Details

sample77.0ms

Algorithm

intervals

Results

33.0ms	103×	body	2560	valid
17.0ms	77×	body	1280	valid
7.0ms	245×	body	80	nan
6.0ms	42×	body	640	valid
2.0ms	21×	body	320	valid
0.0ms	6×	body	160	valid
0.0ms	7×	body	80	valid

simplify99.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 0.4b

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))
0.4b	(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×	`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:

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)))

series119.0ms

Counts

3 → 9

Calls

3 calls:

86.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
29.0ms	(* 5.0 (* v v))
3.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify41.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (33.0ms)

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

prune186.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.0b	(expm1 (log1p (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
0.2b	(* 5.0 (* v v))
0.4b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
11×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `acos-asin` `expm1-log1p` `frac-2neg` `div-sub` `div-exp` `associate-r` `clear-num` `*-commutative` `div-inv` `expm1-udef` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

10.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.0ms	(expm1 (log1p (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)))

series247.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
133.0ms	(expm1 (log1p (acos (/ (- 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)))

simplify42.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	361	749
1	1295	678
2	5001	676

prune238.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (exp (log1p (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 1)
0.0b	(exp (log1p (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
0.2b	(* 5.0 (* v v))
0.4b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
13×	`add-cube-cbrt`
9×	`pow1` `add-exp-log` `prod-diff` `add-cbrt-cube`
7×	`add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`exp-prod` `fma-neg` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`rem-exp-log` `difference-of-squares`
1×	`acos-asin` `sub-neg` `expm1-def` `log1p-udef` `flip3--` `diff-log` `difference-of-sqr-1` `associate-r` `*-commutative` `flip--` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 76

Calls

4 calls:

5.0ms	(- (exp (log1p (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 1)
1.0ms	(exp (log1p (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)))

series282.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(- (exp (log1p (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 1)
125.0ms	(exp (log1p (acos (/ (- 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)))

simplify64.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 3 (56.0ms)

Iter	Nodes	Cost
0	253	928
1	768	744
2	2173	718
3	5001	633

prune199.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 5.0 (pow v 2))
0.4b	(acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)))
1.0b	(cbrt (pow (acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0))) 3))
1.0b	(pow (acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0))) 3)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
12×	`cbrt-prod`
10×	`add-exp-log` `unpow-prod-down`
8×	`associate-r`
7×	`add-cbrt-cube`
6×	`cube-prod`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr` `sqr-pow`
3×	`pow-unpow` `associate-l` `prod-exp`
2×	`cube-mult` `pow-to-exp` `unpow3` `pow-exp` `unpow2`
1×	`acos-asin` `pow-pow` `pow1/3` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `rem-cube-cbrt`

Counts

4 → 87

Calls

4 calls:

5.0ms	(* 5.0 (pow v 2))
0.0ms	(acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)))
1.0ms	(cbrt (pow (acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0))) 3))
1.0ms	(pow (acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0))) 3)

series79.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* 5.0 (pow v 2))
3.0ms	(acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)))
3.0ms	(cbrt (pow (acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0))) 3))
47.0ms	(pow (acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0))) 3)

simplify40.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	214	833
1	793	775
2	5002	769

prune256.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

regimes119.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	12
1	20	12

end0.0ms

sample2.3s

Algorithm

intervals

Results

978.0ms	2939×	body	2560	valid
557.0ms	2517×	body	1280	valid
218.0ms	8010×	body	80	nan
201.0ms	1267×	body	640	valid
74.0ms	648×	body	320	valid
33.0ms	418×	body	160	valid
10.0ms	211×	body	80	valid