Details

sample143.0ms

Algorithm

intervals

Results

79.0ms	168×	body	1280	valid
31.0ms	125×	body	640	valid
8.0ms	51×	body	320	valid
7.0ms	142×	body	80	valid
2.0ms	23×	body	160	valid

simplify71.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	7
1	40	7
2	92	7
3	163	7
4	405	7
5	865	7
6	1189	7
7	2771	7
8	5001	7

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 45.1b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (* 0.5 (sin re)) (- (exp (- im)) (exp im)))
4.2b	(- (exp (- im)) (exp im))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

27×	`prod-diff`
26×	`add-sqr-sqrt` `*-un-lft-identity`
22×	`add-cube-cbrt`
11×	`distribute-rgt-in` `distribute-lft-in`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`associate-r`
4×	`add-log-exp`
3×	`sub-neg` `fma-neg` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`expm1-log1p-u` `flip3--` `associate-*r/` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
1×	`diff-log` `associate-l` `*-commutative`

Counts

2 → 74

Calls

2 calls:

11.0ms	(* (* 0.5 (sin re)) (- (exp (- im)) (exp im)))
6.0ms	(- (exp (- im)) (exp im))

series112.0ms

Counts

2 → 6

Calls

2 calls:

74.0ms	(* (* 0.5 (sin re)) (- (exp (- im)) (exp im)))
38.0ms	(- (exp (- im)) (exp im))

simplify49.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	371	1102
1	1544	774
2	5001	722

prune153.0ms

Filtered

80 candidates to 43 candidates (53.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	76	4	80
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	77	4	81

Merged error: 0.1b

Counts

81 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/60 (pow im 5) (* 2 im))
0.0b	(- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im)))
0.1b	(* 1/3 (pow im 3))
0.1b	(* (* 0.5 (sin re)) (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

54×	`prod-diff`
48×	`add-sqr-sqrt`
41×	`*-un-lft-identity`
37×	`add-cube-cbrt`
20×	`distribute-rgt-in` `distribute-lft-in`
17×	`associate-r`
14×	`add-exp-log`
11×	`add-cbrt-cube`
10×	`distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in`
9×	`pow1`
8×	`add-log-exp`
6×	`fma-neg` `prod-exp`
4×	`expm1-log1p-u` `unpow-prod-down` `cube-prod` `associate-l` `cbrt-unprod` `log1p-expm1-u` `unswap-sqr`
3×	`sub-neg` `pow-prod-down`
2×	`flip3--` `diff-log` `associate-r/` `-commutative` `flip--` `fma-udef` `distribute-lft-out--` `difference-of-squares` `sqr-pow`
1×	`associate--l-` `neg-sub0` `cube-mult` `pow-to-exp` `unpow3` `neg-log` `pow-exp` `associate--r+`

Counts

4 → 150

Calls

4 calls:

1.0ms	(fma 1/60 (pow im 5) (* 2 im))
6.0ms	(- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im)))
6.0ms	(* 1/3 (pow im 3))
10.0ms	(* (* 0.5 (sin re)) (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im))))

series372.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(fma 1/60 (pow im 5) (* 2 im))
57.0ms	(- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im)))
37.0ms	(* 1/3 (pow im 3))
165.0ms	(* (* 0.5 (sin re)) (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im))))

simplify87.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	586	2644
1	2556	1682
2	5002	1670

prune365.0ms

Filtered

162 candidates to 79 candidates (48.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	155	7	162
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	155	11	166

Merged error: 0.0b

Counts

166 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (cbrt (fma 1/60 (pow im 5) (* 2 im))) (cbrt (fma 1/60 (pow im 5) (* 2 im))))
0.6b	(cbrt (fma 1/60 (pow im 5) (* 2 im)))
0.6b	(cbrt (fma 1/60 (pow im 5) (* 2 im)))
0.6b	(cbrt (fma 1/60 (pow im 5) (* 2 im)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

