	`frac-times`
26×	`add-cube-cbrt`
22×	`prod-exp` `cbrt-unprod`
18×	`cbrt-undiv` `div-exp`
15×	`associate-r/` `associate-l/` `associate-/l/`
14×	`associate-l`
12×	`distribute-lft-out--`
11×	`pow1`
10×	`flip3--` `flip--` `difference-of-squares`
9×	`frac-sub`
7×	`div-inv`
6×	`add-log-exp`
5×	`associate-/r*`
4×	`pow-prod-down` `associate-/r/` `unswap-sqr`
3×	`sub-neg` `distribute-lft-out`
2×	`distribute-rgt-in` `distribute-lft-in` `*-commutative`
1×	`frac-2neg` `flip3-+` `diff-log` `clear-num` `flip-+` `associate-/l*`

Counts

4 → 179

Calls

4 calls:

16.0ms	(- (/ 1.0 a) (/ 1.0 b))
47.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
65.0ms	(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
20.0ms	(* (/ PI 2.0) (/ 1.0 (+ b a)))

series286.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (/ 1.0 a) (/ 1.0 b))
94.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
102.0ms	(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
55.0ms	(* (/ PI 2.0) (/ 1.0 (+ b a)))

simplify41.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	987	1768
1	5002	1458

prune572.0ms

Filtered

191 candidates to 132 candidates (69.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

286×	`add-sqr-sqrt`
265×	`times-frac`
232×	`*-un-lft-identity`
85×	`distribute-lft-out--`
84×	`associate-r`
80×	`add-cube-cbrt`
73×	`difference-of-squares`
59×	`add-exp-log` `add-cbrt-cube`
28×	`div-inv`
22×	`prod-exp` `cbrt-unprod`
18×	`cbrt-undiv` `div-exp`
14×	`associate-l`
12×	`associate-/l*`
11×	`pow1`
6×	`frac-times` `associate-*l/` `associate-/r/` `add-log-exp`
5×	`associate-/r*`
4×	`flip3--` `associate-*r/` `pow-prod-down` `flip--` `unswap-sqr`
3×	`associate-/l/` `distribute-lft-out`
2×	`*-commutative` `frac-sub`
1×	`sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `clear-num` `flip-+`

Counts

4 → 276

Calls

4 calls:

16.0ms	(- (/ 1.0 a) (/ 1.0 b))
81.0ms	(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)))
48.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
20.0ms	(* (/ PI 2.0) (/ 1.0 (+ b a)))

series247.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (/ 1.0 a) (/ 1.0 b))
93.0ms	(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)))
47.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
69.0ms	(* (/ PI 2.0) (/ 1.0 (+ b a)))

simplify54.0ms

Algorithm

egg-herbie

Counts

288 → 288

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1233	2895
1	5002	2585

prune656.0ms

Filtered

288 candidates to 190 candidates (66.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

regimes69.0ms

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

sample586.0ms

Algorithm

intervals

Results

422.0ms

9614×

body

valid