Details

sample131.0ms

Algorithm

intervals

Results

56.0ms	102×	body	2560	valid
26.0ms	69×	body	1280	valid
17.0ms	248×	body	80	nan
11.0ms	37×	body	640	valid
4.0ms	20×	body	320	valid
4.0ms	26×	body	160	valid
0.0ms	2×	body	80	valid

simplify96.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	7
1	43	7
2	84	7
3	155	7
4	262	7
5	454	7
6	2878	7
7	5001	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

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))
0.7b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite23.0ms

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×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `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 → 69

Calls

3 calls:

14.0ms	(/ (- 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)))

series109.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify39.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	349	623
1	1288	567
2	5001	565

prune177.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (cbrt (- (* v v) 1.0)) (cbrt (- (* v v) 1.0)))
0.0b	(* (/ 1 (* (cbrt (- (* v v) 1.0)) (cbrt (- (* v v) 1.0)))) (/ (- 1.0 (* 5.0 (* v v))) (cbrt (- (* v v) 1.0))))
0.2b	(* 5.0 (* v v))
0.7b	(acos (* (/ 1 (* (cbrt (- (* v v) 1.0)) (cbrt (- (* v v) 1.0)))) (/ (- 1.0 (* 5.0 (* v v))) (cbrt (- (* v v) 1.0)))))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt`
56×	`add-exp-log`
36×	`times-frac`
35×	`cbrt-prod` `associate-r`
32×	`*-un-lft-identity`
29×	`add-cube-cbrt`
26×	`cbrt-div`
25×	`associate-l`
24×	`prod-exp`
23×	`add-cbrt-cube`
18×	`pow1`
15×	`div-exp`
14×	`unswap-sqr`
13×	`flip3--` `flip--`
12×	`cbrt-unprod`
10×	`associate-/r/`
9×	`frac-times`
7×	`cbrt-undiv` `swap-sqr` `difference-of-squares`
6×	`pow1/3` `pow-prod-down`
5×	`associate-r/` `associate-l/`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`pow-sqr` `pow-prod-up` `div-inv`
1×	`pow2` `acos-asin` `pow-plus`

Counts

4 → 169

Calls

4 calls:

23.0ms	(* (cbrt (- (* v v) 1.0)) (cbrt (- (* v v) 1.0)))
95.0ms	(* (/ 1 (* (cbrt (- (* v v) 1.0)) (cbrt (- (* v v) 1.0)))) (/ (- 1.0 (* 5.0 (* v v))) (cbrt (- (* v v) 1.0))))
6.0ms	(* 5.0 (* v v))
1.0ms	(acos (* (/ 1 (* (cbrt (- (* v v) 1.0)) (cbrt (- (* v v) 1.0)))) (/ (- 1.0 (* 5.0 (* v v))) (cbrt (- (* v v) 1.0)))))

series332.0ms

Counts

4 → 12

Calls

4 calls:

220.0ms	(* (cbrt (- (* v v) 1.0)) (cbrt (- (* v v) 1.0)))
84.0ms	(* (/ 1 (* (cbrt (- (* v v) 1.0)) (cbrt (- (* v v) 1.0)))) (/ (- 1.0 (* 5.0 (* v v))) (cbrt (- (* v v) 1.0))))
24.0ms	(* 5.0 (* v v))
4.0ms	(acos (* (/ 1 (* (cbrt (- (* v v) 1.0)) (cbrt (- (* v v) 1.0)))) (/ (- 1.0 (* 5.0 (* v v))) (cbrt (- (* v v) 1.0)))))

simplify112.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	855	2604
1	4098	2274
2	5002	2112

prune442.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (acos (* (/ 1 (* (cbrt (- (* v v) 1.0)) (cbrt (- (* v v) 1.0)))) (/ (- 1.0 (* 5.0 (* v v))) (cbrt (- (* v v) 1.0))))))
0.0b	(expm1 (log1p (acos (* (/ 1 (* (cbrt (- (* v v) 1.0)) (cbrt (- (* v v) 1.0)))) (/ (- 1.0 (* 5.0 (* v v))) (cbrt (- (* v v) 1.0)))))))
0.2b	(* 5.0 (* v v))
0.7b	(acos (* (/ 1 (* (cbrt (- (* v v) 1.0)) (cbrt (- (* v v) 1.0)))) (/ (- 1.0 (* 5.0 (* v v))) (cbrt (- (* v v) 1.0)))))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`add-sqr-sqrt`
5×	`expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity`
4×	`log1p-expm1-u` `add-log-exp`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
1×	`acos-asin` `log1p-udef` `expm1-log1p` `log1p-expm1` `associate-r` `*-commutative` `expm1-udef` `unswap-sqr`

Counts

4 → 53

Calls

4 calls:

0.0ms	(log1p (acos (* (/ 1 (* (cbrt (- (* v v) 1.0)) (cbrt (- (* v v) 1.0)))) (/ (- 1.0 (* 5.0 (* v v))) (cbrt (- (* v v) 1.0))))))
0.0ms	(expm1 (log1p (acos (* (/ 1 (* (cbrt (- (* v v) 1.0)) (cbrt (- (* v v) 1.0)))) (/ (- 1.0 (* 5.0 (* v v))) (cbrt (- (* v v) 1.0)))))))
6.0ms	(* 5.0 (* v v))
1.0ms	(acos (* (/ 1 (* (cbrt (- (* v v) 1.0)) (cbrt (- (* v v) 1.0)))) (/ (- 1.0 (* 5.0 (* v v))) (cbrt (- (* v v) 1.0)))))

series244.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(log1p (acos (* (/ 1 (* (cbrt (- (* v v) 1.0)) (cbrt (- (* v v) 1.0)))) (/ (- 1.0 (* 5.0 (* v v))) (cbrt (- (* v v) 1.0))))))
125.0ms	(expm1 (log1p (acos (* (/ 1 (* (cbrt (- (* v v) 1.0)) (cbrt (- (* v v) 1.0)))) (/ (- 1.0 (* 5.0 (* v v))) (cbrt (- (* v v) 1.0)))))))
24.0ms	(* 5.0 (* v v))
9.0ms	(acos (* (/ 1 (* (cbrt (- (* v v) 1.0)) (cbrt (- (* v v) 1.0)))) (/ (- 1.0 (* 5.0 (* v v))) (cbrt (- (* v v) 1.0)))))

simplify44.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	163	863
1	444	738
2	1312	738
3	5001	738

prune179.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

localize10.0ms

Local error

Found 4 expressions with local error:

0.7b	(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))))
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)))))

rewrite10.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 91

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)))))

series45.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(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))))
16.0ms	(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

103 → 103

Iterations

Useful iterations: 3 (98.0ms)

Iter	Nodes	Cost
0	132	1070
1	439	956
2	2385	912
3	5002	881

prune167.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.7b

regimes92.0ms

Accuracy

0% (0.1b remaining)

Error of 0.6b against oracle of 0.5b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	19
1	20	19

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.5s	2979×	body	2560	valid
938.0ms	2515×	body	1280	valid
527.0ms	7769×	body	80	nan
354.0ms	1256×	body	640	valid
137.0ms	639×	body	320	valid
63.0ms	410×	body	160	valid
20.0ms	201×	body	80	valid