7.0ms	(* (cbrt (fma 1/60 (pow im 5) (* 2 im))) (cbrt (fma 1/60 (pow im 5) (* 2 im))))
1.0ms	(cbrt (fma 1/60 (pow im 5) (* 2 im)))
1.0ms	(cbrt (fma 1/60 (pow im 5) (* 2 im)))
1.0ms	(cbrt (fma 1/60 (pow im 5) (* 2 im)))

series2.2s

Counts

4 → 12

Calls

4 calls:

582.0ms	(* (cbrt (fma 1/60 (pow im 5) (* 2 im))) (cbrt (fma 1/60 (pow im 5) (* 2 im))))
558.0ms	(cbrt (fma 1/60 (pow im 5) (* 2 im)))
558.0ms	(cbrt (fma 1/60 (pow im 5) (* 2 im)))
530.0ms	(cbrt (fma 1/60 (pow im 5) (* 2 im)))

simplify107.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (96.0ms)

Iter	Nodes	Cost
0	293	1041
1	911	965
2	3966	833
3	5001	800

prune424.0ms

Filtered

93 candidates to 72 candidates (77.4%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	91	13	104

Merged error: 0.0b

Counts

104 → 13

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* 0.5 (sin re)) (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im))))
0.2b	(* (sqrt (* (* 0.5 (sin re)) (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im))))) (sqrt (* (* 0.5 (sin re)) (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im))))))
12.4b	(sqrt (* (* 0.5 (sin re)) (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im)))))
12.4b	(sqrt (* (* 0.5 (sin re)) (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im)))))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

148×	`pow1`
80×	`pow-prod-down`
66×	`sqrt-pow1`
36×	`prod-diff`
31×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
27×	`add-cube-cbrt`
20×	`distribute-rgt-in` `distribute-lft-in` `associate-*r/`
17×	`pow-prod-up`
16×	`sqrt-div`
14×	`pow1/2`
11×	`add-exp-log` `pow-sqr` `add-cbrt-cube`
9×	`flip3--` `associate-r` `flip--`
6×	`distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in` `sqrt-prod`
5×	`associate-l`
4×	`expm1-log1p-u` `frac-times` `swap-sqr` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`sub-neg` `associate-l/` `-commutative`
1×	`pow2` `pow-plus` `sqrt-unprod` `rem-square-sqrt` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 172

Calls

4 calls:

11.0ms	(* (* 0.5 (sin re)) (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im))))
19.0ms	(* (sqrt (* (* 0.5 (sin re)) (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im))))) (sqrt (* (* 0.5 (sin re)) (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im))))))
13.0ms	(sqrt (* (* 0.5 (sin re)) (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im)))))
13.0ms	(sqrt (* (* 0.5 (sin re)) (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im)))))

series736.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(* (* 0.5 (sin re)) (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im))))
206.0ms	(* (sqrt (* (* 0.5 (sin re)) (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im))))) (sqrt (* (* 0.5 (sin re)) (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im))))))
176.0ms	(sqrt (* (* 0.5 (sin re)) (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im)))))
180.0ms	(sqrt (* (* 0.5 (sin re)) (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im)))))

simplify134.0ms

Algorithm

egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 2 (104.0ms)

Iter	Nodes	Cost
0	817	3309
1	3683	2550
2	5001	2518

prune437.0ms

Filtered

184 candidates to 85 candidates (46.2%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	180	4	184
Fresh	3	7	10
Picked	0	1	1
Done	0	2	2
Total	183	14	197

Merged error: 0.0b

Counts

197 → 14

regimes336.0ms

Accuracy

0% (0.7b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 0.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	10
1	28	10
2	28	10

end0.0ms

sample4.2s

Algorithm

intervals

Results

2.3s	4669×	body	1280	valid
933.0ms	3694×	body	640	valid
292.0ms	1802×	body	320	valid
222.0ms	4341×	body	80	valid
104.0ms	983×	body	160	valid