Details

sample114.0ms

Algorithm

intervals

Results

43.0ms	85×	body	2560	valid
28.0ms	84×	body	1280	valid
14.0ms	243×	body	80	nan
11.0ms	45×	body	640	valid
5.0ms	25×	body	320	valid
1.0ms	10×	body	160	valid
1.0ms	7×	body	80	valid

simplify97.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	19	7
1	42	7
2	77	7
3	146	7
4	242	7
5	417	7
6	2789	7
7	5001	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.6b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.2b	(* 5.0 (* v v))
0.6b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
4×	`associate-/r*` `difference-of-squares`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `associate-/l*` `add-log-exp`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `acos-asin` `frac-2neg` `div-sub` `div-exp` `associate-r` `clear-num` `*-commutative` `div-inv` `unswap-sqr`

Counts

3 → 63

Calls

3 calls:

10.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
6.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series110.0ms

Counts

3 → 9

Calls

3 calls:

82.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
25.0ms	(* 5.0 (* v v))
3.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify39.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	336	587
1	1261	535
2	5002	531

prune166.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.0b	(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
0.2b	(* 5.0 (* v v))
0.6b	(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
14×	`add-cube-cbrt`
13×	`times-frac`
11×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
6×	`add-log-exp` `difference-of-squares`
4×	`associate-/r*`
3×	`flip3--` `associate-l` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod` `associate-/l*`
2×	`asin-acos` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `associate-r` `clear-num` `*-commutative` `div-inv` `distribute-lft-out--` `associate--r-` `unswap-sqr`

Counts

4 → 79

Calls

4 calls:

10.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
11.0ms	(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
7.0ms	(* 5.0 (* v v))
1.0ms	(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series149.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
30.0ms	(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
30.0ms	(* 5.0 (* v v))
4.0ms	(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify46.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	409	840
1	1459	784
2	5001	780

prune223.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (- 1.0 (* 5.0 (* v v))) (+ v (sqrt 1.0))) (- v (sqrt 1.0)))
0.0b	(/ (- 1.0 (* 5.0 (* v v))) (+ v (sqrt 1.0)))
0.2b	(* 5.0 (* v v))
1.6b	(asin (/ (/ (- 1.0 (* 5.0 (* v v))) (+ v (sqrt 1.0))) (- v (sqrt 1.0))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

204×	`times-frac`
177×	`*-un-lft-identity`
166×	`add-sqr-sqrt`
89×	`add-cube-cbrt`
38×	`difference-of-squares`
25×	`distribute-lft-out`
21×	`associate-/l*`
19×	`sqrt-prod` `distribute-lft-out--`
18×	`associate-/r/`
16×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r*`
9×	`pow1` `div-inv`
8×	`flip3-+` `flip-+`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`div-sub` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `associate-/l/`
2×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`asin-acos` `associate-r` `*-commutative` `unswap-sqr`

Counts

4 → 213

Calls

4 calls:

24.0ms	(/ (/ (- 1.0 (* 5.0 (* v v))) (+ v (sqrt 1.0))) (- v (sqrt 1.0)))
11.0ms	(/ (- 1.0 (* 5.0 (* v v))) (+ v (sqrt 1.0)))
7.0ms	(* 5.0 (* v v))
1.0ms	(asin (/ (/ (- 1.0 (* 5.0 (* v v))) (+ v (sqrt 1.0))) (- v (sqrt 1.0))))

series337.0ms

Counts

4 → 12

Calls

4 calls:

210.0ms	(/ (/ (- 1.0 (* 5.0 (* v v))) (+ v (sqrt 1.0))) (- v (sqrt 1.0)))
83.0ms	(/ (- 1.0 (* 5.0 (* v v))) (+ v (sqrt 1.0)))
31.0ms	(* 5.0 (* v v))
12.0ms	(asin (/ (/ (- 1.0 (* 5.0 (* v v))) (+ v (sqrt 1.0))) (- v (sqrt 1.0))))

simplify123.0ms

Algorithm

egg-herbie

Counts

225 → 225

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	888	3496
1	4306	3286
2	5001	3278

prune547.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.5b

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
1.0b	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b	(* (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `acos-asin` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 83

Calls

4 calls:

0.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
1.0ms	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0ms	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
7.0ms	(* (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

series46.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
21.0ms	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
17.0ms	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
4.0ms	(* (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

simplify110.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 3 (100.0ms)

Iter	Nodes	Cost
0	125	1008
1	461	888
2	2367	844
3	5001	813

prune133.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.5b

regimes110.0ms

Accuracy

0% (0.4b remaining)

Error of 0.9b against oracle of 0.5b and baseline of 0.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	12
1	18	12

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.4s	3022×	body	2560	valid
831.0ms	2511×	body	1280	valid
446.0ms	8041×	body	80	nan
305.0ms	1234×	body	640	valid
118.0ms	642×	body	320	valid
52.0ms	399×	body	160	valid
14.0ms	192×	body	80	valid