Details

sample78.0ms

Algorithm

intervals

Results

32.0ms	95×	body	2560	valid
16.0ms	73×	body	1280	valid
8.0ms	274×	body	80	nan
6.0ms	38×	body	640	valid
2.0ms	19×	body	320	valid
2.0ms	21×	body	160	valid
1.0ms	10×	body	80	valid

simplify94.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.9b

localize8.0ms

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))
0.9b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite18.0ms

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:

9.0ms	(/ (- 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)))

series116.0ms

Counts

3 → 9

Calls

3 calls:

82.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
24.0ms	(* 5.0 (* v v))
8.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify37.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (31.0ms)

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

prune163.0ms

Filtered

72 candidates to 55 candidates (76.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.0b	(exp (log (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
0.2b	(* 5.0 (* v v))
0.9b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

13.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
1.0ms	(exp (log (acos (/ (- 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)))

series113.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
3.0ms	(exp (log (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
24.0ms	(* 5.0 (* v v))
3.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify39.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	365	766
1	1310	699
2	5002	677

prune221.0ms

Filtered

90 candidates to 64 candidates (71.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.9b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
0.9b	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
0.9b	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
0.9b	(* (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))))
6.0ms	(* (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

series41.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
16.0ms	(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)))))

simplify109.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 3 (98.0ms)

Iter	Nodes	Cost
0	125	1002
1	427	888
2	2342	844
3	5002	813

prune177.0ms

Filtered

95 candidates to 47 candidates (49.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.9b	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
0.9b	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
0.9b	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
0.9b	(* (* (sqrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) (sqrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))) (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

60×	`sqrt-pow1`
51×	`pow1`
36×	`pow1/2`
34×	`pow-prod-up`
16×	`add-sqr-sqrt`
14×	`sqrt-prod`
9×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
8×	`pow-sqr`
7×	`pow-prod-down`
6×	`pow-plus` `associate-r`
4×	`add-log-exp`
3×	`rem-sqrt-square` `prod-exp` `cbrt-unprod`
2×	`sqrt-unprod` `swap-sqr` `unswap-sqr`
1×	`associate-l` `*-commutative`

Counts

4 → 91

Calls

4 calls:

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))))
1.0ms	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
30.0ms	(* (* (sqrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) (sqrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))) (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

series60.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
22.0ms	(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))))
5.0ms	(* (* (sqrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) (sqrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))) (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

simplify183.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	216	1004
1	625	777
2	3789	745
3	5002	745

prune187.0ms

Filtered

103 candidates to 46 candidates (44.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.8b

regimes105.0ms

Accuracy

0% (0.0b remaining)

Error of 0.6b against oracle of 0.6b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	9
1	12	9

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.0s	2953×	body	2560	valid
580.0ms	2518×	body	1280	valid
227.0ms	7966×	body	80	nan
210.0ms	1252×	body	640	valid
77.0ms	629×	body	320	valid
36.0ms	421×	body	160	valid
14.0ms	227×	body	80	valid